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Title: | The nonexistence of symmetric equilibria in anonymous games with compact action spaces | Authors: | Rath, K.P. Yeneng, S. Shinji, Y. |
Keywords: | Atomless game Cournot-Nash equilibrium distribution (CNED) Symmetric CNED Symmetrization |
Issue Date: | 1995 | Citation: | Rath, K.P.,Yeneng, S.,Shinji, Y. (1995). The nonexistence of symmetric equilibria in anonymous games with compact action spaces. Journal of Mathematical Economics 24 (4) : 331-346. ScholarBank@NUS Repository. | Abstract: | In an anonymous game the payoff of a player depends upon the player's own action and the action distribution of all the players. If the game is atomless and the set of actions is finite, or countably infinite and compact, then there is a symmetric equilibrium distribution. Furthermore, every equilibrium distribution can be symmetrized. This note provides three examples to the effect that the conditions in these results cannot be relaxed. The first example is a game with atoms and finite actions which has no symmetric equilibrium distribution. In the second example, the game is atomless, the action space is uncountable and not every equilibrium distribution can be symmetrized. The third example shows that a symmetric equilibrium distribution may not exist in an atomless game with the interval [ - 1, 1]as the action space. A general construction then exhibits that given any uncountable compact metric space, there is an atomless game over that space which has no symmetric equilibrium distribution. A sufficient condition for an equilibrium distribution to be symmetrized is also given. © 1995. | Source Title: | Journal of Mathematical Economics | URI: | http://scholarbank.nus.edu.sg/handle/10635/104321 | ISSN: | 03044068 |
Appears in Collections: | Staff Publications |
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