Cournot tatonnement and potentials

Kukushkin, Nikolai S. (2012): Cournot tatonnement and potentials.

Abstract

We study what topological assumptions should be added to the acyclicity of individual best response improvements in order to ensure the existence of a (pure strategy) Nash equilibrium as well as the possibility to reach a Nash equilibrium in the limit of a best response improvement path.

• Item Type: MPRA Paper
• Language: English
• Keywords: Cournot tatonnement; Cournot potential; game with structured utilities; aggregative game
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Bernheim, B.D., 1984. Rationalizable strategic behavior. Econometrica 52, 1007-1028.

Dubey, P., O. Haimanko, and A. Zapechelnyuk, 2006. Strategic complements and substitutes, and potential games. Games and Economic Behavior 54, 77-94.

Facchinei, F., V. Piccialli, and M. Sciandrone, 2011. Decomposition algorithms for generalized potential games. Computational Optimization and Applications 50, 237-262.

Germeier, Yu.B., and I.A. Vatel', 1974. On games with a hierarchical vector of interests. Izvestiya Akademii Nauk SSSR, Tekhnicheskaya Kibernetika, 3, 54-69 [in Russian; English translation in Engineering Cybernetics 12(3), 25-40 (1974)].

Huang, Z., 2002. Fictitious play in games with a continuum of strategies. Ph.D. Thesis, State University of New York at Stony Brook, Department of Economics.

Jensen, M.K., 2010. Aggregative games and best-reply potentials. Economic Theory 43, 45-66.

Kandori, M., and R. Rob, 1995. Evolution of equilibria in the long run: A general theory and applications. Journal of Economic Theory 65, 383-414.

Kukushkin, N.S., 1994. A condition for the existence of a Nash equilibrium in games with public and private objectives. Games and Economic Behavior 7, 177-192.

Kukushkin, N.S., 2004. Best response dynamics in finite games with additive aggregation. Games and Economic Behavior 48, 94-110.

Kukushkin, N.S., 2005. ``Strategic supplements" in games with polylinear interactions. EconWPA Paper #0411008

Kukushkin, N.S., 2007. Congestion games revisited. International Journal of Game Theory 36, 57-83.

Kukushkin, N.S., 2008. Maximizing an interval order on compact subsets of its domain. Mathematical Social Sciences 56, 195-206.

Kukushkin, N.S., 2010. Improvement Paths in Strategic Games: A Topological Approach. Russian Academy of Sciences, Dorodnicyn Computing Center, Moscow, 2010.

Kukushkin, N.S., 2011. Nash equilibrium in compact-continuous games with a potential. International Journal of Game Theory 40, 387-392.

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

Milgrom, P., and J. Roberts, 1990. Rationalizability, learning, and equilibrium in games with strategic complementarities. Econometrica 58, 1255-1277.

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.

Morris, S., and T. Ui, 2004. Best response equivalence. Games and Economic Behavior 49, 260-287.

Moulin, H., 1984. Dominance solvability and Cournot stability. Mathematical Social Sciences 7, 83-102.

Novshek, W., 1985. On the existence of Cournot equilibrium. Review of Economic Studies 52, 85-98.

Powell, M.J.D., 1973. On search directions for minimization algorithms. Mathematical Programming 4, 193-201.

Rosenthal, R.W., 1973. A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65-67.

Shannon, C., 1995. Weak and strong monotone comparative statics. Economic Theory 5, 209-227.

Topkis, D.M., 1979. Equilibrium points in nonzero-sum n-person submodular games. SIAM Journal on Control and Optimization 17, 773-787.

Veinott, A.F., Jr., 1989. Lattice Programming. Unpublished lectures.

Vives, X., 1990. Nash equilibrium with strategic complementarities. Journal of Mathematical Economics 19, 305-321.

Voorneveld, M., 2000. Best-response potential games. Economics Letters 66, 289-295.