Heifetz, Aviad and Meier, Martin and Schipper, Burkhard C (2011): Prudent rationalizability in generalized extensive-form games.
Download (558Kb) | Preview
We define an extensive-form analogue of iterated admissibility, called Prudent Rationalizability (PR). In each round of the procedure, for each information set of a player a surviving strategy of hers is required to be rational vis-a-vis a belief system with a full-support belief on the opponents' previously surviving strategies that reach that information set. Somewhat surprisingly, prudent rationalizable strategies may not refine the set of Extensive-Form Rationalizable (EFR) strategies (Pearce 1984). However, we prove that the paths induced by PR strategy-profiles (weakly) refine the set of paths induced by EFR strategies.
PR applies also to generalized extensive-form games which model mutual unawareness of actions (Heifetz, Meier and Schipper, 2011a). We demonstrate the applicability of PR in the analysis of verifiable communication, and show that it yields the same, full information unraveling prediction as does the unique sequential equilibrium singled out by Milgrom and Roberts (1986); yet, we also show that under unawareness full unraveling might fail.
|Item Type:||MPRA Paper|
|Original Title:||Prudent rationalizability in generalized extensive-form games|
|Keywords:||Prudent rationalizability, caution, extensive-form rationalizability, extensive-form games, unawareness, verifiable communication|
|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
|Depositing User:||Burkhard C Schipper|
|Date Deposited:||18. Apr 2011 21:19|
|Last Modified:||13. Feb 2013 16:03|
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.
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.
Dubey, P. and M. Kaneko (1984). Information patterns and Nash equilibria in extensive games: I, Mathematical Social Sciences 8, 111-139.
Heifetz, A., Meier, M. and B. C. Schipper (2011a). Dynamic unawareness and rationalizable behavior, mimeo.
Heifetz, A., Meier, M. and B. C. Schipper (2011b). Conditional dominance in dynamic games with unawareness, mimeo.
Milgrom, R. and J. Roberts (1986). Relying on the information of interested parties, Rand Journal of Economics 17, 18-32.
Osborne, M. and A. Rubinstein (1994). A course in game theory, MIT Press.
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. (forthcoming). Epistemic game theory: Reasoning and choice, Cambridge University Press.
Reny, P. (1992). Backward induction, normal form perfection and explicable equilibria, Econometrica 60, 627-649.
Robles, J. (2006). Order independence of conditional dominance, mimeo., Victoria University of Wellington.
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.