Repeated Games with Switching Costs: Stationary vs History-Independent Strategies

Yevgeny Tsodikovich (), Xavier Venel () and Anna Zseleva ()
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Yevgeny Tsodikovich: Aix Marseille Univ, CNRS, AMSE, Marseille, France.
Xavier Venel: Dipartimento di Economia e Finanza, LUISS, Rome, Italy., https://sites.google.com/site/xaviervenelsite/home
Anna Zseleva: Maastricht University, School of Business and Economics, Dept. of Quantitative Economics, Maastricht, The Netherlands, http://annazseleva.com/

No 2129, AMSE Working Papers from Aix-Marseille School of Economics, France

Abstract: We study zero-sum repeated games where the minimizing player has to pay a certain cost each time he changes his action. Our contribution is twofold. First, we show that the value of the game exists in stationary strategies, depending solely on the previous action of the minimizing player, not the entire history. We provide a full characterization of the value and the optimal strategies. The strategies exhibit a robustness property and typically do not change with a small perturbation of the switching costs. Second, we consider a case where the minimizing player is limited to playing simpler strategies that are completely history-independent. Here too, we provide a full characterization of the (minimax) value and the strategies for obtaining it. Moreover, we present several bounds on the loss due to this limitation.

Keywords: switching costs; repeated games; stochastic games; zero-sum games (search for similar items in EconPapers)
JEL-codes: C72 C73 (search for similar items in EconPapers)
Pages: 40 pages
Date: 2021-05
New Economics Papers: this item is included in nep-gth and nep-ore
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