RECURSIVE CONSTRUCTION OF A NASH EQUILIBRIUM IN A TWO-PLAYER NONZERO-SUM STOPPING GAME WITH ASYMMETRIC INFORMATION

Royi Jacobovic*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study a discrete-time finite-horizon two-player nonzero-sum stopping game where the filtration of Player 1 is richer than the filtration of Player 2. A major difficulty which is caused by the information asymmetry is that Player 2 may not know whether Player 1 has already stopped the game or not. Furthermore, the classical backward-induction approach is not applicable in the current setup. This is because when the informed player decides not to stop, he reveals information to the uninformed player, and hence the decision of the uninformed player at time t may be determined not only by the play after time t, but also by the play before time t. In the current work we initially show that the expected utility of Player 2 will remain the same even if he knows whether Player 1 has already stopped. Then, this result is applied in order to prove that, under appropriate conditions, a recursive construction in the style of Hamad\`ene and Zhang (2010) converges to a pure-strategy Nash equilibrium.

Original languageEnglish
Pages (from-to)3289-3301
Number of pages13
JournalSIAM Journal on Control and Optimization
Volume60
Issue number6
DOIs
StatePublished - 2022
Externally publishedYes

Keywords

  • Dynkin games
  • Nash equilibrium
  • asymmetric information
  • nonzero-sum games

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