Moscow Institute of Physics and Technology, Institutsky lane 9, Dolgoprudny, Moscow region, 141700, Russian Federation.
Federal Research Center ″Computer Science and Control″ of the Russian Academy of Sciences, Vavilova street 44/2, Moscow, 119333, Russian Federation.
Sci Rep. 2022 Mar 16;12(1):4482. doi: 10.1038/s41598-022-08426-3.
Within the studies of human cooperation, there are gaps that require further investigation. One possible area for growth is developing theoretical concepts which describe high levels of cooperation. In this paper, we present a symmetrical quantal response equilibrium (QRE) in Prisoner's Dilemma game (PD) constructed in Markov strategies (tolerance to defection and mutual cooperation). To prove the adequacy of the resulting equilibrium, we compare it with the previously found Nash equilibrium in PD in Markov strategies: the QRE converges with the Nash equilibrium that corresponds with the theory. Next, we investigate the properties of QRE in PD in Markov strategies by testing it against experimental data. For low levels of rationality, the found equilibrium manages to describe high cooperation. We derive the levels of rationality under which the intersection between Nash and QRE occurs. Lastly, our experimental data suggest that QRE serves as a dividing line between behavior with low and high cooperation.
在人类合作的研究中，存在一些需要进一步调查的空白。一个可能的增长领域是发展描述高水平合作的理论概念。在本文中，我们提出了一个在囚徒困境博弈（PD）中构建的对称量子反应均衡（QRE），采用马尔可夫策略（对背叛的容忍和相互合作）。为了证明所得均衡的充分性，我们将其与 PD 中马尔可夫策略的纳什均衡进行了比较：QRE 与与理论相符的纳什均衡相收敛。接下来，我们通过对实验数据进行检验，研究了 PD 中马尔可夫策略下 QRE 的性质。对于低水平的理性，所发现的均衡成功地描述了高水平的合作。我们推导出了纳什均衡和 QRE 相交的理性水平。最后，我们的实验数据表明，QRE 是区分低合作和高合作行为的分界线。
