Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Palma, Spain.
Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland.
Sci Rep. 2022 Mar 1;12(1):3373. doi: 10.1038/s41598-022-07195-3.
We study the role of local effects and finite size effects in reaching coordination and in equilibrium selection in two-player coordination games. We investigate three update rules - the replicator dynamics (RD), the best response (BR), and the unconditional imitation (UI). For the pure coordination game with two equivalent strategies we find a transition from a disordered state to coordination for a critical value of connectivity. The transition is system-size-independent for the BR and RD update rules. For the IU it is system-size-dependent, but coordination can always be reached below the connectivity of a complete graph. We also consider the general coordination game which covers a range of games, such as the stag hunt. For these games there is a payoff-dominant strategy and a risk-dominant strategy with associated states of equilibrium coordination. We analyse equilibrium selection analytically and numerically. For the RD and BR update rules mean-field predictions agree with simulations and the risk-dominant strategy is evolutionary favoured independently of local effects. When players use the unconditional imitation, however, we observe coordination in the payoff-dominant strategy. Surprisingly, the selection of pay-off dominant equilibrium only occurs below a critical value of the network connectivity and disappears in complete graphs. As we show, it is a combination of local effects and update rule that allows for coordination on the payoff-dominant strategy.
我们研究了局部效应和有限尺寸效应在两人协调博弈中的协调和均衡选择中的作用。我们研究了三种更新规则 - 复制者动力学（RD）、最佳响应（BR）和无条件模仿（UI）。对于具有两个等效策略的纯协调博弈，我们发现对于连接性的临界值，从无序状态到协调的转变。BR 和 RD 更新规则的转变与系统大小无关。对于 IU，它与系统大小有关，但协调总是可以在完全图的连接性以下达到。我们还考虑了一般协调博弈，它涵盖了一系列游戏，如猎鹿游戏。对于这些游戏，有一个收益主导策略和一个风险主导策略，具有相关的均衡协调状态。我们从理论和数值上分析了均衡选择。对于 RD 和 BR 更新规则，平均场预测与模拟一致，风险主导策略独立于局部效应而在进化上受到青睐。然而，当玩家使用无条件模仿时，我们观察到收益主导策略中的协调。令人惊讶的是，收益主导均衡的选择仅在网络连接性的临界值以下发生，并且在完全图中消失。正如我们所展示的，是局部效应和更新规则的组合允许在收益主导策略上进行协调。
