Rationalizability in general situations

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• 作者：Yi-Chun Chen ; Xiao Luo ; Chen Qu
• 关键词：Strategic games ; General preferences ; Rationalizability ; Common knowledge of rationality ; Nash equilibrium
• 刊名：Economic Theory
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：61
• 期：1
• 页码：147-167
• 全文大小：559 KB
• 参考文献：Apt, K.R.: The many faces of rationalizability. B.E. J. Theor. Econ. 7, Article 18 (2007)
  Apt, K.R., Zvesper, J.A.: The role of monotonicity in the epistemic analysis of strategic games. Games 1, 381–394 (2010)CrossRef
  Arieli, I.: Rationalizability in continuous games. J. Math. Econ. 46, 912–924 (2010)CrossRef
  Aumann, R.J.: Subjectivity and correlation in randomized strategies. J. Math. Econ. 1, 67–96 (1974)CrossRef
  Aumann, R.J.: Agreeing to disagree. Ann. Stat. 4, 1236–1239 (1976)CrossRef
  Aumann, R.J.: Interactive epistemology I: knowledge. Int. J. Game Theory 28, 263–300 (1999)CrossRef
  Aumann, R.J., Brandenburger, A.: Epistemic conditions for Nash equilibrium. Econometrica 63, 1161–1180 (1995)CrossRef
  Basu, K., Weibull, J.: Strategy subsets closed under rational behavior. Econ. Lett. 36, 141–146 (1991)CrossRef
  Bergemann, D., Morris, S.: Robust implementation: the role of large type space. In: Cowles Foundation Discussion Paper No. 1519 (2005a)
  Bergemann, D., Morris, S.: Robust mechanism design. Econometrica 73, 1521–1534 (2005b)CrossRef
  Bergemann, D., Morris, S., Tercieux, O.: Rationalizable implementation. J. Econ. Theory 146, 1253–1274 (2011)CrossRef
  Bernheim, B.D.: Rationalizable strategic behavior. Econometrica 52, 1007–1028 (1984)CrossRef
  Bewley, T.: Knightian uncertainty theory: Part I. In: Cowles Foundation Discussion Paper No. 807, Yale University (1986)
  Blume, L., Brandenburger, A., Dekel, E.: Lexicographic probabilities and choice under uncertainty. Econometrica 59, 61–79 (1991)CrossRef
  Borgers, T.: Pure strategy dominance. Econometrica 61, 423–430 (1993)CrossRef
  Brandenburger, A.: The power of paradox: some recent developments in interactive epistemology. Int. J. Game Theory 35, 465–492 (2007)CrossRef
  Brandenburger, A., Dekel, D.: Rationalizability and correlated equilibria. Econometrica 55, 1391–1402 (1987)CrossRef
  Brandenburger, A., Dekel, D.: Hierarchies of beliefs and common knowledge. J. Econ. Theory 59, 189–198 (1993)CrossRef
  Brandenburger, A., Friedenberg, A., Keisler, H.J.: Fixed Points in Epistemic Game Theory. Mimeo, NYU (2011)
  Camerer, C., Weber, M.: Recent developments in modeling preferences: uncertainty and ambiguity. J Risk Uncertain. 5, 325–370 (1992)CrossRef
  Chen, Y.C., Long, N.V., Luo, X.: Iterated strict dominance in general games. Games Econ. Behav. 61, 299–315 (2007)CrossRef
  Chen, Y.C., Luo, X.: An indistinguishability result on rationalizability under general preferences. Econ. Theory 51, 1–12 (2012)CrossRef
  Eichberger, J., Kelsey, D.: Are the treasures of game theory ambiguous? Econ. Theory 48, 313–339 (2011)CrossRef
  Epstein, L.: Preference, rationalizability and equilibrium. J. Econ. Theory 73, 1–29 (1997)CrossRef
  Epstein, L., Wang, T.: “Beliefs about beliefs” without probabilities. Econometrica 64, 1343–1373 (1996)CrossRef
  Fagin, R., Geanakoplos, J., Halpern, J.Y., Vardi, M.Y.: The hierarchical approach to modeling knowledge and common knowledge. Int. J. Game Theory 28, 331–365 (1999)CrossRef
  Gilboa, I., Marinacci, M.: Ambiguity and the Bayesian paradigm. In: Acemoglu, D., Arellano, M., Dekel, E. (eds.) Advances in Economics and Econometrics: Tenth World Congress, vol. 1, pp. 179–242. Cambridge University Press, Cambridge (2013)CrossRef
  Gilboa, I., Schmeidler, D.: Maxmin expected utility with non-unique prior. J. Math. Econ. 18, 141–153 (1989)CrossRef
  Greenberg, J., Gupta, S., Luo, X.: Mutually acceptable courses of action. Econ. Theory 40, 91–112 (2009)CrossRef
  Harsanyi, J.: Games with incomplete information played by “Bayesian” players, I-III. Manag. Sci. 14, 159–182, 320–334, 486–502 (1967–68)
  Heifetz, A.: Common belief in monotonic epistemic logic. Math. Soc. Sci. 32, 109–123 (1996)CrossRef
  Heifetz, A.: Iterative and fixed point common belief. J. Philos. Log. 28, 61–79 (1999)CrossRef
  Heifetz, A., Samet, D.: Topology-free typology of beliefs. J. Econ. Theory 82, 324–341 (1998)CrossRef
  Jara-Moroni, P.: Rationalizability in games with a continuum of players. Games Econ. Behav. 75, 668–684 (2012)CrossRef
  Jech, T.: Set Theory. Springer, Berlin (2003)
  Kunimoto, T., Serrano, R.: A new necessary condition for implementation in iteratively undominated strategies. J. Econ. Theory 146, 2583–2595 (2011)CrossRef
  Lipman, B.L.: A note on the implication of common knowledge of rationality. Games Econ. Behav. 6, 114–129 (1994)CrossRef
  Luce, R.D., Raiffa, H.: Games and Decisions. Wiley, NY (1957)
  Luo, X.: General systems and \(\varphi \) -stable sets—a formal analysis of socioeconomic environments. J. Math. Econ. 36, 95–109 (2001)CrossRef
  Machina, M., Schmeidler, D.: A more robust definition of subjective probability. Econometrica 60, 745–780 (1992)CrossRef
  Mertens, J.F., Zamir, S.: Formulation of Bayesian analysis for games with incomplete information. Int. J. Game Theory 14, 1–29 (1985)CrossRef
  Milgrom, P., Roberts, J.: Rationalizability, learning, and equilibrium in games with strategic complementarities. Econometrica 58, 1255–1278 (1990)CrossRef
  Monderer, D., Samet, D.: Approximating common knowledge with common beliefs. Games Econ. Behav. 1, 170–190 (1989)CrossRef
  Morris, S., Takahashi, S.: Common certainty of rationality revisited. In: Princeton Economic Theory Center Working Paper 010\_2011, Princeton University (2011)
  Moulin, H.: Dominance solvability and Cournot stability. Math. Soc. Sci. 7, 83–102 (1984)CrossRef
  Osborne, M.J., Rubinstein, A.: A Course in Game Theory. MIT Press, Cambridge (1994)
  Pearce, D.G.: Rationalizable strategic behavior and the problem of perfection. Econometrica 52, 1029–1051 (1984)CrossRef
  Perea, A.: Epistemic Game Theory: Reasoning and Choice. Cambridge University Press, Cambridge (2012)CrossRef
  Reny, P.: On the existence of pure and mixed strategy Nash equilibrium in discontinuous games. Econometrica 67, 1029–1056 (1999)CrossRef
  Royden, H.L.: Real Analysis. The Macmillan Company, NY (1968)
  Savage, L.: The Foundations of Statistics. Wiley, NY (1954)
  Schmeidler, D.: Subjective probability and expected utility without additivity. Econometrica 57, 571–587 (1989)CrossRef
  Stinchcombe, M.B.: Countably additive subjective probabilities. Rev. Econ. Stud. 64, 125–146 (1997)CrossRef
  Tan, T., Werlang, S.: The Bayesian foundations of solution concepts of games. J. Econ. Theory 45, 370–391 (1988)CrossRef
  Vannetelbosch, V.J.: Rationalizability and equilibrium in N-person sequential bargaining. Econ. Theory 14, 353–371 (1999)CrossRef
  Yu, H.M.: Rationalizability and the Theory of Large Games (Ph.D. Dissertation). Johns Hopkins University (2010)
  Yu, H.M.: Rationalizability in large games. Econ. Theory 55, 457–479 (2014)CrossRef
  Zimper, A.: Uniqueness conditions for strongly point-rationalizable solutions to games with metrizable strategy sets. J. Math. Econ. 46, 729–751 (2006)CrossRef
  
• 作者单位：Yi-Chun Chen (1)
  Xiao Luo (1)
  Chen Qu (2)
  
  1. Department of Economics, National University of Singapore, Singapore, 117570, Singapore
  2. Department of Economics, BI Norwegian Business School, 0442, Oslo, Norway
  
• 刊物类别：Business and Economics
• 刊物主题：Economics
  Economic Theory
  Economics
  Analysis
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0479

文摘

The main purpose of this paper is to present an analytical framework that can be used to study rationalizable strategic behavior in general situations—i.e., arbitrary strategic games with various modes of behavior. We show that, under mild conditions, the notion of rationalizability defined in general situations has nice properties similar to those in finite games. The major features of this paper are (1) our approach does not require any kind of technical assumptions on the structure of the game, and (2) the analytical framework provides a unified treatment of players’ general preferences, including expected utility as a special case. In this paper, we also investigate the relationship between rationalizability and Nash equilibrium in general games.