# On a private information game without pure strategy equilibria

Article Abstract:

An example of a two-person game of private information without pure strategy equilibria was presented. All the hypotheses of the existence theorems present in the literature on the subject of pure strategy equilibria were satisfied by the example. However, the example failed to account for the fact that the action set of each player is given by the interval (-1,1), which only illustrates the limitations pertaining to the purification of equilibria in a standard setting.

Publication Name: The Journal of Mathematical Economics

Subject: Mathematics

ISSN: 0304-4068

Year: 1999

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# Extremal structures and symmetric equilibria with countable actions

Article Abstract:

Proof concerning the symmetric equilibrium of an atomless anonymous game whose actions may be counted is derived. Specifically, it is shown that symmetric equilibria is attained by a Cournot-Nash equilibrium distribution only if it is an extreme point of the set of all Cournot-Nash equilibrium distributions of the game whose marginals are similar to Cournot-Nash equilibrium. This proof is based on the Krein-Milman theorem.

Publication Name: The Journal of Mathematical Economics

Subject: Mathematics

ISSN: 0304-4068

Year: 1995

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# The nonexistence of symmetric equilibria in anonymous games with compact action spaces

Article Abstract:

Players' actions and action distribution determine payoffs in anonymous games. Symmetric equilibrium distribution in an anonymous game exists when the game is atomless and there is a finite, or countably infinite and compact, set of actions that players can choose from. It is also possible to symmetrize every equilibrium distribution. The presence of these conditions in anonymous games is studied.

Publication Name: The Journal of Mathematical Economics

Subject: Mathematics

ISSN: 0304-4068

Year: 1995

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