Essential equilibria of large generalized games

• Published in: Economic theory Vol. 57; no. 3; pp. 479 - 513
• Main Authors: Correa, Sofía, Torres-Martínez, Juan Pablo
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer 01.11.2014; Springer Berlin Heidelberg; Springer Nature B.V
• Subjects: Analysis; Correspondence; Economic theory; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Economics and Finance; Electoral systems; Enterprise games; Equilibrium; Game Theory; Games; Generalized method of moments; Infinity; Mathematical analysis; Mathematical discontinuity; Mathematical functions; Mathematical vectors; Microeconomics; Nash equilibrium; Objective functions; Objectivity; Pay-off; Prices; Public Finance; Research Article; Respect; Role sets; Social and Behav. Sciences; Stability Pact; Studies; Utility functions; Voting; United States; Large generalized games; Essential sets and components; Essential equilibria; C02; C62; C72
• ISSN: 0938-2259; 1432-0479
• DOI: 10.1007/s00199-014-0821-3

We characterize the essential stability of games with a continuum of players, where strategy profiles may affect objective functions and admissible strategies. Taking into account the perturbations defined by a continuous mapping from a complete metric space of parameters to the space of continuous games, we prove that essential stability is a generic property and every game has a stable subset of equilibria. These results are extended to discontinuous large generalized games assuming that only payoff functions are subject to perturbations. We apply our results in an electoral game with a continuum of Cournot-Nash equilibria, where the unique essential equilibrium is that only politically engaged players participate in the electoral process. In addition, employing our results for discontinuous games, we determine the stability properties of competitive prices in large economies.