Template-type: ReDif-Paper 1.0
Author-Name: Flesch János 
Author-Name: Schoenmakers Gijs 
Author-Name: Vrieze Koos 
Author-workplace-name: METEOR
Title: Stochastic Games on a Product State Space
Abstract: We examine product-games, which are n-player stochastic games satisfying: (1) the state space is a product S(1)×…×S(n); (2) the action space of any player i only depends of the i-th coordinate of the state; (3) the transition probability of moving from s(i) ∈ S(i) to t(i) ∈S(i), on the i-th coordinate S(i)  of the state space, only depends on the action chosen by player i. So, as far as the actions and the transitions are concerned, every player i can play on the i-th coordinate of the product-game without interference of the other players. No condition is imposed on the payoff structure of the game. We focus on product-games with an aperiodic transition structure, for which we present an approach based on so-called communicating states. For the general n-player case, we establish the existence of 0-equilibria, which makes product-games one of the first classes within n-player stochastic games with such a result. In addition, for the special case of two-player zero-sum games of this type, we show that both players have stationary 0-optimal strategies. Both proofs are constructive by nature.
Keywords: Economics (Jel: A)
Series: Research Memoranda
Creation-Date: 2007
Number: 010
File-URL: http://digitalarchive.maastrichtuniversity.nl/fedora/objects/guid:0f33115c-5d59-4b5c-8e57-4d6c036373db/datastreams/ASSET1/content
File-Format: application/pdf
File-Size: 407782
Handle: RePEc:unm:umamet:2007010