Equilibria in ordinal status games

Kukushkin, Nikolai S. (2018): Equilibria in ordinal status games.

Abstract

Several agents choose positions on the real line (e.g., their levels of conspicuous consumption). Each agent's utility depends on her choice and her "status," which, in turn, is determined by the number of agents with greater choices (the fewer, the better). If the rules for the determination of the status are such that the set of the players is partitioned into just two tiers ("top" and "bottom"), then a strong Nash equilibrium exists, which Pareto dominates every other Nash equilibrium. Moreover, the Cournot tatonnement process started anywhere in the set of strategy profiles inevitably reaches a Nash equilibrium in a finite number of steps. If there are three tiers ("top," "middle," and "bottom"), then the existence of a Nash equilibrium is ensured under an additional assumption; however, there may be no Pareto efficient equilibrium. With more than three possible status levels, there seems to be no reasonably general sufficient conditions for Nash equilibrium existence.

• Item Type: MPRA Paper
• Language: English
• Keywords: status game; strong equilibrium; Nash equilibrium; Cournot tatonnement
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Akerlof, G.A., 1997. Social distance and social decisions. Econometrica 65, 1005-1024.

Arrow, K.J. and P.S. Dasgupta, 2009. Conspicuous consumption, inconspicuous leisure. Economic Journal 119, 497-516.

Becker, G. S., K.M. Murphy, and I. Werning, 2005. The equilibrium distribution of income and the market for status. Journal of Political Economy 113, 282-310.

Bilancini, E. and L. Boncinelli, 2008. Ordinal versus cardinal status: Two examples. Economics Letters 101, 17-19.

Clark A.E. and A.J. Oswald, 1998. Comparison-concave utility and following behaviour in social and economic settings. Journal of Public Economics 70, 133-155.

Frank, R.H., 1985a. Choosing the Right Pond: Human Behaviour and the Quest for Status. Oxford University Press, London and New York.

Frank, R.H., 1985b. The demand for unobservable and other positional goods. American Economic Review 75, 101-116.

Haagsma, R., and P.H.M. von Mouche, 2010. Equilibrium social hierarchies: a noncooperative ordinal status game. The B.E. Journal of Theoretical Economics 10, Issue 1 (Contributions)(Article 24).

Kukushkin, N.S., 2018. Better response dynamics and Nash equilibrium in discontinuous games. Journal of Mathematical Economics 74, 68-78.

Kukushkin, N.S., and P. von Mouche, 2018. Cournot tatonnement and Nash equilibrium in binary status games. Economics Bulletin 38(2), 1038-1044.

McLennan, A., P.K. Monteiro, and R. Tourky, 2011. Games with discontinuous payoffs: A strengthening of Reny's existence theorem. Econometrica 79, 1643-1664.

Milchtaich, I., 1996. Congestion games with player-specific payoff functions. Games and Economic Behavior 13, 111-124.

Milgrom, P., and C. Shannon, 1994. Monotone comparative statics. Econometrica 62, 157-180.

Monderer, D., and L.S. Shapley, 1996. Potential games. Games and Economic Behavior 14, 124-143.

Prokopovych, P., 2013. The single deviation property in games with discontinuous payoffs. Economic Theory 53, 383-402.

Rauscher, M., 1992. Keeping up with the Joneses: Chaotic patterns in a status game. Economics Letters 40, 287-290.

Reny, P.J., 1999. On the existence of pure and mixed strategy Nash equilibria in discontinuous games. Econometrica 67, 1029-1056.

Reny, P.J., 2016. Nash equilibrium in discontinuous games. Economic Theory 61, 553-569.

Veblen, T., 1899. The Theory of the Leisure Class. New York: Macmillan.