Variational convergence: Approximation and existence of equilibria in discontinuous games

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14 Scopus citations


We introduce a notion of variational convergence for sequences of games and we show that the Nash equilibrium map is upper semi-continuous with respect to variationally converging sequences. We then show that for a game G with discontinuous payoff, some of the most important existence results of Dasgupta and Maskin, Simon, and Reny are based on constructing approximating sequences of games that variationally converge to G. In fact, this notion of convergence will help simplify these results and make their proofs more transparent. Finally, we use our notion of convergence to establish the existence of a Nash equilibrium for Bertrand-Edgeworth games with very general forms of tie-breaking and residual demand rules.

Original languageEnglish
Pages (from-to)1244-1268
Number of pages25
JournalJournal of Economic Theory
Issue number3
StatePublished - May 2010


  • Bertrand-Edgeworth games
  • Convergence of games
  • Discontinuous games
  • Equilibrium map

ASJC Scopus subject areas

  • Economics and Econometrics


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