Heller, Yuval (2009): Perfect correlated equilibria in stopping games.
Download (327kB) | Preview
We define a new solution concept for an undiscounted dynamic game - a perfect uniform normal-form constant-expectation correlated approximate equilibrium with a canonical and universal correlation device. This equilibrium has the following appealing properties: (1) “Trembling-hand” perfectness - players do not use non-credible threats; (2) Uniformness - it is an approximate equilibrium in any long enough finite-horizon game and in any discounted game with a high enough discount factor; (3) Normal-form correlation - The strategy of a player depends on a private signal he receives before the game starts (which can be induced by “cheap-talk” among the players); (4) Constant expectation - The expected payoff of each player almost does not change when he receives his signal; (5) Universal correlation device - the device does not depend on the specific parameters of the game. (6) Canonical - each signal is equivalent to a strategy. We demonstrate the use of this equilibrium by proving its existence in every undiscounted multi-player stopping game.
|Item Type:||MPRA Paper|
|Original Title:||Perfect correlated equilibria in stopping games|
|Keywords:||stochastic games, stopping games, correlated equilibrium, perfect equilibrium, Ramsey Theorem.|
|Subjects:||C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games; Evolutionary Games; Repeated Games|
|Depositing User:||Yuval Heller|
|Date Deposited:||11. Sep 2009 06:37|
|Last Modified:||13. Feb 2013 02:55|
R.J. Aumann, Subjectivity and Correlation in Randomized Strategies. J. Math. Econ., 1 (1974),67-96.
R.J. Aumann, Correlated equilibrium as an expression of Bayesian rationality, Econometrica 55 (1987), 1-18.
R.J. Aumann, M. Maschler, Repeated games with incomplete information. The MIT press (1995).
J. Bulow, P. Klemperer, The Generalized War of Attrition, Amer. Econ. Rev. 89:1(. 2001), 175-189.
R. Christie-David, M. Chaudhry and W. Khan, News releases, market integration, and market leadership, The Journal of Financial Research XXV(2) (2002), 223-245.
A. Dhillon, J.F. Mertens, Perfect correlated equilibria. Journal of Economic Theory 68 (1996), 279-302.
E. B. Dynkin, Game variant of a problem on optimal stopping. Soviet Math. Dokl. 10 (1969), 270-274.
C.H. Fine, L. Li, Equilibrium exit in stochastically declining industries. Games Econ. Behav. 1 (1989), 40-59.
F. Forges, An Approach to Communication Equilibria, Econometrica 54 (1986), 1375-1385.
D. Fudenberg, J.Tirole, Preemption and Rent Equalization in the Adoption of New Technology. Rev. Econ. Stud., LII (1985), 383-401.
D. Fudenberg, J. Tirole, A Theory of Exit in Duopoly. Econometrica, 54 (1986), 943-960.
P. Ghemawat, B. Nalebuff. Exit. RAND J. Econ. 16 (1985),184-194.
V. Krishna, J. Morgan, An Analysis of the War of Attrition and the All-Pay Auction. Journal of Economic Theory, 72 (1997), 343±62.
J.W. Mamer. Monotone stopping games. J. Appl. Prob. 24 (1987), 386-401.
A. Mashiah-Yaakovi. Subgame Perfect Equilibria in Stopping Games. mimeo (2008).
H. Morimoto. Non-zero–sum discrete parameter stochastic games with stopping times. Probab. Theory Related Fields 72 (1986), 155-160.
Myerson, R. B. (1986a), Multistage Games with Communication, Econometrica 54, 323-358.
Myerson R (1986b), Acceptable and predominant correlated equilibria, Int. J. Game Theory 15 (3), 133-154.
Nalebuff, B, Riley JG (1985), Asymmetric Equilibria in the War of Attrition. Journal of Theoretical Biology, 113: 517-27.
P. Neumann, D. Ramsey, and K. Szajowski. Randomized stopping times in Dynkin games. Z. Angew. Math. Mech. 82 (2002), 811–819.
J. Neveu, Discrete-parameters Martingales. Borth-Holland, Amsterdam (1975).
A.S. Nowak and K. Szajowski. Nonzero-sum stochastic games. In Stochastic and Differential Games (M. Bardi, T. E. S. Raghavan and T. Parthasarathy, eds.) 297-342 (1999). Birkhäuser, Boston.
Y. Ohtsubo. On a discrete-time non-zero–sum Dynkin problem with monotonicity. J. Appl. Probab. 28 (1991), 466-472.
F. Ramsey, On a problem of formal logic. Proc. London Math. Soc. 30 (1930), 264-286.
D. Rosenberg, E. Solan, N. Vielle, Stopping games with randomized strategies. Probab. Theory Related Fields 119 (2001), 433-451.
R. Selten, Spieltheoretische behandlung eines oligopolmodells mit nachfragetr a gheit. Zeitschrift fur die gesamte Staatswissenschaft 121(1965), 301-324.
Selten R, Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory 4 (1975), 25-55.
E. Shmaya, E. Solan, Two-player nonzero-sum stopping games in discrete time, Annals of Probability 32 (2004), 2733-2764.
A. Shmida, B. Peleg, Strict and Symmetric Correlated Equilibria Are the Distributions of the ESS's of Biological Conflicts with Asymmetric Roles, in Understanding Strategic Interaction, ed. by W. Albers, W. Güth, P. Hammerstein, B. Moldovanu, E. van Damme. Springer-Verlag (1997), 149-170.
E. Solan, N. Vieille, Quitting games, Mathematics of Operations Research 26 (2001), 265-285.
E. Solan, V. Vohra, Correlated Equilibrium in Quitting Games, Mathematics of Operations Research 26 (2001), 601-610.
E. Solan, V. Vohra, Correlated equilibrium payoffs and public signaling in absorbing games, Int J Game Theory 31 (2002), 91-121.
Available Versions of this Item
Perfect correlated equilibria in stopping games. (deposited 12. Jun 2009 03:09)
- Perfect correlated equilibria in stopping games. (deposited 11. Sep 2009 06:37) [Currently Displayed]