Better Reply Security and Existence of Equilibria in Differential Games

Research output: Contribution to journalArticlepeer-review


We establish the existence of Nash equilibria in a large class of differential games. More specifically, we show that certain differential games are compact and better reply secure when the strategy space is equipped with the weak topology. Therefore, we can claim that such games must have Nash equilibria even when the payoffs of some of the players are discontinuous. On one hand, verifying better reply security with respect to a nonmetrizable weak topology is technically involved and requires a number of theoretical tools from functional analysis. On the other hand, our approach will allow us to generalize a number of current existence results regarding linear-quadratic differential games, games of evasion and pursuit, as well as some classic differential games in economics.

Original languageEnglish
Pages (from-to)325-340
Number of pages16
JournalDynamic Games and Applications
Issue number3
StatePublished - Sep 2013


  • Better reply security
  • Differential games
  • Games of evasion and pursuit
  • Linear-quadratic differential games
  • Open-loop Nash equilibrium
  • Weak topology

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • Economics and Econometrics
  • Statistics and Probability
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Computer Graphics and Computer-Aided Design


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