Strategic complements and substitutes, and potential games. (English) Zbl 1129.91004

Summary: We show that games of strategic complements, or substitutes, with aggregation are “pseudo-potential” games. The upshot is that they possess Nash equilibria in pure strategies (NE), even if the strategy sets are not convex; and that various dynamic processes converge to NE. In particular, NE exist in Cournot oligopoly with indivisibilities in production.
Our notion of aggregation is quite general and enables us to take a unified view of several disparate models.


91A10 Noncooperative games
Full Text: DOI


[1] Amir, R., Cournot oligopoly and the theory of supermodular games, Games econ. behav., 15, 132-148, (1996) · Zbl 0859.90034
[2] Bulow, J.I.; Geanakoplos, J.D.; Klemperer, P.D., Multimarket oligopoly: strategic substitutes and complements, J. polit. economy, 93, 488-511, (1985)
[3] Dasgupta, P.; Heal, G., Economic theory and exhaustible resources, (1979), Cambridge Univ. Press, Cambridge Economics Handbooks · Zbl 0421.90004
[4] Diamond, D.W.; Dybvig, P., Bank runs, deposit insurance, and liquidity, J. polit. economy, 91, 401-419, (1983) · Zbl 1341.91135
[5] Diamond, P., Aggregate demand management in search equilibrium, J. polit. economy, 90, 881-894, (1982)
[6] DindoŇ°, M., Mezzetti, C., 2003. Better-reply dynamic and global convergence to Nash equilibrium in aggregative games. Working paper. University of North Carolina
[7] Dubey, P., Haimanko, O., Zapechelnyuk, A., 2004. Strategic complements and substitutes, and potential games. Discussion paper # 04-11. Monaster Center for Economic Research, Ben-Gurion University of the Negev, Beer Sheva, Israel · Zbl 1129.91004
[8] Fudenberg, D.; Tirole, J., Dynamic models of oligopoly, (1986), Hardwood Academic Chur, Switzerland
[9] Huang, Z., 2002. Fictitious play for games with a continuum of strategies. PhD dissertation. Department of Economics, SUNY at Stony Brook
[10] Katz, M.; Shapiro, C., Technology adoption in the presence of network externalities, J. polit. economy, 94, 822-841, (1986)
[11] Kukushkin, N.S., A fixed-point theorem for decreasing mappings, Econ. letters, 46, 23-26, (1994) · Zbl 0816.90140
[12] Kukushkin, N.S., Best response dynamics in finite games with additive aggregation, Games econ. behav., 48, 94-110, (2004) · Zbl 1117.91305
[13] Milgrom, P.; Roberts, J., Rationalizability, learning, and equilibrium in games with strategic complementarities, Econometrica, 58, 1255-1277, (1990) · Zbl 0728.90098
[14] Milgrom, P.; Shannon, C., Monotone comparative statics, Econometrica, 62, 157-180, (1994) · Zbl 0789.90010
[15] Monderer, D.; Shapley, L., Potential games, Games econ. behav., 14, 124-143, (1996) · Zbl 0862.90137
[16] Morris, S.; Ui, T., Best response equivalence, Games econ. behav., (2004), In press · Zbl 1102.91006
[17] Novshek, W., On the existence of Cournot equilibrium, Rev. econ. stud., 52, 85-98, (1985) · Zbl 0547.90011
[18] Shapley, L., 1994. Lecture notes in game theory. Handouts # 9 and 10. Eco 145. Department of Economics, UCLA
[19] Tirole, J., The theory of industrial organization, (1988), MIT Press Cambridge, MA
[20] Vives, X., Nash equilibrium with strategic complementarities, J. math. econ., 19, 305-321, (1990) · Zbl 0708.90094
[21] Voorneveld, M., Best-response potential games, Econ. letters, 66, 289-295, (2000) · Zbl 0951.91008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.