Sequential correlated equilibrium in stopping games

Heller, Yuval (2009): Sequential correlated equilibrium in stopping games. Forthcoming in: Operations Research No. Forthcoming

Abstract

In many situations, such as trade in stock exchanges, agents have many instances to act even though the duration of interactions take a relatively short time. The agents in such situations can often coordinate their actions in advance, but coordination during the game consumes too much time. An equilibrium in such situations has to be sequential in order to handle mistakes made by players. In this paper, we present a new solution concept for infinite-horizon dynamic games, which is appropriate for such situations: a sequential constant-expectation normal-form correlated approximate equilibrium. Under additional assumptions, we show that every such game admits this kind of equilibrium.

• Item Type: MPRA Paper
• Language: English
• Keywords: stochastic games, stopping games, correlated equilibrium, sequential equilibrium, Ramsey Theorem, distribution equilibrium
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games; Evolutionary Games; Repeated Games

References

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.