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A Note On Repeated Games With Vanishing Actions

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    (School of Business, Public Administration and Technology & Financial Engineering Laboratory, University of Twente, POB 217, 7500 AE Enschede, The Netherlands)

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    A two-person general-sum repeated game with vanishing actions is an infinitely repeated game where the players face the following restrictions. Each action must be used by player k ∈ {1,2} at least once in every rk ∈ ℕ consecutive stages, otherwise the action vanishes for the remaining play. We assume that the players wish to maximize their limiting average rewards over the entire time-horizon.A strategy-pair is jointly convergent if for each action pair a number exists to which the relative frequency with which this action pair is chosen, converges with probability one. A pair of feasible rewards is called individually rational if each player receives at least the threat-point reward, i.e., the amount which he can guarantee himself regardless of what the opponent does given r1, r2 and the actions available in the long run. In a repeated game with vanishing actions, there may exist multiple threat points which are endogenous to the play.We prove that all individually-rational jointly-convergent pure-strategy rewards can be supported by an equilibrium. Furthermore, each convex combination of individually-rational jointly-convergent pure-strategy rewards, can be supported by an equilibrium for m × n-games provided r1 > m ≥ 2, r2 > n ≥ 2.

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    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

    Volume (Year): 07 (2005)
    Issue (Month): 01 ()
    Pages: 107-115

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    Handle: RePEc:wsi:igtrxx:v:07:y:2005:i:01:p:107-115
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