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Games 2017, 8(4), 47; doi:10.3390/g8040047

Construction of Subgame-Perfect Mixed-Strategy Equilibria in Repeated Games

1
Department of Mathematics and Systems Analysis, Aalto University School of Science, P.O. Box 11100, FI-00076 Aalto, Finland
2
Department of Data Science and Knowledge Engineering, Maastricht University, P.O. Box 616, 6200MD Maastricht, The Netherlands
*
Author to whom correspondence should be addressed.
Received: 26 July 2017 / Revised: 28 September 2017 / Accepted: 18 October 2017 / Published: 1 November 2017
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Abstract

This paper examines how to construct subgame-perfect mixed-strategy equilibria in discounted repeated games with perfect monitoring. We introduce a relatively simple class of strategy profiles that are easy to compute and may give rise to a large set of equilibrium payoffs. These sets are called self-supporting sets, since the set itself provides the continuation payoffs that are required to support the equilibrium strategies. Moreover, the corresponding strategies are simple as the players face the same augmented game on each round but they play different mixed actions after each realized pure-action profile. We find that certain payoffs can be obtained in equilibrium with much lower discount factor values compared to pure strategies. The theory and the concepts are illustrated in 2 × 2 games. View Full-Text
Keywords: repeated game; mixed strategy; subgame perfection; payoff set repeated game; mixed strategy; subgame perfection; payoff set
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Berg, K.; Schoenmakers, G. Construction of Subgame-Perfect Mixed-Strategy Equilibria in Repeated Games. Games 2017, 8, 47.

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