1.1.1 John von Neumann, Zur Theorie der Gesellschaftsspiele, Mathematische Annalen
1
ƷᄂᆮᲵǼȭԧᲬʴDzȸȠƴ᧙ƢǔȜȬȫƷᄂᆮᲦƓǑƼȕȬȃǷǧƱȕǩȳȷȎǤȞȳ
ȟȋȞȃǯǹ‫ྸܭ‬Ტ1928Უ
Ჵฆӳ৆ဦᲵȢȫDzȳǷȥȆȫȳƷฆӳ৆ဦ (1928)ᲵȄǧȫ
ȡȭƷ‫( ྸܭ‬1913)ᲵWaldgrave (1713) Ʒฆӳ৆ဦƱȟȋȞȃǯǹҾྸᲵSteinhaus(1925)
1.1 von Neumann ƷȟȋȞȃǯǹ‫ྸܭ‬ƱƜǕǛƱǓLJƘᛅ᫆
ƨࢨ᪪ƴƭƍƯᲦ࢘଺Ʒᅹ‫ܖ‬ႎ଺ˊᏑ୎ƱƷ᧙ᡲƴသॖƠƯᜒ፯ƢǔᲨ
von Neumann-Morgenstern Ʒᓸ୿ƀDzȸȠྸᛯƱኺฎᘍѣƁ(1944) ƷЈ༿ЭࢸǛɶ࣎
ƱƠƨDzȸȠྸᛯƷ᱁ଢ஖ƔǒᲦJ.F.Nash ƷྸᛯLJưƷႆ‫ޒ‬ƱᲦƦǕƕኺฎ‫ܖ‬ƴӏDžƠ
1 ƸơNJƴ
ኺฎ‫ܖ‬Ӫ II
DzȸȠྸᛯƷᛓဃ
Ʒᛯʗ (1953)
100, 295-320. ᒍᚪᲴin Tucker, A.W. and R.D.Luce, ed., Contributions to the Theory
of Games IV, Annals of Mathematics Studies 40, 1959.
1.1.2 E. Zermelo, Uber eine Anwendung der Mengenlehre auf die Theorie des Schachspiels,
Proceedings of the Fifth International Congress of Mathematicians 2, 501-4.
1.1.3 E.Borel, Sur les Jeux o interviennent l’hasard et l’habilit des joueurs, Elements de la
theorie des probabilites, J.Hermann, ed. 1924, 204-24.
1.1.4 Hugo Steinhaus, Definitions for a Theory of Games and Pursuit, Mysl Akademicka
1, 1925, 13–14.
1.2 von Neumann-Morgenstern Ʒᓸ୿Ʊ᧙ᡲƢǔᛅ᫆
ᅈ˟ᅹ‫ܖ‬ƷƨNJƷૠ‫ܖ‬ᲵңщDzȸȠƱ‫ܭܤ‬ᨼӳᲵࠀКᚐᲵ‫ྸܭנ܍‬Ჵπྸႎ૾ඥ
1.2.1 John von Neumann and O.Morgenstern, Theory of Games and Economic Behavior,
Princeton University Press, 1944.
2
1.3 von Neumann Ʒ‫ר‬ᘖȢȇȫᲦኺฎ‫ܖ‬ƓǑƼᐯࠁ‫ف‬഻ೞ఺
ɧሁࡸСኖƱኺฎȢȇȫᲵȕǩȳȷȎǤȞȳƷȬȳȞᲢᲫᲳᲭᲱᲣƱᚌ᜿Ʒɧѣໜ‫ྸܭ‬
1.5 Nash Ʒʩฏբ᫆ƱȊȃǷȥȷȗȭǰȩȠ
1.5.1 John F.Nash, Jr. The Bargaining Problem, Econometrica 18, 1950, 155-62.
1.5.2 John Nash, Two-Person Cooperative Games, Econometrica 21, 1953, 128-40.
ᲢᲫᲳᲮᲫᲣ
1.3.1 John von Neumann, Über ein ekonomisches Gleichungssystem und eine Verallge-
meinerung des Brouwerschen Fixpunktszatzes, Ergebnisse eines Mathematik Kolloquiums 8, 1937, 73-83.
1.6
ӳྸࣱᲦ᬴ܱƓǑƼᨂ‫ܭ‬ƞǕƨӳྸࣱ
1.6.1 J.Robinson, An Iterative Method of Solving a Game, Annals of Mathematics 54,
1951 296-301.
1.6.2 M.O.Rabin, Effective Computability of Winning Strategies, Contribution to the The-
1.4 Nash Ʒ᩼ңщDzȸȠƱɧѣໜ‫ྸܭ‬
᩼ңщDzȸȠƱȊȃǷȥ‫ר‬ᘖᲵϙ΂Ʊ‫ྸܭנ܍‬Ჵᚐ᣷Ʊᡶ҄DzȸȠ
ory of Games, M.D.Dresher et al eds., Annals of Mathematics Studies 39, 1957, 147157.
1.4.1 John F.Nash, Jr., Equilibrium Points in N-Person Games, Proceedings of the Na-
tional Academy of Sciences 36, 1950, 48-9.
1.4.2 John Nash, Non-Cooperative Games, Annals of Mathematics 54(2) September 1951,
286-95.
3
Ӌᎋ૨ྂ
[1] R.J.Aumann, Game Theory, The New Palgrave: Game Theory, J.Eatwell, M.Milgate
and P.Newman eds., The Macmillan Press, 1987.
[2] H.W.Kuhn and S.Nasar (eds.), The Essential John Nash, Princeton University Press,
2002.
4
[3] ᤠஙήဏᲦDzȸȠྸᛯƷ‫᧏ޒ‬Ღிʮ‫୿׋‬Ღ1973.
[4] Y.Varoufakis (ed.), Game Theory, Critical Concepts in the Social Sciences Vol.1 Foundations, Routledge, 2001.
[5] R.Weintraub(ed), Toward a History of Game Theory, Duke Univerity Press, 1992.
ǴȳǻǹᲦ1933 ųƋǔ‫୿׋‬᫾ƴ৑ᔺƷႸ᥵ƷɶưᲦᐯЎᐯ៲Ǜਫ਼᠍ƠƯƍƳƍႸ᥵Ƣ
ǂƯƷႸ᥵ǛƭƘǔƜƱƴƳƬƨᲨƠƔƠᲦƦƷႸ᥵ᐯ៲ƸƦǕƴਫ਼᠍ƢǂƖƩǖ
ƏƔᲹ
ȴǡȳȷȀȳȄǣ
ųƢǂƯƷࠊƷࠊᧈƴƭƍƯᲦƦƷࠊƴ˰LJƳƍࠊᧈƸƢǂƯᲦཎ
КࠊƱƍƏࠊƴ˰ǜưƍǔƱƢǔᲨƜƷཎКࠊƷࠊᧈƸƲƜƴ˰ǜưƍǔƔᲹᲢཎ
КࠊƩƱƢǔƱཎКࠊƴƸ˰ǜưƍƳƍƸƣưƋǓᲦཎКࠊˌ‫ٳ‬ƩƱƢǔƱཎКࠊ
2 ȑȩȉȃǯǹ
A. ǫȳȈȫƷȑȩȉȃǯǹᲴų M ǛƢǂƯƷᨼӳƷᨼӳᲦP(M) ǛƦƷǂƖᨼӳƱƢǔ
ƱƖᲦP(M) Ƹ M ƷᙲእưƋǔƱӷ଺ƴ M ǛᙲእƱƠƯԃljᲨǑǓദᄩƴᚕƏƱᲦǂƖ
ᨼӳ P(M) ƷຜࡇƸᨼӳ M ƷຜࡇǑǓ‫ٻ‬ƖƘᲦӷ଺ƴᲦP(M) Ƹ M ƷᢿЎᨼӳưNjƋǔ
ƔǒᲦP(M) ƷຜࡇƸᨼӳ M ƷຜࡇˌɦưƋǔᲨᲢᲫᲲᲳᲱ࠰ᲱஉᲬᲲଐ˄ᲦȇȇǭȳȈǁƷ৖ኡᲣ
B. ȩȃǻȫƷȑȩȉȃǯǹᲴU := {M|M M} ƱƢǔƱᲦU ∈ U ưƸƳƘᲦU U ưNj
ƴ˰ǜưƍǔƜƱƴƳǔᲣ
Შ
C. ȪǷȣȸȫƷȑȩȉȃǯǹᲴųžᲫᲱ૨‫ˌ܌‬ϋư‫ܭ‬፯ưƖƳƍஇ‫ݱ‬ƷૠſƸᲫᲱ૨‫܌‬
ư‫ܭ‬፯ƞǕƯƍǔᲨ
ᲢᲫᲳᲪᲯ࠰ᲰஉᲣ
ƜǕƸșȪȸƴǑƬƯᲫᲳᲪᲰ࠰ƴǘƔǓǍƢƘᚕƍ੭ƑǒǕƨȪǷȣȸȫƷȑȩ
ȉȃǯǹưƋǔᲨƳƓᲦƜƷȪǷȣȸȫƷȑȩȉȃǯǹǍžᅶƸƏƦƭƖưƢſƱƍƏ
žƏƦƭƖƷȑȩȉȃǯǹſ
Ტ᲼ᲽᲰɭኔᲦǯȬǿʴǨȔȡȋȇǹᲣƕᲦࢸ࠰ᲦஊӸƳDzȸ
ƳƍᲨ
ᲢᲫᲳᲪᲬ࠰ᲰஉᲫᲰଐᲦȕȬȸDzǁƷ৖ኡᲣ
ƜƷȩȃǻȫƷȑȩȉȃǯǹƸᲦᨼӳˌ‫ٳ‬ƷಒࣞǛဇƍƯƓǒƣᲦᨼӳƷಒࣞƦƷNj
ƷƷɧ‫ܦ‬μƞǛᇢႎƴƋǒǘƢჳႽƱƠƯஊӸᲨLJƨᲦˌɦƷǑƏƳȐȸǸȧȳNjƋǔᲨ
ȩȃǻȫᲦૠྸՋ‫ܖ‬λᧉᲦ1919 ųƋǔ஭Ʒ࠿‫ދ‬ƸᲦᐯЎưƻƛǛЧǒƳƍ஭ʴƷƻƛ
ƷLjǛЧǔᲨưƸᲦƦƷ࠿‫ދ‬ƸᐯЎƷƻƛǛЧǔƷƩǖƏƔᲨ
ȇȫ [3] Ʒɧ‫ܦ‬μࣱ‫ྸܭ‬ᲦƞǒƴȁȣǤȆǣȳ [2] ǍdzȫȢǴȭȕ [5] ƷȩȳȀȠࣱƴႆ
‫ޒ‬ƠƨᲨ
ȑǺȫ ᲴƓLJƑƕദႺᎍƳǒ༃Ư᫢ƏƧᲨƏƦƭƖƳǒ໲ƍƯ᫢ƏƧᲨƞƋᲦƲƪǒƩ
Ʊ᭸ƴբǘǕƯᲦƋƳƨƸ˴ƱሉƑǔƩǖƏƔᲹ
5
ɧѣໜ‫ྸܭ‬ưӸ᭗ƍᲦȖȩǦȯȸᲢᲫᲲᲬᲭᲧᲫᲲᲳᲫᲣƷž੎ɶࢷſᲢ᳊ưƋǔƔLJ
3 ૠ‫ܖ‬Ʒүೞ
ƨƸ᳊ưƳƍᲣƸஊᨂƷ‫ئ‬ӳƷLjദƠƍᲦƱƍƏᇌ‫ئ‬ᲨƢǂƯƷΨƕ᳊Ǜ฼ឱƠƳƍƱ
ƍƘƭNjƷȑȩȉȃǯǹƷЈྵƴǑǓᲦƜǕǒǛΰ஌ƠƯᲦᨼӳᛯƷᲦƻƍƯƸૠ‫ܖ‬
ƷүೞǛ૔ƏƨNJƷѐщƕƳƞǕƨᲨƦǕǒƴƸᲦ‫ٻ‬ƖƘЎƚƯᲦᛯྸɼ፯ᲦႺᚇɼ፯
ˎ‫ܭ‬ƠƯჳႽƕࢽǒǕƨƱƠƯNjᲦ᳊Ǜ฼ƨƢΨƕƋǔƱƍƏƜƱƴƸƳǒƳƍᲨ
ƠƔƠᲦƋLJǓƴNjૠ‫ܖ‬Ʒ‫ݣ‬ᝋǛᨂ‫ܭ‬Ƣǔᇌ‫ئ‬ƳƷưɼ්ƴƸƳǓƑƳƔƬƨƕᲦʻ
ଐưNjƦƷ᣻ᙲࣱƸ‫ڂ‬ǘǕƯƍƳƍᲢᚘምᛯᲦConstructive Mathematics ƳƲᲣᲨ
ƓǑƼ࢟ࡸɼ፯ƕƋǔᲨ
Šᛯྸɼ፯
6
ȩȃǻȫȷțȯǤȈȘȃȉƷƀȗȪȳǭȔǢȷȞȆȞȆǣǫƁƴˊᘙƞǕǔᇌ
Š࢟ࡸɼ፯
ȒȫșȫȈƸᲦૠ‫ܖ‬ǛπྸኒƱਖ਼ᛯᙹЩƴᢩΨƠᲦƜƷ࢟ࡸႎ˳ኒƷ໯ჳႽࣱᲦ
‫ئ‬Შᛯྸ‫ܖ‬ƴǑƬƯᲦᐯ໱ૠᛯᲦܱૠᛯᲦᚐௌ࠹˴‫ܖ‬ƳƲǛನሰᲨȩȠǼǤ̖఍ưஊӸƳ
ƭLJǓᲦԡ᫆᳊ƱƦƷԁ‫ܭ‬ƕӷ଺ƴ‫ྸܭ‬ƱƳǔƜƱƸƳƍᲦƱƍƏᚰଢǛ‫঺ܦ‬ƢǔƜƱ
ȩȠǼǤᲢᲫᲳᲪᲭᲧᲫᲳᲭᲪᲣNjƜƷ්ǕǛƘljᲨ
ƴǑƬƯᲦȑȩȉȃǯǹƔǒᐯဌưƠƔNjႺᚇɼ፯ưƸ્ూƤƟǔǛࢽƳƍ‫ٶ‬ƘƷӞχ
ƠƔƠᲦӕǓৢƍƕƖǘNJƯ༁ᩃƴƳǔᲨ
ႎૠ‫ܖ‬ǛNjԃljμૠ‫ܖ‬ƷͤμࣱǛ̬ᚰƠǑƏƱƍƏᚘဒǛਖ਼ᡶƠƨᲨ
࢟ࡸႎ˳ኒƷ໯ჳႽࣱƷᚰଢƱƸᲦ࢟ࡸႎ˳ኒᲢƭLJǓૠ‫ܖ‬ᲣƦƷNjƷǛ‫ݣ‬ᝋƱƢǔ
ŠႺᚇɼ፯
ǫȳȈȫƷᨼӳᛯƴ‫ݣ‬ƢǔஇNjນƠƍ৤ЙᎍƸᲦƔƭƯƷࠖưƋƬƨǯȭȍȃ
ǫȸưƋǔᲨžᐯ໱ૠƸᅕƕоƬƨᲨƦƷ˂ƷૠƸʴ᧓ƕ˺ƬƨƴƢƗƳƍſžπᲢȑǤᲣ
ƷឬឭࣱƳƲƲǜƳ᣻ᙲࣱƕƋǔƱƍƏƷƩᲨƦǜƳૠƸ‫נ܍‬ƠƳƍƱƍƏƷƴſᲨ
ƢǂƯƷૠ‫ܖ‬ႎ‫ݣ‬ᝋǛᐯ໱ૠƴᢩΨƢǔƜƱᲷምᘐ҄ᲦƸƠƔƠᲦƖǘNJƯ᣻ᙲᲢDzȸ
ȇȫƷɧ‫ܦ‬μࣱ‫ྸܭ‬ƷᚰଢᲦᚘምᛯᲦdzȳȔȥȸǿȷǵǤǨȳǹᲣ
Შ
7
ૼƠƍЎ᣼ưƋǔᲨƜƷॖԛưƜǕƸឬૠ‫ܖ‬Ტmeta-mathematicsᲣLJƨƸᚰଢᛯᲢproof
theoryᲣƱƍǘǕǔᲨ
ȚǢȎƷᐯ໱ૠᛯᲦȒȫșȫȈƴǑǔȦȸǯȪȃȉ࠹˴‫ܖ‬ƷπྸኒᲦ᳔᳀ᲢȄǧȫȡ
ȭȷȕȩȳDZȫᲣᨼӳᛯᲦ᲼᳁ᲢșȫȊǤǹȷDzȸȇȫᲣᨼӳᛯƳƲƕ࢟ࡸ҄ƞǕƨπྸ
ኒƷ̊ưƋǔᲨLJƨᲦȕǩȳȷȎǤȞȳƷƀ᣽‫܇‬щ‫ܖ‬Ʒૠ‫ܖ‬ႎؕᄽƁ[7, 1927] ƸᲦȒȫ
șȫȈȷȗȭǰȩȠƴࢼƏ᣽‫܇‬щ‫ܖ‬Ʒžπྸ҄ſǛႸਦƠƨNjƷƱLjǔƜƱƕưƖǔᲨ
8
4 DzȸȇȫƷɧ‫ܦ‬μࣱ‫ྸܭ‬ƱȒȫșȫȈƷᙸௐƯƵ‫ٹ‬
ŠDzȸȇȫƷɧ‫ܦ‬μࣱ‫ྸܭ‬
ǦǤȸȳưᲦȒȫșȫȈƨƪƷˁʙǛදॖขƘᙸ‫ܣ‬ƬƯƍƨDzȸȇ
ȫᲢᲫᲳᲪᲰᲧᲫᲳᲱᲲᲣƸᲦᲫᲳᲭᲫ࠰ᲦഏƷʙܱǛᚰଢƠƨᲨLJƣᲦπྸ҄ƞǕƨ໯
ƠƯྸᚐƢǔƜƱƕưƖǔᲨ
DzȸȠྸᛯᛓဃЭࢸƷૠ‫ܖ‬ӪႎᏑ୎Ʒእ੨ǛኳƑǔЭƴᲦDzȸȇȫƷɧ‫ܦ‬μࣱ‫ˌྸܭ‬
ࢸƴࢽǒǕƨྸࣱƷᨂမǛƋǒǘƢ᫏˩ƷኽௐǛʚƭƋƛƯƓƜƏᲨ
ჳႽƳምᘐƷྸᛯƴƸᲦᚰଢNjƦƷԁ‫ܭ‬ƷᚰଢNjɧӧᏡƳᛯྸࡸƕ‫נ܍‬ƢǔƜƱᲢᇹᲫ
ɧ‫ܦ‬μࣱ‫ྸܭ‬ᲣᲵƞǒƴᲦ໯ჳႽƳྸᛯƷɶưƸƦƷྸᛯᐯ៲ƕ໯ჳႽưƋǔƜƱƸᚰଢ
ưƖƳƍƜƱᲢᇹᲬɧ‫ܦ‬μࣱ‫ྸܭ‬ᲣưƋǔᲨ*1 Შ
ƜƏƠƯᲦȒȫșȫȈȷȗȭǰȩȠƸኳ໩ǛᡇƑǔƕᲦƜǕƸNjƪǖǜૠ‫ܖ‬ᐯ˳Ʒኳ
ŠȁȥȸȪȳǰೞ఺Ʒͣഥբ᫆ Turing [11, 1936]
˓ॖƴɨƑǒǕƨȗȭǰȩȠᲢȁȥȸȪȳǰೞ఺Უ
ƕ˓ॖƷλщƴ‫ݣ‬ƠƯͣഥƢǔᲢᚘምǛኳʕƠƯኽௐǛЈщƢǔᲣƔԁƔƸൿ‫ܭ‬ɧᏡư
ƋǔᲨ
໩ǛॖԛƢǔNjƷưƸƳƍᲨƱƘƴᲦȕǩȳȷȎǤȞȳƸƜǕˌࢸᲦᄩྙႎᛯྸǍᐯࠁ
‫ف‬഻ೞ఺ᲢࢸƴႆᙸƞǕƨᲾ᳈᲻ƷᐯࠁᙐᙌƷҾྸᲣᲦᚘምೞƳƲǛԃljφ˳ႎբ᫆Ʒ
ᄂᆮǛᡫƠƯᲦኺ᬴ႎเඡƔǒᢒƘƳƍƱƜǖưƷૠ‫ܖ‬ႎоᡯࣱƷࢫлǛᙸЈƢǑƏƴ
ƳǔᲨɧ‫ܦ‬μࣱ‫ྸܭ‬ƷЈྵˌЭƷᲦDzȸȠྸᛯƷᛓဃǛԓƛǔᛯ૨ƀᅈ˟ႎDzȸȠƷྸ
*2 ƸᲦ
ᛯƁ
ƀ᣽‫܇‬щ‫ܖ‬Ʒૠ‫ܖ‬ႎؕᄽƁ
Ტ1927Უƕཋྸ‫ܖ‬ƴƓƚǔ᠗ƔƠƍžπྸ҄ſƷᚾLj
ưƋƬƨƷƱӷಮᲦʴ᧓Ʒᅈ˟ႎᘍѣƷžπྸ҄ſƷᚾLjưƋƬƨƕᲦɧ‫ܦ‬μࣱ‫ˌྸܭ‬
ࢸƷƀDzȸȠƷྸᛯƱኺฎᘍѣƁ*3 ƸᲦƜƷ૾ӼƴඝƬƨᅈ˟ᅹ‫ܖ‬Ʒƀૠ‫҄ܖ‬ƁƷᚾLjƱ
ŠȩȳȀȠૠƷ‫ נ܍‬Chaitin [2, 1966]
Წᡶ‫᧏ޒ‬ƷӲ᪮Ʒ͌ƕᲦ‫ר‬ឋƳdzǤȳǛ৲ƛƯᘙƳǒᲫᲦᘻ
ƳǒᲪƱൿ‫ܭ‬ƠƯࢽǒǕǔЗƱғКƕƭƔƳƍǑƏƳܱૠƕ‫נ܍‬ƢǔᲨ
ƜƷ‫ྸܭ‬ƸƞǒƴᲦƋǔᆔƷ૾ᆉࡸᲢਦૠႎȇǣǪȕǡȳȈǹ૾ᆉࡸᲣƷᚐƷ̾ૠƕ
ஊᨂ̾ưƋǔƔ໯ᨂ̾ưƋǔƔǛൿ‫ܭ‬ƢǔƷƸᲦdzǤȳǛ৲ƛƯൿ‫ܭ‬ƢǔƷƱӷơưƋ
ǔƱƍƏʙܱᲢChaitin [2]ᲣǛ‫ݰ‬ƖᲦLJƨᲦDzȸȠྸᛯƷ௒ኵLjưƸᲦȊȃǷȥ‫ר‬ᘖƷ̾
ૠƕஊᨂƔ໯ᨂƔƸᲦμƘӷơॖԛƴƓƍƯȩȳȀȠưƋǔǑƏƳDzȸȠƕ‫נ܍‬ƢǔᲦ
*1
ദᄩƳϋܾƴƭƍƯƸ Boolos and Jeffrey [1] ƳƲӋༀƷƜƱ
*2
von Neumann [8, 1928]
Neumann and Morgenstern [9, 1944]
*3
ƱƍƏʙܱƴᘍƖბƘNjƷưƋǔƜƱƕଢǒƔƴƳƬƯƍǔᲢPrasad [10]ᲣᲨᛇኬƸɶ‫ޛ‬
[6] ƷИሁႎᚐᛟǛӋༀᲨ
9
Ӌᎋ૨ྂ
[1] Boolos,G. and R.Jeffrey, Computability and Logic Cambridge University Press, Cambridge (1974).
[2] Chaitin, G.J., On the Length of Programs for Computing Finite Binary Sequences,
J.ACM 13 547 (1966)
[3] Gödel,K. Über Formal Unentscheidbare Sätze der Principia Mathematica und Verwandter System I, Monatschefte Math. Phys. 38 173–98 (1931)
[4] ࠼ແųͤᲦ್ဋɟദᲦDzȸȇȫƷɭမᲦෙᯚᅈᲦᲫᲳᲲᲱ࠰Შ
[5] Kolmogorov, A.N., Three Approaches to the Quantitative Definition of Information,
Prob.Info.Transmission 1, no.1, 1 (1965)
[6] ɶ‫پ࠴ޛ‬ᲦȊȃǷȥ‫ר‬ᘖƷȩȳȀȠࣱƴƭƍƯƷᙾ୿Ღɤဋ‫˟ܖ‬ᩃᛏᲳᲭࠇᲫӭᲦ
259–266ᲦᲬᲪᲪᲪ࠰.
[7] von Neumann, John, Mathematische Begrundung der Quantenmechanik. Nachrichten
von der Gesellschaft der Wissenschaften Su Göttingen 1 (1927).
[8] von Neumann, John, Zur Theorie der Gesellschahtsspiele, Mathematische Annalen 100
295–320 (1928)
[9] von Neumann, John and Oskar Morgenstern, Theory of Games and Economic Behavior,
11
10
Princeton University Press, (1944)
[10] Prasad, K., Computability and Randomness of Nash Equilibrium in Infinite Games,
Journal of Mathematical Economics 20 429–442, (1991).
[11] Turing.A.M.,On Computable Numbers, with an Application to the Entscheidungsproblem, Proc. Lond. Math. Soc. 42 230–65; 43 544–6 (1936).
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