NS  Vol.6 No.13 , August 2014
Equilibria Immune to Deviations by Coalitions in Infinite Horizon Non-Cooperative Games
Abstract: Infinite horizon discrete time non-cooperative games with observable actions of players and discounting of future single period payoffs are a suitable tool for analyzing emergence and sustainability of cooperation between all players because they do not contain the last period. A subgame perfect equilibrium is a standard solution concept for them. It requires only immunity to unilateral deviations in any subgame. It does not address immunity to deviations by coalitions. In particular, it does not rule out cooperation based on punishments of unilateral deviations that the grand coalition would like to forgive. We first briefly review concepts of renegotiation-proofness that rule out such forgiveness. Then we discuss the concept of strong perfect equilibrium that requires immunity to all deviations by all coalitions in all subgames. In games with only one level of players (e.g. members of the population engaged in the same type of competitive activity), it fails to exist when the Pareto efficient frontier of the set of single period payoff vectors has no sufficiently large flat portion. In such a case, it is not possible to punish unilateral deviations in a weakly Pareto efficient way. In games with two levels of players (e.g. members of two populations with symbiotic relationship, while activities within each population are competitive), it is possible to overcome this problem. The sum of benefits of all players during a punishment can be the same as when nobody is punished but its distribution between the two populations can be altered in favor of the punishers.  
Cite this paper: Horniaček, M. (2014) Equilibria Immune to Deviations by Coalitions in Infinite Horizon Non-Cooperative Games. Natural Science, 6, 1122-1127. doi: 10.4236/ns.2014.613100.

[1]   Axelrod, R. (1984) The Evolution of Cooperation. Basic Books (A Division of Harper Collins Publishers), New York.

[2]   Osborne, M. and Rubinstein, A. (1995) A Course in Game Theory. 2nd Printing, MIT Press, Cambridge, MA.

[3]   Selten, R. (1965) Spieltheoretische Behandlung eines Oligopolmodells mit Nachfrageträgheit. Zeitschrift für die Gesamte Staatswissenschaft, 121, 301-324 and 667-689.

[4]   Selten, R. (1975) Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games. International Journal of Game Theory, 4, 25-55.

[5]   Farrell, J. and Maskin, E. (1989) Renegotiation in Repeated Games. Games and Economic Behavior, 1, 327-360.

[6]   Bernheim, B.D. and Ray, D. (1989) Collective Dynamic Consistency in Repeated Games. Games and Economic Behavior, 1, 295-326.

[7]   Maskin, E. and Tirole, J. (1988) A Theory of Dynamic Oligopoly II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles. Econometrica, 56, 571-599.

[8]   Farrell, J. (1993) Renegotiation in Repeated Oligopoly Games. Mimeo. University of California at Berkeley, Berkeley.

[9]   Horniacek, M. (1996) The Approximation of a Strong Perfect Equilibrium in a Discounted Supergame. Journal of Mathematical Economics, 25, 85-107.

[10]   Horniacek, M. (2011) Cooperation and Efficiency in Markets. Lecture Notes in Economics and Mathematical Systems. Springer, Heidelberg.

[11]   Rubinstein, A. (1980) Strong Perfect Equilibrium in Supergames. International Journal of Game Theory, 9, 1-12.

[12]   Bernheim, B.D., Peleg, B. and Whinston, M.D. (1987) Coalition-Proof Nash Equilibria I. Concepts. Journal of Economic Theory, 42, 1-12.

[13]   Radner, R. (1985) Repeated Principal-Agent Games with Discounting. Econometrica, 53, 1173-1198.