Payoffs of an outcome (see src/python/gambit/lib/outcome.pxi) are accessed via the __getitem__ and __setitem__ operators. This currently accepts only integer player indices. It should be extended to accept text strings (identifying player labels), or Player objects, as appropriate. See for instance how payoff() is implemented on mixed and behavior strategy profiles for a model.

When we first worked on the Cython wrapper for Python, Cython did not yet have explicit C++ support, so we had to use some workarounds. Cython now has direct C++ support, so it should be safe to remove those circumlocutions.

The branch cython_cxx illustrates the tasks that will need to be done. The process should be mechanical; however, be sure to run the nosetests just to be sure!

Information on the C++ wrapping features in Cython can be found at:

http://docs.cython.org/src/userguide/wrapping_CPlusPlus.html

When solving the game (below, in .nfg format) in floating point, gambit-lcp terminates with an "internal error." What occurs is there is numerical instability in pivoting due to degeneracy in the game. An improved exception handler should identify when this occurs and print a more informative message, suggesting solving using exact rational arithmetic instead.

NFG 1 R "Biterror Game" { "Terrorist" "State" }

{ { "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" "15" "16" "17" "18" "19" "20" }
{ "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" "15" "16" "17" "18" "19" "20" "21" "22" "23" "24" "25" "26" "27" "28" "29" "30" "31" "32" "33" "34" "35" "36" "37" "38" "39" "40" "41" "42" "43" "44" "45" "46" "47" "48" "49" "50" "51" "52" "53" "54" "55" "56" "57" "58" "59" "60" "61" "62" "63" "64" "65" "66" "67" "68" "69" "70" "71" "72" "73" "74" "75" "76" "77" "78" "79" "80" "81" "82" "83" "84" "85" "86" "87" "88" "89" "90" "91" "92" "93" "94" "95" "96" "97" "98" "99" "100" "101" "102" "103" "104" "105" "106" "107" "108" "109" "110" "111" "112" "113" "114" "115" "116" "117" "118" "119" "120" "121" "122" "123" "124" "125" "126" "127" "128" "129" "130" "131" "132" "133" "134" "135" "136" "137" "138" "139" "140" "141" "142" "143" "144" "145" "146" "147" "148" "149" "150" "151" "152" "153" "154" "155" "156" "157" "158" "159" "160" "161" "162" "163" "164" "165" "166" "167" "168" "169" "170" "171" "172" "173" "174" "175" "176" "177" "178" "179" "180" "181" "182" "183" "184" "185" "186" "187" "188" "189" "190" "191" "192" "193" "194" "195" "196" "197" "198" "199" "200" "201" "202" "203" "204" "205" "206" "207" "208" "209" "210" "211" "212" "213" "214" "215" "216" "217" "218" "219" "220" "221" "222" "223" "224" "225" "226" "227" "228" "229" "230" "231" "232" "233" "234" "235" "236" "237" "238" "239" "240" "241" "242" "243" "244" "245" "246" "247" "248" "249" "250" "251" "252" "253" "254" "255" "256" "257" "258" "259" "260" "261" "262" "263" "264" "265" "266" "267" "268" "269" "270" "271" "272" "273" "274" "275" "276" "277" "278" "279" "280" "281" "282" "283" "284" "285" "286" "287" "288" "289" "290" "291" "292" "293" "294" "295" "296" "297" "298" "299" "300" "301" "302" "303" "304" "305" }
}
""
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{ "" 2.12 , 0.00 }
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{ "" 1.11 , -0.50 }
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{ "" 1.11 , -0.50 }
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{ "" 5.32 , -4.80 }
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{ "" 2.14 , -1.73 }
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{ "" 0.24 , 0.00 }
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{ "" 30.28 , -28.65 }
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{ "" 1.11 , -0.50 }
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{ "" 2.63 , -2.22 }
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{ "" 2.84 , -2.42 }
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{ "" 2.12 , 0.00 }
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{ "" 0.92 , 0.00 }
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{ "" 1.11 , -0.50 }
{ "" 0.58 , 0.00 }
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{ "" 1.34 , -1.04 }
{ "" 1.21 , -0.91 }
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{ "" 0.94 , -0.68 }
{ "" 2.61 , -2.35 }
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{ "" 2.12 , 0.00 }
{ "" 7.20 , -5.57 }
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{ "" 2.28 , -1.52 }
{ "" 0.70 , 0.00 }
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{ "" 0.52 , 0.00 }
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{ "" 4.62 , -4.23 }
{ "" 2.77 , -2.41 }
{ "" 2.47 , -2.15 }
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{ "" 1.50 , -1.21 }
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{ "" 2.12 , 0.00 }
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{ "" 0.70 , 0.00 }
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{ "" 2.12 , 0.00 }
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{ "" 2.28 , -1.52 }
{ "" 0.70 , 0.00 }
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{ "" 0.39 , 0.00 }
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{ "" 0.70 , 0.00 }
{ "" 1.11 , -0.50 }
{ "" 1.69 , -1.11 }
{ "" 3.22 , -2.68 }
{ "" 5.01 , -4.49 }
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{ "" 3.45 , -3.04 }
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{ "" 2.77 , -2.41 }
{ "" 2.47 , -2.15 }
{ "" 0.30 , 0.00 }
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{ "" 2.12 , 0.00 }
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{ "" 0.70 , 0.00 }
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{ "" 2.77 , -2.41 }
{ "" 2.24 , -1.92 }
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{ "" 0.26 , 0.00 }
{ "" 2.64 , -2.40 }
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{ "" 1.69 , -1.11 }
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{ "" 2.47 , -2.15 }
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{ "" 2.73 , -2.48 }
{ "" 0.24 , 0.00 }
{ "" 2.12 , 0.00 }
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{ "" 0.52 , 0.00 }
{ "" 1.49 , -1.03 }
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{ "" 0.39 , 0.00 }
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{ "" 3.60 , -3.32 }
{ "" 1.66 , -1.40 }
{ "" 1.96 , -1.70 }
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{ "" 0.35 , 0.00 }
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{ "" 2.12 , 0.00 }
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{ "" 0.52 , 0.00 }
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{ "" 1.96 , -1.70 }
{ "" 0.24 , 0.00 }
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{ "" 2.92 , -2.51 }
{ "" 0.39 , 0.00 }
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{ "" 2.12 , 0.00 }
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{ "" 0.47 , 0.00 }
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{ "" 0.47 , 0.00 }
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{ "" 2.14 , -1.90 }
{ "" 2.12 , 0.00 }
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{ "" 0.47 , 0.00 }
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{ "" 0.47 , 0.00 }
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{ "" 0.39 , 0.00 }
{ "" 0.35 , 0.00 }
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{ "" 2.92 , -2.51 }
{ "" 0.39 , 0.00 }
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{ "" 0.74 , -0.50 }
{ "" 2.12 , 0.00 }
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{ "" 1.69 , -1.11 }
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{ "" 2.92 , -2.51 }
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{ "" 2.63 , -2.22 }
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{ "" 3.73 , -3.37 }
{ "" 1.53 , -1.20 }
{ "" 3.06 , -2.76 }
{ "" 1.18 , -0.89 }
{ "" 0.62 , -0.34 }
{ "" 2.03 , -1.77 }
{ "" 2.43 , -2.17 }
{ "" 2.14 , -1.90 }
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{ "" 1.64 , 0.00 }
{ "" 6.41 , -5.50 }
{ "" 0.76 , 0.00 }
{ "" 3.10 , -2.39 }
{ "" 1.42 , -0.80 }
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{ "" 2.73 , -2.18 }
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{ "" 2.63 , -2.22 }
{ "" 0.39 , 0.00 }
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{ "" 1.18 , -0.89 }
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{ "" 2.43 , -2.17 }
{ "" 0.74 , -0.50 }
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{ "" 1.64 , 0.00 }
{ "" 6.41 , -5.50 }
{ "" 0.76 , 0.00 }
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{ "" 1.42 , -0.80 }
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{ "" 2.73 , -2.18 }
{ "" 6.68 , -6.16 }
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{ "" 2.63 , -2.22 }
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{ "" 0.35 , 0.00 }
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{ "" 1.18 , -0.89 }
{ "" 0.62 , -0.34 }
{ "" 2.11 , -1.85 }
{ "" 2.43 , -2.17 }
{ "" 2.21 , -1.97 }
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{ "" 1.64 , 0.00 }
{ "" 4.12 , -3.21 }
{ "" 0.76 , 0.00 }
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{ "" 1.42 , -0.80 }
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{ "" 2.73 , -2.18 }
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{ "" 5.37 , -4.90 }
{ "" 2.63 , -2.22 }
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{ "" 3.73 , -3.37 }
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{ "" 0.30 , 0.00 }
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{ "" 1.46 , -1.20 }
{ "" 2.04 , -1.78 }
{ "" 2.21 , -1.97 }
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{ "" 1.64 , 0.00 }
{ "" 7.05 , -6.14 }
{ "" 1.75 , -0.99 }
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{ "" 0.62 , 0.00 }
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{ "" 0.52 , 0.00 }
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{ "" 1.66 , -1.40 }
{ "" 1.96 , -1.70 }
{ "" 2.45 , -2.21 }
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{ "" 1.64 , 0.00 }
{ "" 7.05 , -6.14 }
{ "" 1.75 , -0.99 }
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{ "" 0.62 , 0.00 }
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{ "" 1.67 , -1.15 }
{ "" 0.47 , 0.00 }
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{ "" 1.53 , -1.20 }
{ "" 3.24 , -2.94 }
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{ "" 2.14 , -1.90 }
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{ "" 1.64 , 0.00 }
{ "" 7.05 , -6.14 }
{ "" 1.75 , -0.99 }
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{ "" 0.62 , 0.00 }
{ "" 2.15 , -1.57 }
{ "" 3.00 , -2.46 }
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{ "" 5.00 , -4.53 }
{ "" 2.92 , -2.51 }
{ "" 0.39 , 0.00 }
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{ "" 1.53 , -1.20 }
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{ "" 1.36 , -1.06 }
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{ "" 2.37 , -2.11 }
{ "" 2.43 , -2.17 }
{ "" 0.74 , -0.50 }
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{ "" 1.64 , 0.00 }
{ "" 7.05 , -6.14 }
{ "" 1.75 , -0.99 }
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{ "" 0.62 , 0.00 }
{ "" 2.15 , -1.57 }
{ "" 3.00 , -2.46 }
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{ "" 6.77 , -6.30 }
{ "" 3.16 , -2.75 }
{ "" 4.35 , -3.96 }
{ "" 0.35 , 0.00 }
{ "" 1.53 , -1.20 }
{ "" 3.24 , -2.94 }
{ "" 1.36 , -1.06 }
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{ "" 2.37 , -2.11 }
{ "" 2.43 , -2.17 }
{ "" 2.47 , -2.23 }
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{ "" 1.64 , 0.00 }
{ "" 4.12 , -3.21 }
{ "" 1.75 , -0.99 }
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{ "" 0.62 , 0.00 }
{ "" 2.15 , -1.57 }
{ "" 3.00 , -2.46 }
{ "" 5.01 , -4.49 }
{ "" 5.37 , -4.90 }
{ "" 3.16 , -2.75 }
{ "" 4.35 , -3.96 }
{ "" 3.73 , -3.37 }
{ "" 1.53 , -1.20 }
{ "" 0.30 , 0.00 }
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{ "" 0.62 , -0.34 }
{ "" 1.46 , -1.20 }
{ "" 2.04 , -1.78 }
{ "" 2.47 , -2.23 }
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{ "" 1.64 , 0.00 }
{ "" 7.05 , -6.14 }
{ "" 1.75 , -0.99 }
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{ "" 0.62 , 0.00 }
{ "" 2.15 , -1.57 }
{ "" 3.00 , -2.46 }
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{ "" 2.14 , -1.73 }
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{ "" 1.53 , -1.20 }
{ "" 3.24 , -2.94 }
{ "" 1.36 , -1.06 }
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{ "" 2.37 , -2.11 }
{ "" 2.43 , -2.17 }
{ "" 0.24 , 0.00 }
{ "" 6.15 , -4.03 }
{ "" 1.64 , 0.00 }
{ "" 8.24 , -7.33 }
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{ "" 3.10 , -2.39 }
{ "" 2.29 , -1.67 }
{ "" 0.58 , 0.00 }
{ "" 3.93 , -3.39 }
{ "" 0.52 , 0.00 }
{ "" 1.49 , -1.03 }
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{ "" 4.69 , -4.31 }
{ "" 3.73 , -3.37 }
{ "" 1.53 , -1.20 }
{ "" 2.85 , -2.55 }
{ "" 1.92 , -1.62 }
{ "" 0.62 , -0.34 }
{ "" 1.66 , -1.40 }
{ "" 1.96 , -1.70 }
{ "" 2.45 , -2.21 }
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{ "" 1.64 , 0.00 }
{ "" 8.79 , -7.88 }
{ "" 3.73 , -2.97 }
{ "" 3.10 , -2.39 }
{ "" 2.29 , -1.67 }
{ "" 0.58 , 0.00 }
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{ "" 1.67 , -1.15 }
{ "" 0.47 , 0.00 }
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{ "" 1.53 , -1.20 }
{ "" 3.42 , -3.12 }
{ "" 1.92 , -1.62 }
{ "" 0.62 , -0.34 }
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{ "" 2.43 , -2.17 }
{ "" 2.14 , -1.90 }
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{ "" 1.64 , 0.00 }
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{ "" 3.73 , -2.97 }
{ "" 3.10 , -2.39 }
{ "" 2.29 , -1.67 }
{ "" 0.58 , 0.00 }
{ "" 3.82 , -3.28 }
{ "" 4.28 , -3.76 }
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{ "" 0.41 , 0.00 }
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{ "" 3.73 , -3.37 }
{ "" 1.53 , -1.20 }
{ "" 3.00 , -2.70 }
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{ "" 0.62 , -0.34 }
{ "" 1.48 , -1.22 }
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{ "" 1.25 , -1.01 }
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{ "" 1.64 , 0.00 }
{ "" 8.79 , -7.88 }
{ "" 3.73 , -2.97 }
{ "" 3.10 , -2.39 }
{ "" 2.29 , -1.67 }
{ "" 0.58 , 0.00 }
{ "" 3.93 , -3.39 }
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{ "" 2.92 , -2.51 }
{ "" 0.39 , 0.00 }
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{ "" 1.53 , -1.20 }
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{ "" 2.96 , -2.70 }
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{ "" 0.74 , -0.50 }
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{ "" 1.64 , 0.00 }
{ "" 8.79 , -7.88 }
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{ "" 0.58 , 0.00 }
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{ "" 6.91 , -6.44 }
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{ "" 0.35 , 0.00 }
{ "" 1.53 , -1.20 }
{ "" 3.65 , -3.36 }
{ "" 1.92 , -1.62 }
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{ "" 1.64 , 0.00 }
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{ "" 3.10 , -2.39 }
{ "" 2.29 , -1.67 }
{ "" 0.58 , 0.00 }
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{ "" 1.53 , -1.20 }
{ "" 0.30 , 0.00 }
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{ "" 1.46 , -1.20 }
{ "" 2.04 , -1.78 }
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{ "" 1.64 , 0.00 }
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{ "" 0.58 , 0.00 }
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{ "" 1.53 , -1.20 }
{ "" 1.66 , -1.37 }
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{ "" 0.26 , 0.00 }
{ "" 2.30 , -2.04 }
{ "" 2.30 , -2.06 }
{ "" 6.15 , -4.03 }
{ "" 1.64 , 0.00 }
{ "" 8.79 , -7.88 }
{ "" 3.73 , -2.97 }
{ "" 3.10 , -2.39 }
{ "" 2.29 , -1.67 }
{ "" 0.58 , 0.00 }
{ "" 3.93 , -3.39 }
{ "" 5.32 , -4.80 }
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{ "" 2.14 , -1.73 }
{ "" 1.20 , -0.81 }
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{ "" 1.53 , -1.20 }
{ "" 3.65 , -3.36 }
{ "" 1.92 , -1.62 }
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{ "" 2.50 , -2.24 }
{ "" 2.43 , -2.17 }
{ "" 0.24 , 0.00 }
{ "" 12.51 , -10.39 }
{ "" 1.64 , 0.00 }
{ "" 3.11 , -2.20 }
{ "" 3.81 , -3.04 }
{ "" 3.10 , -2.39 }
{ "" 3.40 , -2.79 }
{ "" 4.19 , -3.61 }
{ "" 0.55 , 0.00 }
{ "" 0.52 , 0.00 }
{ "" 1.49 , -1.03 }
{ "" 2.88 , -2.47 }
{ "" 4.69 , -4.31 }
{ "" 3.73 , -3.37 }
{ "" 1.53 , -1.20 }
{ "" 1.90 , -1.60 }
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{ "" 0.62 , -0.34 }
{ "" 1.46 , -1.20 }
{ "" 1.96 , -1.70 }
{ "" 2.45 , -2.21 }
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{ "" 1.64 , 0.00 }
{ "" 3.11 , -2.20 }
{ "" 3.81 , -3.04 }
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{ "" 3.40 , -2.79 }
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{ "" 0.55 , 0.00 }
{ "" 1.67 , -1.15 }
{ "" 0.47 , 0.00 }
{ "" 2.88 , -2.47 }
{ "" 4.15 , -3.76 }
{ "" 3.73 , -3.37 }
{ "" 1.53 , -1.20 }
{ "" 1.90 , -1.60 }
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{ "" 0.62 , -0.34 }
{ "" 1.46 , -1.20 }
{ "" 2.43 , -2.17 }
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{ "" 1.64 , 0.00 }
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{ "" 3.81 , -3.04 }
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{ "" 3.40 , -2.79 }
{ "" 4.19 , -3.61 }
{ "" 0.55 , 0.00 }
{ "" 5.74 , -5.22 }
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{ "" 2.88 , -2.47 }
{ "" 0.39 , 0.00 }
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{ "" 1.53 , -1.20 }
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{ "" 0.62 , -0.34 }
{ "" 1.46 , -1.20 }
{ "" 2.43 , -2.17 }
{ "" 0.74 , -0.50 }
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{ "" 1.64 , 0.00 }
{ "" 3.11 , -2.20 }
{ "" 3.81 , -3.04 }
{ "" 3.10 , -2.39 }
{ "" 3.40 , -2.79 }
{ "" 4.19 , -3.61 }
{ "" 0.55 , 0.00 }
{ "" 5.74 , -5.22 }
{ "" 5.65 , -5.18 }
{ "" 2.88 , -2.47 }
{ "" 4.89 , -4.50 }
{ "" 0.35 , 0.00 }
{ "" 1.53 , -1.20 }
{ "" 1.90 , -1.60 }
{ "" 0.59 , -0.30 }
{ "" 0.62 , -0.34 }
{ "" 1.46 , -1.20 }
{ "" 2.43 , -2.17 }
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{ "" 12.51 , -10.39 }
{ "" 1.64 , 0.00 }
{ "" 3.11 , -2.20 }
{ "" 3.81 , -3.04 }
{ "" 3.10 , -2.39 }
{ "" 3.40 , -2.79 }
{ "" 4.19 , -3.61 }
{ "" 0.55 , 0.00 }
{ "" 5.32 , -4.80 }
{ "" 4.16 , -3.69 }
{ "" 2.14 , -1.73 }
{ "" 1.20 , -0.81 }
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{ "" 1.53 , -1.20 }
{ "" 1.90 , -1.60 }
{ "" 0.59 , -0.30 }
{ "" 0.62 , -0.34 }
{ "" 1.46 , -1.20 }
{ "" 2.43 , -2.17 }
{ "" 0.24 , 0.00 }
{ "" 25.23 , -23.11 }
{ "" 1.64 , 0.00 }
{ "" 8.24 , -7.33 }
{ "" 7.76 , -7.00 }
{ "" 3.10 , -2.39 }
{ "" 6.93 , -6.31 }
{ "" 7.92 , -7.33 }
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{ "" 0.52 , 0.00 }
{ "" 1.49 , -1.03 }
{ "" 2.92 , -2.51 }
{ "" 0.39 , 0.00 }
{ "" 3.73 , -3.37 }
{ "" 1.53 , -1.20 }
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{ "" 3.30 , -3.01 }
{ "" 0.62 , -0.34 }
{ "" 1.66 , -1.40 }
{ "" 1.96 , -1.70 }
{ "" 0.74 , -0.50 }
{ "" 31.16 , -29.04 }
{ "" 1.64 , 0.00 }
{ "" 8.24 , -7.33 }
{ "" 9.74 , -8.98 }
{ "" 3.10 , -2.39 }
{ "" 8.67 , -8.05 }
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{ "" 6.01 , -5.46 }
{ "" 0.52 , 0.00 }
{ "" 1.49 , -1.03 }
{ "" 3.37 , -2.96 }
{ "" 4.69 , -4.31 }
{ "" 0.35 , 0.00 }
{ "" 1.53 , -1.20 }
{ "" 2.85 , -2.55 }
{ "" 3.30 , -3.01 }
{ "" 0.62 , -0.34 }
{ "" 1.66 , -1.40 }
{ "" 1.96 , -1.70 }
{ "" 2.45 , -2.21 }
{ "" 10.81 , -8.69 }
{ "" 1.64 , 0.00 }
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{ "" 3.04 , -2.28 }
{ "" 3.10 , -2.39 }
{ "" 2.85 , -2.23 }
{ "" 3.78 , -3.20 }
{ "" 1.09 , -0.55 }
{ "" 0.52 , 0.00 }
{ "" 1.49 , -1.03 }
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{ "" 4.62 , -4.23 }
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{ "" 1.53 , -1.20 }
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{ "" 0.30 , 0.00 }
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{ "" 1.53 , -1.27 }
{ "" 1.96 , -1.70 }
{ "" 2.45 , -2.21 }
{ "" 23.32 , -21.20 }
{ "" 1.64 , 0.00 }
{ "" 8.24 , -7.33 }
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{ "" 3.10 , -2.39 }
{ "" 6.38 , -5.76 }
{ "" 7.45 , -6.87 }
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{ "" 0.52 , 0.00 }
{ "" 1.49 , -1.03 }
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{ "" 3.04 , -2.74 }
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{ "" 1.66 , -1.40 }
{ "" 1.96 , -1.70 }
{ "" 0.24 , 0.00 }
{ "" 25.23 , -23.11 }
{ "" 1.64 , 0.00 }
{ "" 9.53 , -8.61 }
{ "" 7.76 , -7.00 }
{ "" 3.10 , -2.39 }
{ "" 6.93 , -6.31 }
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{ "" 0.47 , 0.00 }
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{ "" 0.39 , 0.00 }
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{ "" 3.51 , -3.22 }
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{ "" 2.03 , -1.77 }
{ "" 2.43 , -2.17 }
{ "" 0.74 , -0.50 }
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{ "" 1.64 , 0.00 }
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{ "" 10.05 , -9.28 }
{ "" 3.10 , -2.39 }
{ "" 8.98 , -8.36 }
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{ "" 7.76 , -7.00 }
{ "" 3.10 , -2.39 }
{ "" 6.93 , -6.31 }
{ "" 7.92 , -7.33 }
{ "" 6.88 , -6.33 }
{ "" 6.32 , -5.79 }
{ "" 5.00 , -4.53 }
{ "" 2.92 , -2.51 }
{ "" 0.39 , 0.00 }
{ "" 0.35 , 0.00 }
{ "" 1.53 , -1.20 }
{ "" 4.46 , -4.16 }
{ "" 3.51 , -3.22 }
{ "" 0.62 , -0.34 }
{ "" 3.02 , -2.76 }
{ "" 2.43 , -2.17 }
{ "" 0.74 , -0.50 }
{ "" 23.74 , -21.62 }
{ "" 1.64 , 0.00 }
{ "" 4.12 , -3.21 }
{ "" 7.76 , -7.00 }
{ "" 3.10 , -2.39 }
{ "" 6.75 , -6.13 }
{ "" 7.16 , -6.58 }
{ "" 3.49 , -2.95 }
{ "" 5.01 , -4.49 }
{ "" 5.00 , -4.53 }
{ "" 2.92 , -2.51 }
{ "" 0.39 , 0.00 }
{ "" 3.73 , -3.37 }
{ "" 1.53 , -1.20 }
{ "" 0.30 , 0.00 }
{ "" 2.15 , -1.86 }
{ "" 0.62 , -0.34 }
{ "" 1.46 , -1.20 }
{ "" 2.04 , -1.78 }
{ "" 0.74 , -0.50 }
{ "" 10.81 , -8.69 }
{ "" 1.64 , 0.00 }
{ "" 3.76 , -2.84 }
{ "" 3.04 , -2.28 }
{ "" 3.10 , -2.39 }
{ "" 2.85 , -2.23 }
{ "" 3.78 , -3.20 }
{ "" 1.09 , -0.55 }
{ "" 5.85 , -5.32 }
{ "" 5.00 , -4.53 }
{ "" 2.67 , -2.26 }
{ "" 0.39 , 0.00 }
{ "" 3.73 , -3.37 }
{ "" 1.53 , -1.20 }
{ "" 2.17 , -1.87 }
{ "" 0.30 , 0.00 }
{ "" 0.62 , -0.34 }
{ "" 1.53 , -1.27 }
{ "" 2.43 , -2.17 }
{ "" 0.74 , -0.50 }
{ "" 20.78 , -18.66 }
{ "" 1.64 , 0.00 }
{ "" 3.30 , -2.38 }
{ "" 6.16 , -5.40 }
{ "" 3.10 , -2.39 }
{ "" 5.63 , -5.01 }
{ "" 6.63 , -6.05 }
{ "" 3.06 , -2.51 }
{ "" 3.34 , -2.82 }
{ "" 3.64 , -3.18 }
{ "" 2.34 , -1.93 }
{ "" 0.39 , 0.00 }
{ "" 3.73 , -3.37 }
{ "" 1.53 , -1.20 }
{ "" 1.66 , -1.37 }
{ "" 1.74 , -1.45 }
{ "" 0.62 , -0.34 }
{ "" 0.26 , 0.00 }
{ "" 2.30 , -2.04 }
{ "" 0.74 , -0.50 }
{ "" 23.74 , -21.62 }
{ "" 1.64 , 0.00 }
{ "" 4.12 , -3.21 }
{ "" 7.84 , -7.08 }
{ "" 3.10 , -2.39 }
{ "" 6.75 , -6.13 }
{ "" 7.16 , -6.58 }
{ "" 3.49 , -2.95 }
{ "" 5.01 , -4.49 }
{ "" 5.37 , -4.90 }
{ "" 4.15 , -3.74 }
{ "" 6.25 , -5.86 }
{ "" 0.35 , 0.00 }
{ "" 1.53 , -1.20 }
{ "" 0.30 , 0.00 }
{ "" 2.15 , -1.86 }
{ "" 0.62 , -0.34 }
{ "" 1.46 , -1.20 }
{ "" 2.04 , -1.78 }
{ "" 3.41 , -3.17 }
{ "" 10.81 , -8.69 }
{ "" 1.64 , 0.00 }
{ "" 3.76 , -2.84 }
{ "" 3.04 , -2.28 }
{ "" 3.10 , -2.39 }
{ "" 2.85 , -2.23 }
{ "" 3.78 , -3.20 }
{ "" 1.09 , -0.55 }
{ "" 5.85 , -5.32 }
{ "" 5.65 , -5.18 }
{ "" 2.67 , -2.26 }
{ "" 4.62 , -4.23 }
{ "" 0.35 , 0.00 }
{ "" 1.53 , -1.20 }
{ "" 2.17 , -1.87 }
{ "" 0.30 , 0.00 }
{ "" 0.62 , -0.34 }
{ "" 1.53 , -1.27 }
{ "" 2.43 , -2.17 }
{ "" 2.47 , -2.23 }
{ "" 20.78 , -18.66 }
{ "" 1.64 , 0.00 }
{ "" 3.30 , -2.38 }
{ "" 6.16 , -5.40 }
{ "" 3.10 , -2.39 }
{ "" 5.63 , -5.01 }
{ "" 6.63 , -6.05 }
{ "" 3.06 , -2.51 }
{ "" 3.34 , -2.82 }
{ "" 3.64 , -3.18 }
{ "" 2.34 , -1.93 }
{ "" 4.50 , -4.11 }
{ "" 0.35 , 0.00 }
{ "" 1.53 , -1.20 }
{ "" 1.66 , -1.37 }
{ "" 1.74 , -1.45 }
{ "" 0.62 , -0.34 }
{ "" 0.26 , 0.00 }
{ "" 2.30 , -2.04 }
{ "" 2.30 , -2.06 }
{ "" 23.32 , -21.20 }
{ "" 1.64 , 0.00 }
{ "" 10.08 , -9.16 }
{ "" 7.00 , -6.24 }
{ "" 3.10 , -2.39 }
{ "" 6.38 , -5.76 }
{ "" 7.45 , -6.87 }
{ "" 6.01 , -5.46 }
{ "" 5.32 , -4.80 }
{ "" 4.16 , -3.69 }
{ "" 2.14 , -1.73 }
{ "" 1.20 , -0.81 }
{ "" 0.35 , 0.00 }
{ "" 1.53 , -1.20 }
{ "" 4.22 , -3.92 }
{ "" 3.04 , -2.74 }
{ "" 0.62 , -0.34 }
{ "" 2.50 , -2.24 }
{ "" 2.43 , -2.17 }
{ "" 0.24 , 0.00 }
{ "" 23.32 , -21.20 }
{ "" 1.64 , 0.00 }
{ "" 4.12 , -3.21 }
{ "" 7.00 , -6.24 }
{ "" 3.10 , -2.39 }
{ "" 6.38 , -5.76 }
{ "" 7.16 , -6.58 }
{ "" 3.49 , -2.95 }
{ "" 5.01 , -4.49 }
{ "" 4.16 , -3.69 }
{ "" 2.14 , -1.73 }
{ "" 1.20 , -0.81 }
{ "" 3.73 , -3.37 }
{ "" 1.53 , -1.20 }
{ "" 0.30 , 0.00 }
{ "" 2.15 , -1.86 }
{ "" 0.62 , -0.34 }
{ "" 1.46 , -1.20 }
{ "" 2.04 , -1.78 }
{ "" 0.24 , 0.00 }
{ "" 10.81 , -8.69 }
{ "" 1.64 , 0.00 }
{ "" 3.76 , -2.84 }
{ "" 3.04 , -2.28 }
{ "" 3.10 , -2.39 }
{ "" 2.85 , -2.23 }
{ "" 3.78 , -3.20 }
{ "" 1.09 , -0.55 }
{ "" 5.32 , -4.80 }
{ "" 4.16 , -3.69 }
{ "" 2.14 , -1.73 }
{ "" 1.20 , -0.81 }
{ "" 3.73 , -3.37 }
{ "" 1.53 , -1.20 }
{ "" 2.17 , -1.87 }
{ "" 0.30 , 0.00 }
{ "" 0.62 , -0.34 }
{ "" 1.53 , -1.27 }
{ "" 2.43 , -2.17 }
{ "" 0.24 , 0.00 }
{ "" 17.38 , -15.26 }
{ "" 7.20 , -5.57 }
{ "" 0.92 , 0.00 }
{ "" 5.33 , -4.57 }
{ "" 0.70 , 0.00 }
{ "" 4.77 , -4.15 }
{ "" 5.59 , -5.01 }
{ "" 1.86 , -1.31 }
{ "" 1.67 , -1.15 }
{ "" 0.47 , 0.00 }
{ "" 2.84 , -2.42 }
{ "" 4.15 , -3.76 }
{ "" 2.77 , -2.41 }
{ "" 2.47 , -2.15 }
{ "" 1.34 , -1.04 }
{ "" 1.21 , -0.91 }
{ "" 1.57 , -1.29 }
{ "" 0.94 , -0.68 }
{ "" 2.50 , -2.24 }
{ "" 2.14 , -1.90 }
{ "" 17.38 , -15.26 }
{ "" 7.20 , -5.57 }
{ "" 0.92 , 0.00 }
{ "" 5.33 , -4.57 }
{ "" 0.70 , 0.00 }
{ "" 4.77 , -4.15 }
{ "" 5.59 , -5.01 }
{ "" 1.86 , -1.31 }
{ "" 4.70 , -4.18 }
{ "" 4.86 , -4.39 }
{ "" 2.84 , -2.42 }
{ "" 0.39 , 0.00 }
{ "" 2.77 , -2.41 }
{ "" 2.47 , -2.15 }
{ "" 1.34 , -1.04 }
{ "" 1.21 , -0.91 }
{ "" 1.57 , -1.29 }
{ "" 0.94 , -0.68 }
{ "" 2.61 , -2.35 }
{ "" 0.74 , -0.50 }
{ "" 17.38 , -15.26 }
{ "" 7.20 , -5.57 }
{ "" 0.92 , 0.00 }
{ "" 5.33 , -4.57 }
{ "" 0.70 , 0.00 }
{ "" 4.77 , -4.15 }
{ "" 5.59 , -5.01 }
{ "" 1.86 , -1.31 }
{ "" 4.70 , -4.18 }
{ "" 4.16 , -3.69 }
{ "" 2.14 , -1.73 }
{ "" 1.20 , -0.81 }
{ "" 2.77 , -2.41 }
{ "" 2.47 , -2.15 }
{ "" 1.34 , -1.04 }
{ "" 1.21 , -0.91 }
{ "" 1.57 , -1.29 }
{ "" 0.94 , -0.68 }
{ "" 2.61 , -2.35 }
{ "" 0.24 , 0.00 }
{ "" 17.38 , -15.26 }
{ "" 24.23 , -22.59 }
{ "" 0.92 , 0.00 }
{ "" 5.33 , -4.57 }
{ "" 12.32 , -11.62 }
{ "" 4.77 , -4.15 }
{ "" 5.59 , -5.01 }
{ "" 1.86 , -1.31 }
{ "" 1.67 , -1.15 }
{ "" 0.47 , 0.00 }
{ "" 2.84 , -2.42 }
{ "" 0.39 , 0.00 }
{ "" 6.53 , -6.18 }
{ "" 3.64 , -3.31 }
{ "" 1.34 , -1.04 }
{ "" 1.21 , -0.91 }
{ "" 3.93 , -3.65 }
{ "" 0.94 , -0.68 }
{ "" 2.50 , -2.24 }
{ "" 0.74 , -0.50 }
{ "" 17.38 , -15.26 }
{ "" 17.19 , -15.55 }
{ "" 0.92 , 0.00 }
{ "" 5.33 , -4.57 }
{ "" 5.49 , -4.79 }
{ "" 4.77 , -4.15 }
{ "" 5.59 , -5.01 }
{ "" 1.86 , -1.31 }
{ "" 1.67 , -1.15 }
{ "" 0.47 , 0.00 }
{ "" 2.84 , -2.42 }
{ "" 4.15 , -3.76 }
{ "" 0.35 , 0.00 }
{ "" 3.64 , -3.31 }
{ "" 1.34 , -1.04 }
{ "" 1.21 , -0.91 }
{ "" 3.26 , -2.98 }
{ "" 0.94 , -0.68 }
{ "" 2.50 , -2.24 }
{ "" 2.14 , -1.90 }
{ "" 17.38 , -15.26 }
{ "" 7.69 , -6.06 }
{ "" 0.92 , 0.00 }
{ "" 5.33 , -4.57 }
{ "" 5.35 , -4.65 }
{ "" 4.77 , -4.15 }
{ "" 5.59 , -5.01 }
{ "" 1.86 , -1.31 }
{ "" 1.67 , -1.15 }
{ "" 0.47 , 0.00 }
{ "" 2.84 , -2.42 }
{ "" 4.15 , -3.76 }
{ "" 4.30 , -3.94 }
{ "" 0.33 , 0.00 }
{ "" 1.34 , -1.04 }
{ "" 1.21 , -0.91 }
{ "" 1.12 , -0.84 }
{ "" 0.94 , -0.68 }
{ "" 1.78 , -1.52 }
{ "" 2.14 , -1.90 }
{ "" 17.38 , -15.26 }
{ "" 3.60 , -1.96 }
{ "" 0.92 , 0.00 }
{ "" 5.33 , -4.57 }
{ "" 3.94 , -3.24 }
{ "" 4.77 , -4.15 }
{ "" 5.59 , -5.01 }
{ "" 1.86 , -1.31 }
{ "" 1.67 , -1.15 }
{ "" 0.47 , 0.00 }
{ "" 2.84 , -2.42 }
{ "" 4.15 , -3.76 }
{ "" 4.12 , -3.76 }
{ "" 1.30 , -0.97 }
{ "" 1.34 , -1.04 }
{ "" 1.21 , -0.91 }
{ "" 0.28 , 0.00 }
{ "" 0.94 , -0.68 }
{ "" 2.40 , -2.14 }
{ "" 2.14 , -1.90 }
{ "" 17.38 , -15.26 }
{ "" 17.19 , -15.55 }
{ "" 0.92 , 0.00 }
{ "" 5.33 , -4.57 }
{ "" 5.49 , -4.79 }
{ "" 4.77 , -4.15 }
{ "" 5.59 , -5.01 }
{ "" 1.86 , -1.31 }
{ "" 4.70 , -4.18 }
{ "" 4.86 , -4.39 }
{ "" 2.84 , -2.42 }
{ "" 0.39 , 0.00 }
{ "" 0.35 , 0.00 }
{ "" 3.93 , -3.61 }
{ "" 1.34 , -1.04 }
{ "" 1.21 , -0.91 }
{ "" 3.26 , -2.98 }
{ "" 0.94 , -0.68 }
{ "" 2.61 , -2.35 }
{ "" 0.74 , -0.50 }
{ "" 17.38 , -15.26 }
{ "" 7.69 , -6.06 }
{ "" 0.92 , 0.00 }
{ "" 5.33 , -4.57 }
{ "" 5.35 , -4.65 }
{ "" 4.77 , -4.15 }
{ "" 5.59 , -5.01 }
{ "" 1.86 , -1.31 }
{ "" 4.70 , -4.18 }
{ "" 4.86 , -4.39 }
{ "" 2.84 , -2.42 }
{ "" 0.39 , 0.00 }
{ "" 4.30 , -3.94 }
{ "" 0.33 , 0.00 }
{ "" 1.34 , -1.04 }
{ "" 1.21 , -0.91 }
{ "" 1.12 , -0.84 }
{ "" 0.94 , -0.68 }
{ "" 1.78 , -1.52 }
{ "" 0.74 , -0.50 }
{ "" 17.38 , -15.26 }
{ "" 3.60 , -1.96 }
{ "" 0.92 , 0.00 }
{ "" 5.33 , -4.57 }
{ "" 3.94 , -3.24 }
{ "" 4.77 , -4.15 }
{ "" 5.59 , -5.01 }
{ "" 1.86 , -1.31 }
{ "" 4.70 , -4.18 }
{ "" 4.86 , -4.39 }
{ "" 2.84 , -2.42 }
{ "" 0.39 , 0.00 }
{ "" 4.12 , -3.76 }
{ "" 1.30 , -0.97 }
{ "" 1.34 , -1.04 }
{ "" 1.21 , -0.91 }
{ "" 0.28 , 0.00 }
{ "" 0.94 , -0.68 }
{ "" 2.40 , -2.14 }
{ "" 0.74 , -0.50 }
{ "" 17.38 , -15.26 }
{ "" 7.69 , -6.06 }
{ "" 0.92 , 0.00 }
{ "" 5.33 , -4.57 }
{ "" 5.35 , -4.65 }
{ "" 4.77 , -4.15 }
{ "" 5.59 , -5.01 }
{ "" 1.86 , -1.31 }
{ "" 4.70 , -4.18 }
{ "" 4.86 , -4.39 }
{ "" 2.84 , -2.42 }
{ "" 5.01 , -4.62 }
{ "" 0.35 , 0.00 }
{ "" 0.33 , 0.00 }
{ "" 1.34 , -1.04 }
{ "" 1.21 , -0.91 }
{ "" 1.12 , -0.84 }
{ "" 0.94 , -0.68 }
{ "" 1.78 , -1.52 }
{ "" 2.64 , -2.40 }
{ "" 17.38 , -15.26 }
{ "" 3.60 , -1.96 }
{ "" 0.92 , 0.00 }
{ "" 5.33 , -4.57 }
{ "" 3.94 , -3.24 }
{ "" 4.77 , -4.15 }
{ "" 5.59 , -5.01 }
{ "" 1.86 , -1.31 }
{ "" 4.70 , -4.18 }
{ "" 4.86 , -4.39 }
{ "" 2.84 , -2.42 }
{ "" 5.01 , -4.62 }
{ "" 0.35 , 0.00 }
{ "" 1.30 , -0.97 }
{ "" 1.34 , -1.04 }
{ "" 1.21 , -0.91 }
{ "" 0.28 , 0.00 }
{ "" 0.94 , -0.68 }
{ "" 2.40 , -2.14 }
{ "" 2.64 , -2.40 }
{ "" 17.38 , -15.26 }
{ "" 17.19 , -15.55 }
{ "" 0.92 , 0.00 }
{ "" 5.33 , -4.57 }
{ "" 5.49 , -4.79 }
{ "" 4.77 , -4.15 }
{ "" 5.59 , -5.01 }
{ "" 1.86 , -1.31 }
{ "" 4.70 , -4.18 }
{ "" 4.16 , -3.69 }
{ "" 2.14 , -1.73 }
{ "" 1.20 , -0.81 }
{ "" 0.35 , 0.00 }
{ "" 3.93 , -3.61 }
{ "" 1.34 , -1.04 }
{ "" 1.21 , -0.91 }
{ "" 3.26 , -2.98 }
{ "" 0.94 , -0.68 }
{ "" 2.61 , -2.35 }
{ "" 0.24 , 0.00 }

In behavior strategy profiles (libgambit/behav.h), there are several pairs of functions that do essentially the same thing, just on different objects:

• GetRealizProb and GetInfosetProb compute the probability of reaching a node and an information set, respectively;
• GetNodeValue and GetInfosetValue compute the expected payoff conditional on reaching a node and an information set, respectively.

It seems cleaner to call these, e.g., GetRealizProb and GetPayoff, respectively, and use overloading. GetActionValue could also be relabeled GetPayoff as well.

This would require some straightforward replacements throughout the C++ code as well as the Cython wrapper.

In any event, irrespective of the proposed C++ change, there is a need to expose GetRealizProb(GameNode) in Cython, as it is currently omitted.

In the Python API, the set-like operations intersection and difference can result in what would be an invalid support profile (i.e., one in which one or more players does not have any strategies). This should raise an appropriate Python exception.

The normal form game below has a bifurcation on the principal branch.

gambit-logit -l 4 -s 5 < test2.nfg
enters an infinite loop (it jumps back and forth between two lambdas), and

gambit-logit -l 4 -s 4 < test2.nfg
goes back to sub-zero lambdas.

Introduce a parameter which limits the total number of steps taken, to avoid the infinite loop. (Avoiding retracing one's steps is much trickier.)

NFG 1 R "State 2 5 6" 
{ "P1" "P2" "P3" } { 9 6 5 }

8.0000000000000 8.0000000000000 8.0000000000000 8.3328072000000 7.5007892000000 7.5007892000000 8.7123829968928 6.9314155046608 6.9314155046608 9.1100831924459 6.3348572078112 6.3348572078112 9.5107136506471 5.7339361259461 5.7339361259461 9.9110679257601 5.1334037792839 5.1334037792839 10.3111444892446 4.5332868653876 4.5332868653876 10.7111457342632 3.9332817992730 3.9332817992730 11.1111393153621 3.3332864823521 3.3332864823521 7.5007892000000 8.3328072000000 7.5007892000000 7.8512196429849 7.8512196429849 7.1073178579092 8.2251330097314 7.3037722487602 6.5866954821313 8.6185469794645 6.7151336240134 6.0010371734226 9.0181452791976 6.1151167682714 5.3997913410819 9.4185670705195 5.5141293953536 4.7980915412635 9.8187892342593 4.9137167346558 4.1975200302472 10.2188546410418 4.3136311144568 3.5974395410115 10.6188640814749 3.7136331128590 2.9974597208816 6.9314155046608 8.7123829968928 6.9314155046608 7.3037722487602 8.2251330097314 6.5866954821313 7.6854092035759 7.6854092035759 6.1124663547498 8.0782497342711 7.1053041297683 5.5506637768997 8.4761584321020 6.5092519726354 4.9562081244940 8.8757648586844 5.9092395388094 4.3549874207118 9.2757950134079 5.3088020067293 3.7537982242785 9.6758805137847 4.7085667809879 3.1533346544399 10.0759260644985 4.1084905123807 2.5532381911255 6.3348572078112 9.1100831924459 6.3348572078112 6.7151336240134 8.6185469794645 6.0010371734226 7.1053041297683 8.0782497342711 5.5506637768997 7.5020331309835 7.5020331309835 5.0122462545077 7.9003332467425 6.9100132825507 4.4310682912837 8.2993158124452 6.3122428424554 3.8346968721547 8.6988621712238 5.7126011965427 3.2344018050622 9.0987562231095 5.1124892934825 2.6337040040723 9.4987597256731 4.5123522371592 2.0333202933936 5.7339361259461 9.5107136506471 5.7339361259461 6.1151167682714 9.0181452791976 5.3997913410819 6.5092519726354 8.4761584321020 4.9562081244940 6.9100132825507 7.9003332467425 4.4310682912837 7.3103910751478 7.3103910751478 3.8623855538371 7.7098423462787 6.7147077364317 3.2736852467235 8.1092096136857 6.1163571358014 2.6766929726482 8.5088338154894 5.5167790141378 2.0768688380300 8.9087111081408 4.9167766746082 1.4764673173306 5.1334037792839 9.9110679257601 5.1334037792839 5.5141293953536 9.4185670705195 4.7980915412635 5.9092395388094 8.8757648586844 4.3549874207118 6.3122428424554 8.2993158124452 3.8346968721547 6.7147077364317 7.7098423462787 3.2736852467235 7.1153345719485 7.1153345719485 2.6920181642274 7.5150539461519 6.5181290915284 2.0995791905615 7.9146549717493 5.9193235238626 1.5019310603402 8.3143984848291 5.3196784248673 0.9022283690317 7.5007892000000 7.5007892000000 8.3328072000000 7.8512196429849 7.1073178579092 7.8512196429849 8.2251330097314 6.5866954821313 7.3037722487602 8.6185469794645 6.0010371734226 6.7151336240134 9.0181452791976 5.3997913410819 6.1151167682714 9.4185670705195 4.7980915412635 5.5141293953536 9.8187892342593 4.1975200302472 4.9137167346558 10.2188546410418 3.5974395410115 4.3136311144568 10.6188640814749 2.9974597208816 3.7136331128590 7.1073178579092 7.8512196429849 7.8512196429849 7.5026425875317 7.5026425875317 7.5026425875317 7.8721370919583 7.0291331343051 7.0291331343051 8.2549632457203 6.4670530337598 6.4670530337598 8.6493623749223 5.8708699680866 5.8708699680866 9.0487865574437 5.2681248011319 5.2681248011319 9.4493387752813 4.6662554631741 4.6662554631741 9.8497347142131 4.0656490511355 4.0656490511355 10.2498777157434 3.4655855702236 3.4655855702236 6.5866954821313 8.2251330097314 7.3037722487602 7.0291331343051 7.8721370919583 7.0291331343051 7.4160089372577 7.4160089372577 6.6331058310494 7.7958887174489 6.8752335433337 6.1240428324463 8.1832167307620 6.2899048120496 5.5495271825295 8.5789093486196 5.6887958217775 4.9502009597268 8.9788717818291 5.0854473345988 4.3465516272004 9.3797407601355 4.4835806292135 3.7444835106058 9.7802568595650 3.8830222554837 3.1439948216297 6.0010371734226 8.6185469794645 6.7151336240134 6.4670530337598 8.2549632457203 6.4670530337598 6.8752335433337 7.7958887174489 6.1240428324463 7.2629062328513 7.2629062328513 5.6781967413420 7.6475533719683 6.6868421857256 5.1494575421182 8.0385260821899 6.0892737625722 4.5698967850270 8.4362318665384 5.4848205595343 3.9699740322177 8.8370351803433 4.8808366997159 3.3668918474783 9.2381100729426 4.2789610519958 2.7656734038272 5.3997913410819 9.0181452791976 6.1151167682714 5.8708699680866 8.6493623749223 5.8708699680866 6.2899048120496 8.1832167307620 5.5495271825295 6.6868421857256 7.6475533719683 5.1494575421182 7.0741790986120 7.0741790986120 4.6738707269796 7.4627495977695 6.4792501354425 4.1318083996756 7.8575077883567 5.8741258008601 3.5481526417852 8.2572042837206 5.2675026871862 2.9488105463511 8.6585720413026 4.6632496846919 2.3478473907141 4.7980915412635 9.4185670705195 5.5141293953536 5.2681248011319 9.0487865574437 5.2681248011319 5.6887958217775 8.5789093486196 4.9502009597268 6.0892737625722 8.0385260821899 4.5698967850270 6.4792501354425 7.4627495977695 4.1318083996756 6.8675542257520 6.8675542257520 3.6291907309980 7.2599179319191 6.2615590367407 3.0713559061898 7.6575616854621 5.6524203218145 2.4825431853619 8.0583629764810 5.0452075717001 1.8840571857215 6.9314155046608 6.9314155046608 8.7123829968928 7.3037722487602 6.5866954821313 8.2251330097314 7.6854092035759 6.1124663547498 7.6854092035759 8.0782497342711 5.5506637768997 7.1053041297683 8.4761584321020 4.9562081244940 6.5092519726354 8.8757648586844 4.3549874207118 5.9092395388094 9.2757950134079 3.7537982242785 5.3088020067293 9.6758805137847 3.1533346544399 4.7085667809879 10.0759260644985 2.5532381911255 4.1084905123807 6.5866954821313 7.3037722487602 8.2251330097314 7.0291331343051 7.0291331343051 7.8721370919583 7.4160089372577 6.6331058310494 7.4160089372577 7.7958887174489 6.1240428324463 6.8752335433337 8.1832167307620 5.5495271825295 6.2899048120496 8.5789093486196 4.9502009597268 5.6887958217775 8.9788717818291 4.3465516272004 5.0854473345988 9.3797407601355 3.7444835106058 4.4835806292135 9.7802568595650 3.1439948216297 3.8830222554837 6.1124663547498 7.6854092035759 7.6854092035759 6.6331058310494 7.4160089372577 7.4160089372577 7.0527747090492 7.0527747090492 7.0527747090492 7.4313883288485 6.5853751414847 6.5853751414847 7.8069443967043 6.0387072272624 6.0387072272624 8.1948343459388 5.4477081954501 5.4477081954501 8.5933392970658 4.8419945893884 4.8419945893884 8.9955017783718 4.2366627618677 4.2366627618677 9.3972435863876 3.6347501587977 3.6347501587977 5.5506637768997 8.0782497342711 7.1053041297683 6.1240428324463 7.7958887174489 6.8752335433337 6.5853751414847 7.4313883288485 6.5853751414847 6.9797881067098 6.9797881067098 6.2076039164668 7.3523617796359 6.4548350037584 5.7351512158321 7.7321249603276 5.8758992252473 5.1831648101166 8.1267870676602 5.2697832865042 4.5869340146798 8.5297601029003 4.6594523073840 3.9797487722770 8.9334029563088 4.0539676281091 3.3761066681055 4.9562081244940 8.4761584321020 6.5092519726354 5.5495271825295 8.1832167307620 6.2899048120496 6.0387072272624 7.8069443967043 6.0387072272624 6.4548350037584 7.3523617796359 5.7351512158321 6.8362802474084 6.8362802474084 5.3539511005589 7.2135838527159 6.2684941115300 4.8762043431593 7.6028902908805 5.6648616000857 4.3172006529342 8.0042991559144 5.0491108565289 3.7194425564216 8.4098157230740 4.4373321767584 3.1167116927922 4.3549874207118 8.8757648586844 5.9092395388094 4.9502009597268 8.5789093486196 5.6887958217775 5.4477081954501 8.1948343459388 5.4477081954501 5.8758992252473 7.7321249603276 5.1831648101166 6.2684941115300 7.2135838527159 4.8762043431593 6.6503944888731 6.6503944888731 4.4880666217014 7.0361345164773 6.0513845647919 3.9993500317831 7.4319734025209 5.4333157516982 3.4360647623219 7.8363285799873 4.8138659970720 2.8437498895927 6.3348572078112 6.3348572078112 9.1100831924459 6.7151336240134 6.0010371734226 8.6185469794645 7.1053041297683 5.5506637768997 8.0782497342711 7.5020331309835 5.0122462545077 7.5020331309835 7.9003332467425 4.4310682912837 6.9100132825507 8.2993158124452 3.8346968721547 6.3122428424554 8.6988621712238 3.2344018050622 5.7126011965427 9.0987562231095 2.6337040040723 5.1124892934825 9.4987597256731 2.0333202933936 4.5123522371592 6.0010371734226 6.7151336240134 8.6185469794645 6.4670530337598 6.4670530337598 8.2549632457203 6.8752335433337 6.1240428324463 7.7958887174489 7.2629062328513 5.6781967413420 7.2629062328513 7.6475533719683 5.1494575421182 6.6868421857256 8.0385260821899 4.5698967850270 6.0892737625722 8.4362318665384 3.9699740322177 5.4848205595343 8.8370351803433 3.3668918474783 4.8808366997159 9.2381100729426 2.7656734038272 4.2789610519958 5.5506637768997 7.1053041297683 8.0782497342711 6.1240428324463 6.8752335433337 7.7958887174489 6.5853751414847 6.5853751414847 7.4313883288485 6.9797881067098 6.2076039164668 6.9797881067098 7.3523617796359 5.7351512158321 6.4548350037584 7.7321249603276 5.1831648101166 5.8758992252473 8.1267870676602 4.5869340146798 5.2697832865042 8.5297601029003 3.9797487722770 4.6594523073840 8.9334029563088 3.3761066681055 4.0539676281091 5.0122462545077 7.5020331309835 7.5020331309835 5.6781967413420 7.2629062328513 7.2629062328513 6.2076039164668 6.9797881067098 6.9797881067098 6.6265939528601 6.6265939528601 6.6265939528601 6.9991895779405 6.1872752446834 6.1872752446834 7.3721660531645 5.6599320849823 5.6599320849823 7.7645493349678 5.0695194785542 5.0695194785542 8.1703930756576 4.4571965484441 4.4571965484441 8.5774948623744 3.8486765116507 3.8486765116507 4.4310682912837 7.9003332467425 6.9100132825507 5.1494575421182 7.6475533719683 6.6868421857256 5.7351512158321 7.3523617796359 6.4548350037584 6.1872752446834 6.9991895779405 6.1872752446834 6.5749084437039 6.5749084437039 5.8448427973765 6.9502145109756 6.0701612337048 5.3960775640654 7.3403694555856 5.4951199546283 4.8438711213589 7.7465268804101 4.8862662800082 4.2356128086419 8.1566362867079 4.2760037740438 3.6210849968626 3.8346968721547 8.2993158124452 6.3122428424554 4.5698967850270 8.0385260821899 6.0892737625722 5.1831648101166 7.7321249603276 5.8758992252473 5.6599320849823 7.3721660531645 5.6599320849823 6.0701612337048 6.9502145109756 5.3960775640654 6.4605827372325 6.4605827372325 5.0293354538244 6.8537477157412 5.9104956309671 4.5246718548862 7.2729195022027 5.3294185373087 3.8757840817495 7.8125167531284 4.8033879496129 3.0626836747385 5.7339361259461 5.7339361259461 9.5107136506471 6.1151167682714 5.3997913410819 9.0181452791976 6.5092519726354 4.9562081244940 8.4761584321020 6.9100132825507 4.4310682912837 7.9003332467425 7.3103910751478 3.8623855538371 7.3103910751478 7.7098423462787 3.2736852467235 6.7147077364317 8.1092096136857 2.6766929726482 6.1163571358014 8.5088338154894 2.0768688380300 5.5167790141378 8.9087111081408 1.4764673173306 4.9167766746082 5.3997913410819 6.1151167682714 9.0181452791976 5.8708699680866 5.8708699680866 8.6493623749223 6.2899048120496 5.5495271825295 8.1832167307620 6.6868421857256 5.1494575421182 7.6475533719683 7.0741790986120 4.6738707269796 7.0741790986120 7.4627495977695 4.1318083996756 6.4792501354425 7.8575077883567 3.5481526417852 5.8741258008601 8.2572042837206 2.9488105463511 5.2675026871862 8.6585720413026 2.3478473907141 4.6632496846919 4.9562081244940 6.5092519726354 8.4761584321020 5.5495271825295 6.2899048120496 8.1832167307620 6.0387072272624 6.0387072272624 7.8069443967043 6.4548350037584 5.7351512158321 7.3523617796359 6.8362802474084 5.3539511005589 6.8362802474084 7.2135838527159 4.8762043431593 6.2684941115300 7.6028902908805 4.3172006529342 5.6648616000857 8.0042991559144 3.7194425564216 5.0491108565289 8.4098157230740 3.1167116927922 4.4373321767584 4.4310682912837 6.9100132825507 7.9003332467425 5.1494575421182 6.6868421857256 7.6475533719683 5.7351512158321 6.4548350037584 7.3523617796359 6.1872752446834 6.1872752446834 6.9991895779405 6.5749084437039 5.8448427973765 6.5749084437039 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4.4208235035725 5.8000000000000 2.8000000000000 1.8000000000000 

Hi everyone,
I'm trying to execute a Gambit command on OS X v 10.9.1

gambit-enumpure [filename] -Pq

, but it returns me:

gambit-enumpure(7166,0x7fff76274310) malloc: * error for object 0x7fdac04077e0: incorrect checksum for freed object - object was probably modified after being freed.* set a breakpoint in malloc_error_break to debug

Everything goes well if executing the command without the -P switch.

I'm pretty new to OS X, but running the same command on Linux I hadn't any problems.

Guido

There are a number of warnings in header files of the form, e.g.,

./src/labenski/include/wx/plotctrl/plotctrl.h:29: warning: type attributes ignored after type is already defined
./src/labenski/include/wx/plotctrl/plotctrl.h:30: warning: type attributes ignored after type is already defined
./src/labenski/include/wx/plotctrl/plotctrl.h:31: warning: type attributes ignored after type is already defined
./src/labenski/include/wx/plotctrl/plotctrl.h:32: warning: type attributes ignored after type is already defined
./src/labenski/include/wx/plotctrl/plotctrl.h:33: warning: type attributes ignored after type is already defined
./src/labenski/include/wx/plotctrl/plotctrl.h:34: warning: type attributes ignored after type is already defined
./src/labenski/include/wx/plotctrl/plotctrl.h:35: warning: type attributes ignored after type is already defined
./src/labenski/include/wx/plotctrl/plotctrl.h:36: warning: type attributes ignored after type is already defined
./src/labenski/include/wx/plotctrl/plotctrl.h:37: warning: type attributes ignored after type is already defined
./src/labenski/include/wx/plotctrl/plotctrl.h:38: warning: type attributes ignored after type is already defined
./src/labenski/include/wx/plotctrl/plotctrl.h:39: warning: type attributes ignored after type is already defined

These come from the WXDLLEXPORT declarations.

In truth, it is probably the case these attributes can be removed, as we do not have any intention of building the graphical interface code in a library format.

I expect this should be something that can be safely backported to versions based on wx 2.8, and so probably can be done separately from the current wx294 branch.

Branch master_gamerep_python is an attempt to reconcile the new Python API with some ongoing evolution in how game representation is implemented, specifically, the semantics of pure and mixed strategy profiles.

The integration builds, but nosetests fail with a memory error (OS X 10.8, Python 2.7.3):

$ nosetests
Python(54074) malloc: *** error for object 0x7ff779ef24a8: pointer being freed was not allocated
*** set a breakpoint in malloc_error_break to debug
Abort trap: 6

Documentation should be augmented with links to the relevant github pages for submitting issues, grabbing the latest repository (including what 'master' and 'maint' branches mean).

The agent QRE implementation does not inspect the support of the behavior strategy profile when computing the function and Jacobian evaluations. Therefore, if actions are absent from the support, the computation will fail.

This does not cause problems at present with the command-line implementation because only full-support calls are possible. But, this bug will be exposed in due course when it is possible to consider games with restricted action sets.

At present, the output of the QRE tracers are objects which record the value of lambda, and otherwise pass on other calls to the underlying profile.

This has the effect that calling .as_behav() on a mixed strategy QRE returns a (non-QRE) behavior strategy object, thereby losing the lambda information.

The branch belief contains a quick-and-dirty implementation of accessing the belief at a node for a behavior strategy profile.

Required to be able to merge this into the master branch:
(1) Extend the implementation to accept an information set, in which case a list of probabilities (one for each member) should be returned.
(2) Add a few suitable test cases to the test suite to exercise the calls.
(3) Add an entry to the documentation.

Saving games in the .efg and .nfg formats is done via File->Export. This is perhaps not the most intuitive option, and may become even more confusing once the format used by the GTE project is also supported.

Review other packages which deal with multiple file formats, and construct a solution that makes selecting a file format easy for users.

Currently some unexpected behavior may happen whenever using data structures which require objects to be hashable (e.g. using strategies as keys in a dict or as elements in a set).

The implementation of behavior profiles depends on the game having been "canonicalized" - internally having all the nodes and information sets numbered in a certain way.

This has traditionally been done by an explicit call to GameRep::Canonicalize(), which was usually only done once for "efficiency" reasons. However, that was decades ago; the amount of time it takes to canonicalize a game today is trivial. Further, while that is easy when dealing with the graphical interface, making sure games are canonicalized in the Python interface is more tricky.

At a minimum, it seems that all editing operations that affect nodes or information sets should always re-canonicalize the representation internally.

However, there is space here for deeper thinking: rather than using sequential numbering (which means the number of a node or information set can change as the game is edited), some other scheme like UUIDs might be appropriate, with the internal representation of a behavior profile using an associative array to store cached information like beliefs.

There are a few potential complexities with this idea - so this is a project that's suitable for a bit more experienced hands.

The Python API introduces a new concept, the "strategic restriction" of a game, which is an improvement on the way supports are done in C++. How to use this should be documented, especially as it is most useful for dealing with games with dominated strategies.

E.g. in python 2.7 in Windows 7, when running
gambit.qre.ExternalStrategicQREPathTracer().trace_strategic_path(some_game),
receives the following error:

Traceback (most recent call last):
File "", line 1, in
File "build\bdist.win32\egg\gambit\qre.py", line 238, in trace_strategic_path
File "build\bdist.win32\egg\gambit\nash.py", line 30, in launch
File "C:\Python27\lib\subprocess.py", line 630, in init
raise ValueError("close_fds is not supported on Windows "
ValueError: close_fds is not supported on Windows platforms if you redirect stdi
n/stdout/stderr

In the branch correq is some development of tools for analysing correlated equilibria of strategic games. There is not as yet an explicit representation of a correlated strategy profile.

It would be useful to have such an encapsulation of a CorrelatedStrategyProfile. Development should be parallel to the MixedStrategyProfile. It should include at least:

• __getitem__ and __setitem__, which should take contingencies of the game, instead of just a strategy (as MixedStrategyProfile does).
• Computation of expected payoff to each player.
• Determination of whether the strategy is a correlated equilibrium. gambit/correq.py in the correq branch already implements the constraints required for this, which should likely be refactored for use here.

A common request is to have a way to interact with Gambit directly from R.

Someone with some knowledge of R packages should research this possibility, and provide a patch to the ideas page which would outline a suggestion for how such a project should proceed.

I have discovered that the drag-and-drop features of the game tree editor are not working in the wx294 branch, at least on OS X. I have narrowed it down to being a problem on the drop target side; the dragging is being executed correctly (for example, one can drag into a terminal window and see that the text payload of the drag is correct).

It would be useful to confirm whether this is OS X-specific, or if this issue occurs also under Linux or Windows.

On OS X, rearranging players in the strategic game matrix does not work, because of the way the wxSheet class is implemented on that platform.

Implement an alternative method for specifying which players are on the rows and the columns of the matrix, that does not require drag-and-drop.

I have already submitted a pull request with the required changes to fix this but thought it would be a good idea to submit a proper bug report too for future reference.

gcc 4.7 introduces some changes to name lookup, making it more compatible with the standard. One scenario that is afflicted by these is using unqualified names in template classes to call a method from a template base class. This prevents Gambit from compiling with that version of gcc.

The fix is to use this-> with the unqualified names instead of using them directly.

There is a branch correq which contains a preliminary implementation of computing the set of correlated equilibrium payoffs for two-person games.

Some test cases should be written for this, including exercising the contains method for the object representing the set of payoffs.

(Resolving this may require dealing with a few implementation subtleties. It may also be the case that it should be dealt with at the C++ level.)

In Python the __getitem__ operator on a game returns the outcome associated with a particular contingency of strategies. This works well on games where the underlying representation is a table. However, if the underlying representation is a tree, calling this leads to a crash at present.

This operation is completely well-defined even if the underlying representation is a tree. The bit of complexity comes in because if a game has chance moves, the "outcome" associated with a particular contingency of strategies is in fact a probability distribution over possibly multiple outcomes.

One solution would be to create a Python-level or Cython-level class which stands in for an outcome in this case, one which implements its own __getitem__ to return payoffs to each player, which would be computed by taking the expected value over the possible terminal nodes. Note that the C++ PureStrategyProfile already will take care of computing this expected value -- that is to say, the proposed class would just be wrapping a PureStrategyProfile to make it look like an outcome.

In branch correq there is a routine in gambit/correq.py to compute the set of correlated equilibrium payoffs of a game. The set of correlated equilibrium payoffs of any game is a convex set.

Implement a method __contains__ which determines whether a payoff is contained in the set.

The implementations of append_move and insert_move on the Node class in the Python API do not check that the argument passed to the function represents an object (a player or information set) which belongs to the same game as the node. This raises a fatal error. An appropriate check for this condition should be written, and test cases added to exercise it.

As a model, the commit 57ccd66 illustrates a patch which implemented this functionality for setting the player associated with an information set.

The instructions in the documentation for the OS X build are outdated - among other things, the command-line 'gambit' binary does not run under X at all.

Also, notes should be made as to how to build the distribution .dmg file in a standard way.

The Python test suite does not exercise any of the external solver calls. Some should be added using some of the smaller example games in contrib/games.

The gambit-logit command line tool exposes undocumented features for computing MLE estimates of quantal response equilibria from observed date.

Add documentation on these features to the gambit-logit documentation, including, possibly, a tutorial for using the tool at the command line.

The command-line tools currently accept only .efg and .nfg formats. This is unintuitive, as the default save format for the graphical interface is now an XML-based format which embeds the .efg or .nfg representation.

Command-line tools should be able to read the graphical interface format -- and, perhaps, to write to it as well, as the format incorporates support for recording computed profiles.

The graphical interface currently uses TinyXML to do XML manipulation, which is currently included in src/gui. This would need to be refactored out into a separate directory for inclusion in other tools. One should also review whether this is the best XML manipulation solution, or whether there is a newer version of TinyXML which can be included.

In src/libgambit/file.cc, an InvalidFileException is raised when parsing an .efg or .nfg file, but the file is not correctly formed.

As of commit 807505a, it is now possible to pass a more descriptive error message explaining the failure. In particular, this message is reported in the Python interface when an exception is raised.

It would be useful to upgrade the instances of raising the InvalidFileException to provide better feedback in identifying the source of parse failures on these files.

External solver tools are located in an ad-hoc way in dlnash, dlefglogit, and dlnfglogit. On Mac wxStandardPaths is used to locate these in the application bundle. On other platforms, it is simply assumed the tools are in ${PATH} or equivalent.

As a first step, this should be moved to a central facility in the Gambit wxApp instance. For the moment, wxStandardPaths (or similar) should be used across all platforms. At a later step, wxConfig could be used to implement custom pointers to tools.

The replicator dynamics are a simple model of evolution of strategies in a game setting as a function of the fitness of strategies, measured by their expected payoffs. Write a simple model that carries out simulation of the replicator dynamics using the Python API.

With wxWidgets 2.9.5 there was some internal change in how sizing is done. As a result, the wxSheet in src/gui/dleditmove.cc was too small.

This apparently affected wxGrid, see the discussion at http://comments.gmane.org/gmane.comp.lib.wxwidgets.devel/143881 . As wxSheet is based on wxGrid, presumably the same issue applies.

This was corrected in src/gui/dleditmove.cc prior to 13.1.0 by adding an explicit invalidation of the calculated best size. A more robust solution would do this in the wxSheet implementation itself.

The command-line tools accept the game file on stdin. As an extension, optionally, the name of a file containing the game to be analysed could be passed as a command-line option. If a filename is passed on the command-line, this is used; otherwise stdin is used. The behaviour would thus be similar to other command-line tools, e.g. grep(1).

So, the following two calls would be equivalent:

gambit-logit -S mygame.efg
gambit-logit -S < mygame.efg

For extensive games in C++ it is implemented to convert between mixed and behavior strategy profiles. This should be wrapped in the Python interface.

Suggested names: BehavProfile.as_mixed() and MixedProfile.as_behav()

For strategic games, calls to the latter should raise NotImplementedError.

There is an example in the documentation for computing Nash equilibria, which illustrates the difference between solving in extensive and strategic games. Mention of these functions should be added to that documentation.

There are currently two places where text strings are converted into Rational numbers in src/libgambit/rational.cc: operator>>, which works on istreams, and lexical_cast<>, which coverts strings. These two implementations are not identical - for instance, lexical_cast accepts numbers in scientific notation but the operator>> does not.

This creates some inconsistencies in behavior, as the savefile reader src/libgambit/file.cc uses the lexical_cast<> call.

These two functions should be unified into one call, with uniform behavior whether reading from a file or a string.

The Gambit C++ API on for games implements a member IsConstSum(), returning true if and only if a game is constant-sum. This should be exposed in the Python API as a property is_const_sum.

Tips:

• Work from the master_python branch of the repository
• C++ game API is in src/libgambit/game.h
• Python game API is implemented in Cython in src/python/gambit/lib/game.pxi
• Use e.g. the 'root' property on the Game class as a model to work from.

Do not forget to include test cases in gambit/tests to exercise your implementation.

An edge case: tracing agent QRE fails when there is a chance move with zero probability. This occurs because subsequent information sets may be reached with zero probability, which means beliefs are not well-defined.

At such an information set, agent QRE would specify choosing each action at the information set with equal probability.

At the moment, the sequence (1) launch Gambit and then (2) open a game file results in two Gambit windows, the first containing a trivial game and the second the opened game.

Consider re-using a window containing a pristine, unedited "trivial" game -- if one is present -- to load a new game file, to minimise window clutter.

gambit-enumpure, when run on an extensive game, produces output which is surprising to some. What it returns is the "agent" Nash equilibria, i.e., ones which consider only deviations information set by information set.

This is a user interaction issue rather than a technical one. The question is how to have the tool behave the way most people would expect out of the box, but still have access to all the potential features?

How should gambit-enumpure behave on these games?
(1) Perhaps -S (use the strategic form) should be the default at the command line. This would give the expected behavior; then a different switch (perhaps -A) would be used to compute the agent version.
(2) In the graphical interface, also, perhaps -S should always be used, irrespective of whether the user asks for the extensive or strategic form to be used.

The gambit repo does not include copies of files that autotools creates when configuring the package. This means a few additional steps are needed to set up building Gambit from the repository. Update both INSTALL.txt and Sphinx docs with instructions on building from repo.

A new branch has been created to develop wxWidgets 2.9.4 support in the graphical interface. A commit which builds and runs successfully (tested on OS X Mountain Lion) is 0ffb7a5.

Open questions:

• Confirm that this also builds and runs on other platforms.
• Do the changes here break wxWidgets 2.8 support? As yet I have been unable to build wxWidgets 2.8.x on Mountain Lion so have been unable to test.

The tool gambit-nfg2tex will accept an extensive game on the command-line, but it will crash with an unhanded exception. This is because it requests the outcome associated with a contingency, which is not well-defined on an extensive game.

To fix this, it should be enough to ask for the payoff directly using appropriate calls to GetPayoff() on the profile, instead of GetOutcome()

The Gambit C++ API on for games implements a member IsPerfectRecall(), returning true if and only if an extensive game is of perfect recall. This should be exposed in the Python API as a property is_perfect_recall.

Tips:

• Work from the master_python branch of the repository
• C++ game API is in src/libgambit/game.h
• Python game API is implemented in Cython in src/python/gambit/lib/game.pxi
• Use e.g. the 'root' property on the Game class as a model to work from.

Do not forget to include test cases in gambit/tests to exercise your implementation.

There are some patches to 0.2010.09.01 produced by the debian maintainer, which should be reviewed and integrated into the codebase. See

http://patch-tracker.debian.org/package/gambit/

Only the patches against debian sid need to be reviewed and merged.

In both mixed.pxi and behav.pxi in the Cython wrapper, the __setitem__ operator does not raise an exception if an invalid indexing object is passed.

For example:

import gambit
g = gambit.new_table([2,2])
p = g.mixed_profile()
p[0,0] = 0.2