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Better response dynamics and Nash equilibrium in discontinuous games

Kukushkin, Nikolai S. (2017): Better response dynamics and Nash equilibrium in discontinuous games.

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Abstract

Philip Reny's approach to games with discontinuous utility functions can work outside its original context. The existence of Nash equilibrium and the possibility to approach the equilibrium set with a finite number of individual improvements are established, under conditions weaker than the better reply security, for three classes of strategic games: potential games, games with strategic complements, and aggregative games with appropriate monotonicity conditions.

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