2021/02/26 by Yevgeny Tsodikovich, Tsodikovich, Yevgeny, Xavier Venel +3
Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Game Theory and Applications #Game Theory and Voting Systems #Optimization and Control (math.OC) #Stochastic processes and financial applications #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2103.00045
openalex publication_date 2021/02/26 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We study zero-sum repeated games where the minimizing player has to pay a\ncertain cost each time he changes his action. Our contribution is twofold.\nFirst, we show that the value of the game exists in stationary strategies,\ndepending solely on the previous action of the minimizing player, not the\nentire history. We provide a full characterization of the value and the optimal\nstrategies. The strategies exhibit a robustness property and typically do not\nchange with a small perturbation of the switching costs. Second, we consider a\ncase where the minimizing player is limited to playing simpler strategies that\nare completely history-independent. Here too, we provide a full\ncharacterization of the (minimax) value and the strategies for obtaining it.\nMoreover, we present several bounds on the loss due to this limitation.\n