Department of Mathematics, London School of Economics and Political Science, London WC2A 2AE, United Kingdom.
Department of Quantitative Economics, Maastricht University, 6200 MD Maastricht, The Netherlands.
Proc Natl Acad Sci U S A. 2022 Mar 15;119(11):e2105867119. doi: 10.1073/pnas.2105867119. Epub 2022 Mar 8.
SignificanceNash equilibrium, of central importance in strategic game theory, exists in all finite games. Here we prove that it exists also in all infinitely repeated games, with a finite or countably infinite set of players, in which the payoff function is bounded and measurable and the payoff depends only on what is played in the long run, i.e., not on what is played in any fixed finite number of stages. To this end we combine techniques from stochastic games with techniques from alternating-move games with Borel-measurable payoffs.
纳什均衡在战略博弈论中具有核心重要性，它存在于所有有限博弈中。在这里，我们证明了在所有无限重复博弈中，也存在纳什均衡，其中参与者的数量是有限的或可数无限的，收益函数是有界的和可测的，收益只取决于长期内的行动，即不取决于任何固定有限数量阶段内的行动。为此，我们将随机博弈的技术与具有 Borel 可测收益的交替移动博弈的技术相结合。
