Abstract
An information structure in a non-cooperative game determines the signal that each player observes as a function of the strategy profile. Such information structure is called non-manipulable if no player can gain new information by changing his strategy. A Conjectural Equilibrium (CE) (Battigalli in Unpublished undergraduate dissertation, 1987; Battigalli and Guaitoli 1988; Decisions, games and markets, 1997) with respect to a given information structure is a strategy profile in which each player plays a best response to his conjecture about his opponents’ play and his conjecture is not contradicted by the signal he observes. We provide a sufficient condition for the existence of pure CE in games with a non-manipulable information structure. We then apply this condition to prove existence of pure CE in two classes of games when the information that players have is the distribution of strategies in the population.
Similar content being viewed by others
References
Azrieli Y (2007) Thinking categorically about others: a conjectural equilibrium approach. Manuscript
Battigalli P (1987) Comportamento razionale ed equilbrio nei giochi e nelle situazioni sociali. Unpublished undergraduate dissertation. Bocconi University, Milano
Battigalli P (1999) A comment on non-Nash equilibria. Manuscript
Battigalli P, Guaitoli D (1988) Conjectural equilibrium. Manuscript
Battigalli P and Guaitoli D (1997). Conjectural equilibria and rationalizability in a game with incomplete information. In: Battigalli, P, Montesano, A and Panunzi, F (eds) Decisions, games and markets, Kluwer Academic Publishers, Dordrecht
Battigalli P, Gilli M and Molinari MC (1992). Learning and convergence to equilibrium in repeated strategic interactions: an introductory survey. Res Econ 46: 335–378
Dekel E, Fudenberg D and Levine DK (1999). Payoff information and self-confirming equilibrium. J Econ Theory 89: 165–185
Dekel E, Fudenberg D and Levine DK (2004). Learning to play Bayesian games. Games Econ Behav 46: 282–303
Dunford N and Schwartz JT (1988). Linear operators, Part 1. Wiley, New York
Fudenberg D and Levine DK (1993a). Self-confirming equilibrium. Econometrica 61: 523–545
Fudenberg D and Levine DK (1993b). Steady state learning and Nash equilibrium. Econometrica 61: 547–573
Gilli M (1999). On non-Nash equilibria. Games Econ Behav 27: 184–203
Kalai E (2004). Large robust games. Econometrica 72: 1631–1665
Kalai E and Jackson MO (1997). Social learning in recurring games. Games Econ Behav 21: 102–134
Kalai E and Lehrer E (1993a). Rational learning leads to Nash equilibrium. Econometrica 61: 1019–1045
Kalai E and Lehrer E (1993b). Subjective equilibrium in repeated games. Econometrica 61: 1231–1240
Milchtaich I (1996). Congestion games with players—specific payoff functions. Games Econ Behav 13: 111–124
Pearce DG (1984). Rationalizable strategic behavior and the problem of perfection. Econometrica 52: 1029–1050
Rosenthal RW (1973). A class of games possessing pure-strategy Nash equilibrium. Int J Game Theory 2: 65–67
Rubinstein A and Wolinsky A (1994). Rationalizable conjectural equilibrium: between Nash and rationalizability. Games Econ Behav 6: 299–311
Schmeidler D (1973). Equilibrium points of non-atomic games. J Stat Phys 7: 295–300
Author information
Authors and Affiliations
Corresponding author
Additional information
This work is based on a chapter from my Ph.D. dissertation written at the School of Mathematical Sciences of Tel-Aviv University under the supervision of Prof. Ehud Lehrer. I am grateful to Ehud Lehrer as well as to Pierpaolo Battigalli, Yuval Heller, two anonymous referees, an Associate Editor and the Editor for very helpful comments and references.
Rights and permissions
About this article
Cite this article
Azrieli, Y. On pure conjectural equilibrium with non-manipulable information. Int J Game Theory 38, 209–219 (2009). https://doi.org/10.1007/s00182-008-0146-1
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00182-008-0146-1