Abstract
In this chapter, we adopt a history of economic thought approach to highlight the methodological problems encountered by standard game theory in its treatment of strategic reasoning and the consequences this has on the nature of players’ beliefs. We show that whatever contributions in the history of standard game theory; of von Neumann and Morgenstern of Nash of the refinement program in the 1980s and of epistemic game theory; by focusing only on the search for a solution concept, these contributions reduce strategic rationality to the existence of a solution. They reduce a game to a simple “black box,” regardless of how the game is played. We show that such focus on solution concepts is related to the norms of research of the mathematical community. We show in particular that this leads to serious difficulties in the epistemic program of game theory, which aims to define the knowledge and belief structure of players compatible with the concepts of solution. Epistemic game theory is grounded on the idea that to guarantee the existence of a solution, players’ beliefs must be a priori coherent and correct. From that prospect, we show that players’ beliefs are not individual and subjective mental states; regardless of the nature of the players’ beliefs a priori, they are by construction the result of their reasoning and not an element intervening in this reasoning. This means that players’ reasoning about other players’ choices or beliefs is excluded from the analysis of epistemic games, as well as strategic rationality.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The way vNM sees modeling in the TGEB is that setting a new theory requires an heuristic stage allowing a move from nonanalytical and “commonsense considerations” (Giocoli, 2003, p. 248) to formal and mathematical methods. The next step is to provide a general and formal theory which requires conforming to axiomatic methods in order to be rigorous. Then, one should build a rigorous and conceptually general formal theory. Such a theory should be applied to the resolution of some elementary problems to test the conformity of the theory and then to more complicated problems to again test its conformity. Finally, such theory must be employed for predictions (von Neumann & Morgenstern, 1944, pp. 7–8).
- 2.
Léonard (2010, p. 64), however, claims “[a]lthough, in general, maxxminyg(x, y) ≤ minymaxxg(x, y), it is not generally true that the equality holds.”
- 3.
For more details on the indirect proof method see Giocoli (2003, pp. 263–76).
- 4.
The misapprehension of the proof of the minimax theorem of von Neumann in 1928 is according to Léonard (2010, pp. 66–67), explained by von Neumann himself because in his equilibrium growth model of 1937 he makes the formal link between the fixed-point argument of the growth model and the minimax theorem.
- 5.
This is linked to the maxims of behaviors. As explained by Giocoli (2003, p. 235), people must decide to follow a maxim of behavior or not: “there are two types of maxims: the unrestricted maxims, which can be followed regardless of the actions of the other agents, and the restricted maxims, which are followed on the basis of whether the others do the same or not… In the case of unrestricted maxims the choice poses no problems, because the agent’s evaluation is not disturbed by the behavior of other individuals. In general, however, the decision depends upon the agent’s forecasting ability which, in the case of restricted maxims, must also embrace the other agents’ behavior.”
- 6.
Such interpretation in terms of BR reasoning is the most common one but Nash actually presents the NE in terms of countering (see Giocoli, 2003, p. 301 for more details).
- 7.
More specifically, consistency formally entails that the set of players’ beliefs are “the limit of the conditional probabilities induced by players’ strategies in some perturbed game.” (ibid., p. 6).
- 8.
The formal justification for the encoding of players’ hierarchy of beliefs according to the definition of the players’ type is later provided among others by Armbruster and Böge (1979), Böge and Eisele (1979), or Mertens and Zamir (1985), (see Brandenburger 2010). Mertens and Zamir (1985) in particular proved that the type of the player allow encoding of the player’s infinite hierarchy of beliefs.
- 9.
For an epistemological reflection on the concept of “types” in Harsanyi’s work, see Hargreaves Heap and Varoufakis (2004).
- 10.
See Perea (2012, 2014) and Brandenburger (2010) for an historical perspective on the transition from classical to EGT. See Brandenburger (1992, 2007), Geanakoplos (1992), Dekel and Gul (1997), Battigali and Bonnano (1999), Dekel and Siniscalchi (2015) for surveys on the epistemic program on game theory and its main assumptions and results from a formal perspective.
- 11.
The formal proof of the equivalence is given by Brandenburger and Dekel (1993).
- 12.
Friedell (1969, p. 31) more precisely defines the concept of “common opinion” and states the real conditions in which common opinion can rise. Like Lewis, and contrary to Aumann (1976) Friedell is “interested in real life situations” (Perea, 2014, p. 12). Aumann only states that “at a given state ω there is common knowledge of an event E among two persons A and B, if at ω both A and B only deem possible states in E, if at ω both A and B only deem possible states at which A and B only deem possible states in E, and so on, ad infinitum.” (Perea, 2014, p. 13).
- 13.
Giocoli (2003, p. 392) specifies that “[t]he tradition in SEUT is to circumvent the problem either by adding an extra postulate (the sure-thing principle: ibid, pp. 39–40) or by having recourse to an imaginary experiment, — a lottery — able to turn the preferences’ domain into a probabilistic space. The former is the approach originally followed by Savage but it is quite involved, so it is the latter method, first proposed in the early 1960s by Anscombe and Aumann, that has gained acceptance.”
References
Anderlini, L. (1990). Communication, computability and common interest games. Games and Economic Behavior, 27(1), 1–37. https://doi.org/10.1006/game.1998.0652
Anscombe, F. J., & Aumann, R. J. (1963). A definition of subjective probability. Annals of Mathematical Statistics, 34(1), 199–205. https://www.jstor.org/stable/i350097
Armbruster, W., & Böge, W. (1979). Bayesian game theory. In O. Moeschlin, & D. Pallaschke (Eds.), Game theory and related topics. North-Holland.
Aumann, R. (1992). Irrationality. In P. Dasgupta et al., (Eds.), Game theory. Economic analysis of markets and games: Essays in honor of Frank Hahn (pp. 214–227). MIT Press.
Aumann, R. J. (1976). Agreeing to disagree. Annals of Statistics, 4(6), 1236–1239. http://www.jstor.org/stable/2958591
Aumann, R. J. (1985). An axiomatization of the non-transferable utility value. Econometrica, 53(3), 599–612. https://doi.org/10.2307/1911657
Aumann, R. J. (1987a). Correlated equilibrium as an expression of bayesian rationality. Econometrica, 55(1), 1–18. https://doi.org/10.2307/1911154
Aumann, R. J. (1987b). What is game theory trying to accomplish? In K. Arrow & S. Honkapohja (Eds.), Frontiers of economics (pp. 5–46). Basil Blackwell.
Aumann, R. J. (1998). On the Centipede game. Games and Economic Behavior, 23(1), 97–105. https://doi.org/10.1006/game.1997.0605
Aumann, R. J. (2010). In V. Hendricks & O. Roy (Eds.), Epistemic logic: Five questions (pp. 21–33). Automatic Press/VIP.
Aumann, R., & Brandenburger, A. (1995). Epistemic conditions for Nash equilibrium. Econometrica, 63(5), 1161–1180. https://doi.org/10.2307/2171725
Aumann, R. J., & Dreze, J. H. (2008). Rational expectations in games. American Economic Review, 98(1), 72–86. https://doi.org/10.1257/aer.98.1.72
Aumann, R. J., & Sorin, S. (1989). Cooperation and bounded recall. Games and Economic Behavior, 1(1), 5–39. https://doi.org/10.1016/0899-8256(89)90003-1
Bach, C. W., & Tsakas, E. (2012). Pairwise interactive knowledge and Nash equilibrium. Working paper, Maastricht University.
Bacharach, M. (1976). Economics and the theory of games. The Macmillan Press LTD.
Bacharach, M. (1986). The problem of agents’ beliefs in economic theory. In M. Baranzini & R. Scazzieri (Eds.), Foundations of economics (pp. 175–203). Blackwell.
Bacharach, M. (1989). Expecting and affecting. Oxford Economic Papers, 41(2), 339–355. http://www.jstor.org/stable/2663333
Bacharach, M. (1993). Variable universe game. In K. Binmore, A. Kirman, & P. Tami (Eds.), Frontiers of game theory. The MIT Press.
Bacharach, M. (1994). The epistemic structure of a theory of game. Theory and Decision, 37, 7–48. https://doi.org/10.1007/BF01079204
Bacharach, M. (2001). Framing and cognition in economics: The bad news and the goods. Lecture notes, ISER Workshop XIV: Cognitive Processes in Economics.
Bacharach, M. (2006). Beyond individual choice: Team and frame in game theory. In N. Gold, & R. Sugden (Eds.), Princeton University Press.
Bacharach, M., & Bernasconi, M. (1997). The variable frame theory of focal points: An experimental study. Games and Economic Behavior, 19(1), 1–45. https://doi.org/10.1006/game.1997.0546
Bacharach, M., & Hurley, S. (1991). Issues and advances in the foundations of decision theory. In M. Bacharach, & S. Hurley (Eds.), Foundations of decision theory. Blackwell Publishers.
Bacharach, M., & Stahl, O. (2000). Variable-frame level-n theory. Games and Economic Behavior, 32(2), 220–246. https://doi.org/10.1006/game.2000.0796
Battigali, P. (1988). Implementable strategie, prior information and the problem of credibility in extensive games. International Review of Economics and Business, 35, 705–733.
Battigali, P., & Bonnano, G. (1999). Recent results on belief, knowledge and the epistemic foundations of game theory. Research in Economics, 53(2), 149–225. https://doi.org/10.1006/reec.1999.0187
Bernheim, D. (1984). Rationalizable strategic behavior. Econometrica, 52(4), 1007–1028. 0012-9682
Bernheim, D. (1986). Axiomatic characterizations of rational choice in strategic environments. The Scandinavian Journal of Economics, 88(3), 473–488. https://doi.org/10.2307/3440381
Bicchieri, C. (1993). Rationality and coordination. CUP Archive.
Binmore, K. G. (1987). Modeling rational players: Part I. Economics and Philosophy, 3(2), 179–214. https://doi.org/10.1017/S0266267100002893
Binmore, K. G. (1993). De-Bayesing game theory. In K. G. Binmore, A. P. Kirman, & P. Tani (Eds.), Frontiers of game theory. The MIT Press.
Binmore, K. G. (2007). Playing for real. Oxford University Press.
Binmore, K. G. (2009). Rational decisions. Princeton University Press.
Blume, L., Brandenburger, A., & Dekel, E. (1991). Lexicographic probabilities and choice under uncertainty. Econometrica, 59(1), 61–79. https://doi.org/10.2307/2938240
Böge, W., & Eisele, T. (1979). On solutions of Bayesian games. International Journal of Game Theory, 8, 193–215. https://doi.org/10.1007/BF01766706
Bonanno, G., & Nehring, K. (1999). How to make sense of the common prior assumption under incomplete information. International Journal of Game Theory, 28, 409–443. https://doi.org/10.1007/s001820050117
Brandenburger, A. (1992). Lexicographic probabilities and iterated admissibility. In P. Dasgupta, D. Gale, O., Hart & E. Maskin (Eds.), Economic analysis of markets and games (pp. 282–290). MIT Press.
Brandenburger, A. (2007). The power of paradox: Some recent developments in interactive epistemology. International Journal of Game Theory, 35, 465–492. https://doi.org/10.1007/s00182-006-0061-2
Brandenburger, A. (2010). Origins of epistemic game theory. In V. Hendricks & O. Roy (Eds.), Epistemic logic: Five questions (pp. 59–69). Automatic Press.
Brandenburger, A., & Dekel, E. (1987). Rationalizability and correlated equilibria. Econometrica, 55(6), 1391–1402. https://doi.org/10.2307/1913562
Brandenburger, A., & Dekel, E. (1989). The role of common knowledge assumptions in game theory. In F. Hahn (Ed.), The economics of missing markets, information and games. Oxford University Press.
Brandenburger, A., & Dekel, E. (1993). Hierarchies of beliefs and common knowledge. Journal of Economic Theory, 59(1), 189–198. https://doi.org/10.1006/jeth.1993.1012
Cho, I., & Kreps, D. (1987). Signaling games and stable equilibria. Quarterly Journal of Economics, 102(2), 179–221. https://doi.org/10.2307/1885060
Colman, A. M. (1997). Salience and focusing in pure coordination games. Journal of Economic Methodology, 4(1), 61–81. https://doi.org/10.1080/13501789700000004
Colman, A. M. (2004). Reasoning about strategic interaction: Solution concepts in game theory. In K. Manktelow & M. C. Chung (Eds.), Psychology of reasoning: Theoretical and historical perspectives (pp. 287–308). Psychology Press.
Colman, A. M., & Bacharach, M. (1997). Payoff dominance and the Stackelberg heuristic. Theory and Decision, 43(1), 1–19. https://doi.org/10.1023/A:1004911723951
Colman, A. M., Pulford, B. D., & Lawrence, C. L. (2014). Explaining strategic coordination: cognitive hierarchy theory, strong stackelberg reasoning, and team reasoning. Decision, 1(1), 35–58. https://doi.org/10.1037/dec0000001
Cooper, R. W., DeJong, D. V., Forsythe, R., & Ross, T. W. (1990). Selection criteria in coordination games: Some experimental results. American Economic Review, 80(1), 218–233. https://www.jstor.org/stable/2006744
Crawford, V. P., & Haller, H. (1990). Learning how to cooperate: Optimal play in repeated coordination games. Econometrica, 58(3), 571–595. https://doi.org/10.2307/2938191
De Bruin, L. (2009). Overmathematisation in game theory: Pitting the Nash Equilibrium Refinement Programme against the Epistemic Programme. Studies in History and Philosophy of Science, 40(3), 290–300. https://doi.org/10.1016/j.shpsa.2009.06.005
Dekel, E., & Gul, F. (1997). Rationality and knowledge in game theory. In D. Kreps, & K. Wallis (Eds.), Advances in economics and econometrics. Cambridge University Press.
Dekel, E., & Siniscalchi (2015). Epistemic game theory. In H. P. Young, & S. Zamir (Eds.), Handbook of game theory with economic applications (Vol. 4, pp. 619–702). Elsevier Science Publishers.
Farrell, J. (1988). Communication, coordination and Nash equilibrium. Economic Letters, 27(3), 209–214. https://doi.org/10.1016/0165-1765(88)90172-3
Friedell, M. F. (1967). Organizations as semilattices. American Sociological Review, 32(1), 46–54. https://doi.org/10.2307/2091717
Friedell, M. F. (1969). On the structure of shared awareness. Behavioral Science, 14(1), 28–39. https://doi.org/10.1002/bs.3830140105
Fudenberg, D., & Tirole, J. (1991). Perfect Bayesian equilibrium and sequential equilibrium. Journal of Economic Theory, 53(2), 236–260. https://doi.org/10.1016/0022-0531(91)90155-W
Gauthier, D. (1975). Coordination. Dialogue, 14, 195–221. https://doi.org/10.1017/S0012217300043365
Geanakoplos, J. (1992). Common knowledge. Journal of Economic Perspectives, 6(4), 53–82. https://www.jstor.org/stable/2138269
Gilboa, I. (2011). Why the empty shells were not fired: A semi-bibliographical note. Episteme, 8(3), 301–308. https://doi.org/10.3366/epi.2011.0023
Gioccoli, N. (2003). Modeling rational agents: From the interwar economics to early modern game theory. Edward Elgar.
Govindan, S., & Wilson, R. (2008). Refinements of nash equilibrium. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.772081
Grüne-Yanoff, T., & Lehtinen, A. (2012). Philosophy of game theory. In U. Mäki (Ed.), Handbook of the philosophy of economics (pp. 531–576). North-Holland.
Gul, F. (1998). A comment on Aumann’s Bayesian view. Econometrica, 66(4), 923–927. https://doi.org/10.2307/2999578
Hargreaves Heap, S.P., & Varoufakis, Y. (2004). Game theory: A critical text, (2nd ed.). London: Routledge.
Harsanyi, J. C. (1967/68). Games with incomplete information played by ‘Bayesian’ players. Management Science, 14(3–5–7), 159–182, 320–334, 486–502. https://doi.org/10.1287/mnsc.14.3.159; https://doi.org/10.1287/mnsc.14.5.320; https://doi.org/10.1287/mnsc.14.7.486
Harsanyi, J. C. (1975). The tracing procedure: A Bayesian approach to defining a solution for n-person non cooperative games. International Journal of Game Theory, 4, 61–94. https://doi.org/10.1007/BF01766187
Harsanyi, J. C. (1976). A solution concept for n-person non cooperative games. International Journal of Game Theory, 5, 211–225. https://doi.org/10.1007/BF01761604
Harsanyi, J. C. (1982a). Comment—Subjective probability and the theory of games: Comments on Kadane and Larkey’s paper. Management Science, 28(2), 120–124. https://doi.org/10.1287/mnsc.28.2.120
Harsanyi, J. C. (1982b). Rejoinder to professors Kadane and Larkey. Management Science, 28(2), 124–125. https://doi.org/10.1287/mnsc.28.2.124a
Harsanyi, J. C. (1995). Games with incomplete information. The American Economic Review, 85(3), 291–303. https://www.jstor.org/stable/2118175
Harsanyi, J. C. (2004). Games with incomplete information played by “Bayesian” players, I–III. Management Science, 50(12), 1804–1824. http://www.jstor.org/stable/30046151
Harsanyi, J. C., & Selten, R. (1972). A generalized Nash solution for two-person bargaining games with incomplete information. Management Science, 18(5), 80–106. https://doi.org/10.1287/mnsc.18.5.80
Harsanyi, J. C., & Selten, R. (1988). A general theory of equilibrium selection in games. MIT Press.
Hart, S. (2006). Robert Aumann’s game and economic theory. The Scandinavian Journal of Economics, 108(2), 185–211. https://www.jstor.org/stable/3877028
Hausman, D. M. (2000). Revealed preference, belief, and game theory. Economics and Philosophy, 16(1), 99–115. https://doi.org/10.1017/S0266267100000158
Hausman, D. M. (2012). Preference, choice, value and welfare. Cambridge University Press.
Heidl, S. (2016). Philosophical problems of behavioural economics. Routledge.
Heifetz, A. (2018). Epistemic game theory: Incomplete information. In S. N. Durlauf, & L. E. Blume (Eds.), The New Palgrave dictionary of economics. Macmillan.
Hillas, J., & Kohlberg, E. (2002). The foundations of strategic equilibrium. In R. Aumann, & S. Hart (Eds.), Handbook of game theory III. Elsevier Science Publishers.
Hurley, S. (1991). Newcomb’s problem, prisoners’ dilemma, and collective action. Synthese, 86(2), 173–196. https://www.jstor.org/stable/20116872
Kadane, J. B., & Larkey, P. D. (1982a). Subjective probability and the theory of games. Management Science, 28(2), 113–120. https://doi.org/10.1287/mnsc.28.2.113
Kadane, J. B., & Larkey, P. D. (1982b). Reply to professor Harsanyi. Management Science, 28(2), 124. https://doi.org/10.1287/mnsc.28.2.124
Kadane, J. B., & Larkey, P. D. (1983). The confusion of is and ought in game theoretic contexts. Management Science, 29(12), 1349–1455. https://doi.org/10.1287/mnsc.29.12.1365
Kaneko, M. (2013). Symposium: Logic and economics-interactions between subjective thinking and objective worlds. Economic Theory, 53(1), 1–8. https://doi.org/10.1007/s00199-012-0737-8
Kohlberg, E. (1975a). Optimal strategies in repeated games with incomplete information. International Journal of Game Theory, 4(1), 7–24.
Kohlberg, E. (1975b). The information revealed in infinitely-repeated games of incomplete information. International Journal of Game Theory, 4(2), 57–59.
Kohlberg, E., & Mertens, J.-F. (1986). On the strategic stability of equilibria. Econometrica, 54(5), 1003–1038. https://doi.org/10.2307/1912320
Kohlberg, E., & Zamir, S. (1974). Repeated games of incomplete information: The symmetric case. Annals of Statistics, 2(5), 1040–1041. https://doi.org/10.1214/aos/1176342824
Kreps, D., & Wilson, R. (1982). Sequential equilibria. Econometrica, 50(4), 863–894. https://doi.org/10.2307/1912767
Kripke, S. A. (1963). Semantical analysis of modal logic I: Normal modal propositional calculi. Mathematical Logic Quarterly, 9(5–6), 67–96. https://doi.org/10.1002/malq.19630090502
Kuhn, H. W., & Tucker, A. W. (1958). John von Neumann’s work in the theory of games and mathematical economics. Bulletin of the American Mathematical Society, 64(3), 100–122.
Lecouteux, G. (2018a). What does “we” want? Team reasoning, game theory, and unselfish behaviours. Revue D’économie Politique, 128(3), 311–332. https://doi.org/10.3917/redp.283.0311
Lecouteux, G. (2018b). Bayesian game theorists and non-Bayesian players. European Journal of the History of Economic Thought, 25(6), 1420–1454. https://doi.org/10.1080/09672567.2018.1523207
Lehtinen, A. (2011). The revealed-preference interpretation of payoffs in game theory. Homo Oeconomicus, 28(3), 265–296.
Léonard, R. J. (1992). Creating a context for game theory. In E. R. Weintraub (Ed.), Toward a history of game theory (pp. 29–76). Duke University Press.
Léonard, R. J. (2010). Von Neumann, Morgenstern, and the creation of game theory: From chess to social science, 1900–1960. Cambridge University Press.
Levi, I. (1995). The common prior assumption in economic theory. Economics and Philosophy, 11(2), 227–253. https://doi.org/10.1017/S0266267100003382
Levi, I. (1998). Prediction, Bayesian deliberation and correlated equilibrium. In W. Leinfellner & E. Köhler (Eds.), Game theory, experience, rationality (pp. 173–185). Springer.
Lewis, D. (1969). Convention. Oxford: Blackwell Publisher.
Lewis, D. (2002). Convention. Blackwell Publisher. (Original work published in 1969)
Lipman, M. (1995). Good thinking. Inquiry: Critical Thinking Across the Disciplines, 15(2), 37–41. https://doi.org/10.5840/inquiryctnews199515224
Luce, R. D., & Raiffa, H. (1957). Games and decisions: Introduction and critical survey. Wiley.
Marschak, J. (1946). Neumann’s and Morgenstern’s new approach to static economics. The Journal of Political Economy., 54(2), 97–115. https://doi.org/10.1086/256327
Mehta, J., Starmer, C., & Sugden, R. (1994a). The nature of salience: An experimental investigation of pure coordination games. The American Economic Review, 84(3), 658–673.
Mehta, J., Starmer, C., & Sugden, R. (1994b). Focal points in pure coordination games: An experimental investigation. Theory and Decision, 36(2), 163–185. https://doi.org/10.1007/BF01079211
Mertens, J.-F. (1971). The value of two-person zero-sum repeated games: The extensive case. International Journal of Game Theory, 1, 217–227. https://doi.org/10.1007/BF01753446
Mertens, J. F., & Zamir, S. (1971). The value of two-person zero-sum repeated games with lack of information on both sides. International Journal of Game Theory, 1, 39–64. https://doi.org/10.1007/BF01753433
Mertens, J.-F., & Zamir, S. (1985). Formulation of Bayesian analysis for games with incomplete information. International Journal of Game Theory, 14, 1–29. https://doi.org/10.1007/BF01770224
Milgrom, P. R. (1981). Good news and bad news: Representation theorems and applications. The Bell Journal of Economics, 12(2), 380–391. https://doi.org/10.2307/3003562
Mirowski, P. (1992). What were von Neumann and Morgenstern trying to accomplish? In E. R. Weintraub (Ed.), Toward a history of game theory (pp. 113–148). Duke University Press.
Monderer, D., & Samet, D. (1989). Approximating common knowledge with common beliefs. Games and Economic Behavior, 1(2), 170–190. https://doi.org/10.1016/0899-8256(89)90017-1
Morgenstern, O. (1928). Wirtschaftprognose: Enie untersuchung ihrer voraussetzungen und möglichkeiten. Julius Springer.
Morgenstern, O. (1935). Vollkommene voraussicht und wirtschaftliches gleichgewicht. Zeitschrift Für Nationalökonomie, 6(3), 337–357.
Morris, S. (1995). The common prior assumption in economic theory. Economics and Philosophy, 11(2), 227–253. https://doi.org/10.1017/S0266267100003382
Myerson, R. B. (1941). An early paper on the refinement of Nash equilibrium. Duke Mathematical Journal, 81(1), 67–75.
Myerson, R. B. (1978). Refinement of the Nash equilibrium concept. International Journal of Game Theory, 2(7), 73–80. https://doi.org/10.1007/bf01753236
Myerson, R. B. (2004). Comments on “Games with incomplete information played by ‘Bayesian’Players, I-III Harsanyi’s games with incomplete information.” Management Science, 50, 1818–1824.
Nash, J. F. (1950a). The bargaining problem. Econometrica, 18(2), 155–162. 0012-9682(1950a04)
Nash, J. F. (1950b). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36(1), 48–49. https://doi.org/10.1073/pnas.36.1.48
Nash, J. F. (1951). Non-cooperative games. Annals of Mathematics, 54(2), 286–295. https://doi.org/10.2307/1969529
Nash, J. F. (1953). Two-person cooperative games. Econometrica, 21, 128–140.
Nash, J. F. (1996). Essays on game theory. Edward Elgar.
Nash, J. F., & Shapley, L. (1950). A simple three-person poker game. In H. W. Kuhn & A. W. Tucker (Eds.), Contributions to the theory of games (pp. 105–116). Annals of Mathematics Studies. Princeton University Press.
Pearce, D. G. (1984). Rationalizable strategic behavior and the problem of perfection. Econometrica, Journal of the Econometric Society, 52(4), 1029–1050. 0012-9682(198407)
Perea, A. (2007). A one-person doxastic characterization of Nash strategies. Synthese, 158(2), 251–271. https://www.jstor.org/stable/27653589
Perea, A. (2012). Epistemic game theory: Reasoning and choice. Cambridge University Press.
Perea, A. (2014). From classical to epistemic game theory. International Game Theory Review, 16(1), 1–22. https://doi.org/10.1142/S0219198914400015
Polak, B. (1999). Epistemic conditions for Nash equilibrium, and common knowledge of rationality. Econometrica, 67(3), 673–676. https://doi.org/10.1111/1468-0262.00043
Ponssard, J. P. (1975a). A note on the LP formulation of zero-sum sequential games with incomplete information. International Journal of Game Theory, 4(1), 1–5. https://doi.org/10.1007/BF01766398
Ponssard, J. P. (1975b). Zero-sum games with “almost” perfect information. Management Science, 21(7), 794–805.
Ponssard, J. P., & Zamir, S. (1973). Zero-sum sequential games with incomplete information. International Journal of Game Theory, 2(1), 99–107. https://doi.org/10.1007/BF01737562
Raiffa, H. (1992). Game theory at the University of Michigan, 1949–1952. In E. R. Weintraub (Ed.), Toward a history of game theory (pp. 165–176). Duke University Press.
Rellstab, U. (1992). New insights into the collaboration between John von Neumann and Oskar Morgenstern on the Theory of game and economic behavior. In E. R. Weintraub (Ed.), Toward a history of game theory (pp. 77–94). Durham: Duke University Press.
Roth, A., Schoumaker, F. (1983). Expectations and reputations in bargaining: An experimental study. American Economic Review, 73(3), 362–72. https://www.jstor.org/stable/1808119
Rubinstein, A. (1989). The electronic mail game: Strategic behavior under “almost common knowledge. The American Economic Review, 79(3), 385–391. https://www.jstor.org/stable/1806851
Rubinstein, A. (2001). A theorist’s view of experiments. European Economic Review, 45(4–6), 615–628. https://doi.org/10.1016/S0014-2921(01)00104-0
Savage, L. J. (1954). The foundations of statistics. Wiley.
Schotter, A. (1976). Selected writings of Oskar Morgenstern. New York: New York University Press.
Schotter, A. (1992). Oskar Morgenstern’s contribution to the development of the theory of games. In E. R. Weintraub (Ed.), Toward a history of game theory (pp. 95–112). Duke University Press.
Selten, R. (1965). Spieltheoretische behandlung eines oligopolmodells mit nachfragetragheit. Zeitschrift fur die Gesamte Staatswissenschaft, 121(301–324), 667–689.
Selten, R. (1975). Reëxamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory, 4, 25–55. https://doi.org/10.1007/BF01766400
Sen, A. (1973). On economic inequality. Oxford University Press. https://doi.org/10.1093/0198281935.001.0001
Shubik, M. (1952). Information, theories of competition, and the theory of games. Journal of Political Economy, 60(2), 145–150. https://www.jstor.org/stable/1825963
Shubik, M. (1992). Game theory at Princeton, 1949–1955: A personal reminiscence. In E. R. Weintraub (Ed.), Toward a history of game theory (pp. 151–164). Duke University Press.
Sorin, S. (1979). A note on the value of zero-sum sequential repeated games with incomplete information. International Journal of Game Theory, 8(4), 217–223. https://doi.org/10.1007/BF01766707
Spohn, W. (1977). Where Luce and Krantz do really generalize Savage’s decision model. Erkenntnis, 11(1), 123–134. https://www.jstor.org/stable/20010536
Stahl, D. O., & Wilson, P. W. (1994). Experimental evidence on players’ models of other players. Journal of Economic Behavior and Organization, 25(3), 309–327. https://doi.org/10.1016/0167-2681(94)90103-1
Stalnaker, R. (1999). Context and content. Oxford University Press.
Sugden, R. (1991). Rational choice: A survey of contributions from economics and philosophy. The Economic Journal, 101(407), 751–785. https://doi.org/10.2307/2233854
Sugden, R. (1993). Thinking as a team: Towards an explanation of nonselfish behavior. Social Philosophy and Policy, 10(1), 69–89. https://doi.org/10.1017/S0265052500004027
Sugden, R. (1995). A theory of focal points. The Economic Journal, 105(430), 533–550. https://doi.org/10.2307/2235016
Sugden, R. (2001). The evolutionary turn in game theory. Journal of Economic Methodology, 8(1), 113–130. https://doi.org/10.1080/13501780010023289
Tan, T. C. C., & Werlang, S. R. D. C. (1988). The Bayesian foundations of solution concepts of games. Journal of Economic Theory, 45(2), 370–391. https://doi.org/10.1016/0022-0531(88)90276-1
Tan, T. C. C., & Werlang, S. R. D. C. (1992). On Aumann’s notion of common knowledge: An alternative approach. Revista Brasileira De Economia, 46(2), 151–166.
Tsakas, E. (2012). Rational belief hierarchies (p. 004). METEOR, Maastricht University School of Business and Economics.
van Damme, E. (1984). A relation between perfect equilibria in extensive form games and proper equilibria in normal form games. International Journal of Game Theory, 13(1), 1–13. https://doi.org/10.1007/BF01769861
van Damme, E. (1989). Stable equilibria and forward induction. Journal of Economic Theory, 48(2), 476–496. https://doi.org/10.1016/0022-0531(89)90038-0
van Damme, E. (1991). Stability and perfection of Nash equilibria. Springer-Verlag.
von Neumann, J. (1959). On the theory of games of strategy. In A.W. Tucker, & R. D. Luce (Eds.), Contributions to the theory of games (Vol. 24, pp. 13–42). (Original work published in 1928. Zur theorie der gesellschaftsspiele. Mathematische Annalen, 100, 295–320).
von Neumann, J. (1984). The formalist foundations of mathematics. In P. Benacerraf, & H. Putnam (Eds.), Philosophy of mathematics. Selected readings (pp. 61–65). Cambridge University Press. (Original work published in 1931).
von Neumann, J., & Morgenstern, O. (1944). The theory of games and economic behaviour. Princeton University Press.
Weintraub, R. (1992). Introduction. In E. R. Weintraub (Ed.), Toward a history of game theory (p. 3). Duke University Press.
Zamir, S. (1971). On the relation between finitely and infinitely repeated games with incomplete information. International Journal of Game Theory., 1, 179–198. https://doi.org/10.1007/BF01753442
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Larrouy, L. (2023). A Critical Assessment of the Evolution of Standard Game Theory. In: On Coordination in Non-Cooperative Game Theory. Springer Studies in the History of Economic Thought. Springer, Cham. https://doi.org/10.1007/978-3-031-36171-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-031-36171-5_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-36170-8
Online ISBN: 978-3-031-36171-5
eBook Packages: Economics and FinanceEconomics and Finance (R0)