On the Strategic Equivalence of Linear Dynamic and Repeated Games

Joachim Hubmer ()

International Game Theory Review (IGTR), 2015, vol. 17, issue 03, 1-11

Abstract: Dynamic (or stochastic) games are, in general, considerably more complicated to analyze than repeated games. This paper shows that for every deterministic dynamic game that islinear in the state, there exists astrategically equivalentrepresentation as a repeated game. A dynamic game is said to be linear in the state if it holds for both the state transition function as well as for the one-period payoff function that (i) they are additively separable in action profiles and states and (ii) the state variables enter linearly. Strategic equivalence refers to the observation that the two sets of subgame perfect equilibria coincide, up to a natural projection of dynamic game strategy profiles on the much smaller set of repeated game histories. Furthermore, it is shown that the strategic equivalence result still holds for certain stochastic elements in the transition function if one allows for additional signals in the repeated game or in the presence of a public correlating device.

Keywords: Dynamic games; stochastic games; repeated games; C73 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0219198915500061

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