SUBGAME CONSISTENT SOLUTION FOR COOPERATIVE STOCHASTIC DYNAMIC GAMES WITH RANDOM HORIZON

David W. K. Yeung () and Leon A. Petrosyan ()
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David W. K. Yeung: SRS Consortium for Advanced Study in Cooperative Dynamic Games, Hong Kong Shue Yan University, Center of Game Theory, St Petersburg State University, St Petersburg, 198904, Russia
Leon A. Petrosyan: Faculty of Applied Mathematics-Control Processes, St Petersburg State University, St Petersburg, 198904, Russia

International Game Theory Review (IGTR), 2012, vol. 14, issue 02, 1-22

Abstract: In cooperative stochastic dynamic games a stringent condition — that of subgame consistency — is required for a dynamically stable cooperative solution. In particular, a cooperative solution is subgame consistent if an extension of the solution policy to a subgame starting at a later time with a state brought about by prior optimal behavior would remain optimal. This paper extends subgame consistent solutions to cooperative stochastic dynamic (discrete-time) games with random horizon. In the analysis new forms of the stochastic Bellman equation and the stochastic Isaacs–Bellman equation in discrete time are derived. Subgame consistent cooperative solutions are obtained for stochastic dynamic games. Analytically tractable payoff distribution mechanisms which lead to the realization of these solutions are developed. This is the first time that subgame consistent solutions for cooperative stochastic dynamic games with random horizon are presented.

Keywords: Stochastic dynamic games; Random horizon; Stochastic Bellman equation; Stochastic Hamilton–Jacobi–Bellman equation (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1142/S0219198912500120

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