Trigger strategy equilibriums in stochastic differential games with information time lags: An analysis of cooperative production strategies

T. Yao, Susan H. Xu, Bin Jiang

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

In the current literature of differential games, most studies formulate optimal strategies in feedback (Markovian) equilibriums and ignore repeated interactions among players. In many real-world settings, however, the competitors' action history may have impacts on a firm's decisions. This paper considers the production strategies for several competing firms in an oligopolistic industry. A firm's profit is determined by a continuous-time stochastic demand shock process together with the production strategies of all firms in the industry. A firm's decision is only observable by other firms after an information time lag, induced by the production lead time. We study a history-dependent trigger strategy, whereby firms adopt the cooperative strategy until a firm fails to do so, and thereafter punish the deviating firm by applying the noncooperative equilibrium. We show that, as long as the information time lag is less than a threshold, the trigger strategy is both a Nash equilibrium and a Pareto optimum. We obtain the analytical solutions to the threshold and investigate how the threshold is affected by market growth rate, market volatility, the number of competitors in the industry, and the risk-free rate. Moreover, we investigate the repeated games in a continuous-time setting and provide a tractable approach to derive the trigger-type repeated equilibrium in a Nash-Cournot framework. While the derivation of equilibrium strategies in a stochastic continuous-time setting can be quite challenging, we obtain a solution that is not only analytically simple but also practically applicable.

Original languageEnglish (US)
Pages (from-to)1197-1220
Number of pages24
JournalSIAM Journal on Control and Optimization
Volume49
Issue number3
DOIs
StatePublished - Jul 20 2011

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Trigger strategy equilibriums in stochastic differential games with information time lags: An analysis of cooperative production strategies'. Together they form a unique fingerprint.

  • Cite this