Dynamic Unawareness and Rationalizable Behavior

Heifetz, Aviad and Meier, Martin and Schipper, Burkhard C (2009): Dynamic Unawareness and Rationalizable Behavior.

Abstract

We define generalized extensive-form games which allow for mutual unawareness of actions. We extend Pearce's (1984) notion of extensive-form (correlated) rationalizability to this setting, explore its properties and prove existence. We define also a new variant of this solution concept, prudent rationalizability, which refines the set of outcomes induced by extensive-form rationalizable strategies. Finally, we define the normal form of a generalized extensive-form game, and characterize in it extensive-form rationalizability by iterative conditional dominance.

• Item Type: MPRA Paper
• Language: English
• Keywords: Unawareness; extensive-form games; extensive-form rationalizability; prudent rationalizability; iterative conditional dominance
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information ; Mechanism Design; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D80 - General; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Asheim, G.B. and A. Perea (2005), Sequential and quasi-perfect rationalizability in extensive games, Games and Economic Behavior 53, 15-42.

Battigalli, P. (1997). On rationalizability in extensive games, Journal of Economic Theory 74, 40-61.

Battigalli, P. and M. Siniscalchi (2002). Strong belief and forward induction reasoning, Journal of Economic Theory 106, 356-391.

Ben Porath, E. and E. Dekel (1992), Signaling future actions and the potential for sacrifice, Journal of Economic Theory 57, 36-51.

Blume, L., Brandenburger, A., and E. Dekel (1991). Lexicographic probabilities and choice under uncertainty, Econometrica 69, 61-79.

Brandenburger, A. and A. Friedenberg (2007). The relationship between rationality on the matrix and the tree, mimeo.

Feinberg, Y. (2004). Subjective reasoning - games with unawareness, mimeo.

Filiz-Ozbay, E. (2007). Incorporating unawareness into contract theory, in: Samet, D. (ed.), Proceedings of the 11th conference on Theoretical Aspects of Rationality and Knowledge, Presses Universitaires de Louvain, 135-144.

Halpern, J. and L. Rego (2006). Extensive games with possibly unaware players, in: Proc. Fifth International Joint Conference on Autonomous Agents and Multiagent Systems, 744-751.

Heifetz, A., Meier, M. and B. C. Schipper (2006). Interactive unawareness, Journal of Economic Theory 130, 78-94.

Herings, P.J.J and V.J. Vannetelbosch (1999). Refinements of rationalizability for normal-form games, International Journal of Game Theory 28, 53-68.

Kohlberg, E. and J.-F. Mertens (1986). On the strategic stability of equilibrium, Econometrica 54, 1003-1037.

Li, J. (2006). Dynamic games with perfect awareness information, mimeo.

Mailath, G., Samuelson, L. and J. Swinkels (1993). Extensive form reasoning in normal form games, Econometrica 61, 273-302.

Ozbay, E. (2007). Unawareness and strategic announcements in games with uncertainty, in: Samet, D. (ed.), Proceedings of the 11th conference on Theoretical Aspects of Rationality and Knowledge, Presses Universitaires de Louvain, pp. 231-238.

Pearce, D.G. (1984). Rationalizable strategic behavior and the problem of perfection, Econometrica 52, 1029-1050.

Perea, A. (2002). A note on the one-deviation property in extensive form games, Games and Economic Behavior 40, 322-338.

Rego, L. and J. Halpern (2007). Generalized Solution Concepts in Games with Possibly Unaware Players, in: Samet, D. (ed.), Proceedings of the 11th conference on Theoretical Aspects of Rationality and Knowledge, Presses Universitaires de Louvain, pp. 253-262.

Reny, P. (1992). Backward induction, normal form perfection and explicable equilibria, Econometrica 60, 627-649.

Rubinstein, A. (1991), Comments on the Interpretation of Game Theory, Econometrica 59, 909-924.

Shimoji, M. and J. Watson (1998). Conditional dominance, rationalizability, and game forms, Journal of Economic Theory 83, 161-195.

Stahl, D. (1995). Lexicographic rationalizability and iterated admissibility, Economics Letters 47, 155-159.

Van Damme, E. (1989). Stable equilibria and forward induction, Journal of Economic Theory 48, 476-496.