Non-Altruistic Equilibria

Ohnishi, Kazuhiro (2018): Non-Altruistic Equilibria.

Abstract

Which choice will a player make if he can make one of two choices in which his own payoffs are equal, but his rival’s payoffs are not equal, i.e. one with a large payoff for his rival and the other with a small payoff for his rival? This paper introduces non-altruistic equilibria for normal form games and extensive form non-altruistic equilibria for extensive form games as equilibrium concepts of noncooperative games by discussing such a problem and examines the connections between their equilibrium concepts and Nash and subgame perfect equilibria that are important and frequently encountered equilibrium concepts.

• Item Type: MPRA Paper
• Language: English
• Keywords: Normal form game, extensive form game, non-altruistic equilibrium.
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Aumann, R. J. (1974). Subjectivity and correlation in randomized strategies. Journal of Mathematical Economics, 1, 67-96.

Aumann, R. J. (1987). Correlated equilibrium as an expression of Bayesian rationality. Econometrica, 55, 1-18.

Bernheim, B. D., Peleg. B., & Whinston, M. D. (1987). Coalition-proof Nash equilibria I: Concepts. Journal of Economic Theory, 42, 1-12.

Cho, I.-K., & Kreps, D. M. (1987). Signaling games and stable equilibria. Quarterly Journal of Economics, 102, 179–222.

De Marco, G., & Morgan, J. (2008a). Friendliness and reciprocity in equilibrium selection. International Game Theory Review, 10, 53-72.

De Marco, G., & Morgan, J. (2008b). Slightly altruistic equilibria. Journal of Optimization Theory and Applications, 137, 347-362.

Fudenberg, D., & Tirole, J. (1991). Game theory. Cambridge, MA: MIT Press.

Fudenberg, D., & Levine, D. K. (1993). Self-confirming equilibrium. Econometrica, 61, 523-545.

Glazer, J., & Rubinstein, A. (1996). An extensive game as a guide for solving a normal game. Journal of Economic Theory, 70, 32-42.

Govindan, S., & Mertens, J.-F. (2004). An equivalent definition of stable equilibria. International Journal of Game Theory, 32, 339-357.

Hart, S. (1992). Games in extensive and strategic forms. In: Aumann, R. J., & Hart, S. (Eds.), Handbook of Game Theory with Economic Applications Volume 1 (pp. 19-40). Amsterdam: Elsevier Science Publishers.

Klonner, S. (2008). Private Information and Altruism in Bidding Roscas. Economic Journal, 118, 775-800.

Kohlberg, E., & Mertens, J.-F. (1986). On the strategic stability of equilibria. Econometrica, 54, 1003-1037.

Kreps, D. M., & Wilson, R. (1982). Sequential equilibria. Econometrica, 50, 863-894.

Kuhn, H. W. (1953). Extensive games and the problem of information. In: Kuhn, H. W., & Tucker, A. W. (Eds.), Contributions to the Theory of Games, Volume II (pp. 193-216). Annals of Mathematics Studies 28. Princeton: Princeton University Press.

Kuhn, H. W. (2003). Lectures on the theory of games. Princeton, NJ: Princeton University Press.

Maskin, E., & Tirole, J. (1988a). A theory of dynamic oligopoly, I: Overview and quantity competition with large fixed costs. Econometrica, 56, 549-569.

Maskin, E., & Tirole, J. (1988b). A theory of dynamic oligopoly, II: price competition, kinked demand curves, and Edgeworth cycles. Econometrica, 56, 571-599.

McKelvey, R. D., & Palfrey, T. R. (1995). Quantal response equilibria for normal form games. Games and Economic Behavior, 10, 6-38.

McKelvey, R., & Palfrey, T. (1998). Quantal response equilibria for extensive form games. Experimental Economics, 1, 9-41.

Mertens, J.-F. (1989). Stable equilibria – a reformulation. Part I: Definition and basic properties. Mathematics of Operations Research, 14, 575-625.

Mertens, J.-F. (1991). Stable equilibria – a reformulation. Part II: Discussion of the definition and further results. Mathematics of Operations Research, 16, 694-753.

Mertens, J.-F. (1995). Two examples of strategic equilibrium. Games and Economic Behavior, 8, 378-388.

Morgan, J., & Scalzo, V. (2008). Variational stability of social Nash equilibria. International Game Theory Review, 10, 53-72

Myerson, R. B. (1978). Refinements of the Nash equilibrium concept. International Journal of Game Theory, 7, 73-80.

Nash, J. F. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Science, 36, 48-49.

Nash, J. F. (1951). Non-cooperative games. Annals of Mathematics, 54, 286-295.

Ohnishi, K. (2001). Commitment and strategic firm behaviour. PhD Dissertation, Osaka University.

Ohnishi, K. (2007). On the payoff representations of normal form games. International Game Theory Review, 9, 477-482.

Ohnishi, K. (2012). A three-stage equilibrium with sunk costs. International Journal of Business Policy and Economics, 5, 81-84.

Rasmusen, E. (2007). Games and information: An introduction to game theory. Malden, MA: Wiley-Blackwell.

Ray, I. (1996). Coalition-proof correlated equilibrium: A definition. Games and Economic Behavior, 17, 56-79.

Ray, I. (2001). On games with identical equilibrium payoffs. Economic Theory, 17, 223-231.

Rosenthal, R. W. (1981). Games of perfect information, predatory pricing, and the chain-store Paradox. Journal of Economic Theory, 25, 92-100.

Rusinowska, A. (2002). Refinements of Nash equilibria in view of jealous or friendly behavior of players. International Game Theory Review, 4, 281-299.

Selten, R. (1965). Spieltheoretische behandlung eines oligopolmodells mit nachfrageträgheit. Zeitschrift für die gesamte Staatswissenschaft, 12, 301-324.

Selten, R. (1975). Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory, 4, 25-55.

Selten, R., & Wooders, M. H. (2001). Cyclic games: An introduction and some examples. Games and Economic Behavior, 34, 138-52.

van Damme, E. (1984). A relationship between perfect equilibria in extensive form games and proper equilibria in normal form games. International Journal of Game Theory, 13, 1-13.

van Damme, E. (1987). Stability and perfection of Nash equilibria. Berlin: Springer-Verlag.