Common information based Markov perfect equilibria for linear-Gaussian games with asymmetric information

Abhishek Gupta, Ashutosh Nayyar, Cedric Langbort, M Tamer Basar

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a class of two-player dynamic stochastic nonzero-sum games where the state transition and observation equations are linear and the primitive random variables are Gaussian. Each of the two players/controllers of the system acquires possibly different dynamic information about the state process and the other controller's past actions and observations. This leads to a dynamic game of asymmetric information among the controllers. Building on our earlier work on finite games with asymmetric information, we devise an algorithm to compute a Nash equilibrium by using the common information among the controllers. We call such equilibria common information based Markov perfect equilibria of the game, which can be viewed as a refinement of Nash equilibrium in games with asymmetric information. If the players' cost functions are quadratic, then we show that under certain conditions a unique common information based Markov perfect equilibrium exists. Furthermore, this equilibrium can be computed by solving a sequence of linear equations. We also show through an example that there could be other Nash equilibria in a game of asymmetric information that are not common information based Markov perfect equilibria.

Original languageEnglish (US)
Pages (from-to)3228-3260
Number of pages33
JournalSIAM Journal on Control and Optimization
Volume52
Issue number5
DOIs
StatePublished - Jan 1 2014

Keywords

  • Dynamic games
  • Games with asymmetric information
  • Stochastic games

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Common information based Markov perfect equilibria for linear-Gaussian games with asymmetric information'. Together they form a unique fingerprint.

Cite this