We study the role of local effects and finite size effects in reaching coordination and in equilibrium selection in different types of two-player coordination games. We investigate three update rules -- the replicator dynamics (RD), the best response (BR), and the unconditional imitation (UI) -- for coordination games on random graphs. Local effects turn out to me significantly more important for the UI update rule. For the pure coordination game with two equivalent strategies we find a transition from a disordered state to a state of full coordination for a critical value of the network connectivity. The transition is system-size-independent for the BR and RD update rules. For the IU update rule 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 it 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.
翻译:我们研究了本地效应和有限规模效应在各类双玩协调游戏中实现协调和均衡选择的作用。我们调查了随机图形协调游戏的三个更新规则 -- -- 复制机动态(RD)、最佳响应(BR)和无条件仿真(UI) -- -- 随机图形协调游戏。对于UI更新规则而言,本地效应对我来说更为重要。对于两个等效战略的纯协调游戏,我们发现从混乱状态向网络连接关键值全面协调状态的过渡。过渡取决于BR和RD更新规则的系统规模。对于IMU更新规则取决于系统规模,但协调总是可以在完整图表的连通性下实现。我们还考虑到涵盖一系列游戏的一般协调游戏,例如星座狩猎。对于这些游戏来说,有一个报酬支配性策略和风险支配性战略,与相关的平衡协调状态有关。我们只分析平衡选择和数值。对于RD和RR更新规则的平均值预测与模拟和RD更新规则的全局效果相关,但协调总是在系统大小规则的连通性下实现。我们独立地观察了系统选择成本战略,而我们则要独立地观察当地货币稳定汇率。