Representing equilibrium aggregates in aggregate games with applications to common agency |
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| Institution: | 1. Paris School of Economics-EHESS, France;2. University of Chicago, Booth School of Business, United States;1. Dept. of Mathematics, University of Bayreuth, Germany;2. Economic Department, SOCIUM, University of Bremen, Germany;3. Dept. of Economics, University of Bayreuth, Germany;1. Department of Econometrics and OR, Tilburg University, The Netherlands;2. Chair of Political Economy, ECON Institute, Karlsruhe Institute of Technology, Germany;3. Economics of Change, Berlin Social Science Center, Germany;4. CESifo, Germany;1. Washington University in St. Louis, United States;2. MIT, United States;1. Imperial College London, UK, and Université d''Evry, France;2. LACL, Université Paris-Est Créteil, France;3. Institute of Computer Science, Polish Academy of Sciences, Poland;1. Faculty of Economics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan;2. Department of Economics, National University of Singapore, AS2 Level 6, 1 Arts Link, Singapore 117570, Singapore |
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| Abstract: | An aggregate game is a normal-form game with the property that each player?s payoff is a function of only his own strategy and an aggregate of the strategy profile of all players. Such games possess properties that can often yield simple characterizations of equilibrium aggregates without requiring that one solves for the equilibrium strategy profile. When payoffs have a quasi-linear structure and a degree of symmetry, we construct a self-generating maximization program over the space of aggregates with the property that the solution set corresponds to the set of equilibrium aggregates of the original n-player game. We illustrate the value of this approach in common-agency games where the players? strategy space is an infinite-dimensional space of nonlinear contracts. We derive equilibrium existence and characterization theorems for both the adverse selection and moral hazard versions of these games. |
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