Continuous-time dynkin games with mixed strategies

Nizar Touzi, Nicolas Vieille

Research output: Contribution to journalArticlepeer-review


Let (X, Y, Z) be a triple of payoff processes defining a Dynkin game R̃(σ,τ) = E[Xσ1{τ>σ + Yτ1{τ<σ} + Zτ1 τ=σ],where σ and τ are stopping times valued in [0, T]. In the case Z = Y, it is well known that the condition X ≤ Y is needed in order to establish the existence of value for the game, i.e., inf τ supσ R̃(σ τ) = sup σ infτR̃(σ, τ). In order to remove the condition X ≤ Y, we introduce an extension of the Dynkin game by allowing for an extended set of strategies, namely, the set of mixed strategies. The main result of the paper is that the extended Dynkin game has a value when Z ≤ Y, and the processes X and Y are restricted to be semimartingales continuous at the terminal time T.

Original languageEnglish (US)
Pages (from-to)1073-1088
Number of pages16
JournalSIAM Journal on Control and Optimization
Issue number4
StatePublished - 2003


  • Dynkin games
  • Minimax theorem
  • Optimal stopping
  • Stochastic analysis

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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