We study the problem of achieving decentralized coordination by a group of strategic decision makers choosing to engage or not in a task in a stochastic setting. First, we define a class of symmetric utility games that encompass a broad class of coordination games, including the popular framework known as \textit{global games}. With the goal of studying the extent to which agents engaging in a stochastic coordination game indeed coordinate, we propose a new probabilistic measure of coordination efficiency. Then, we provide an universal information theoretic upper bound on the coordination efficiency as a function of the amount of noise in the observation channels. Finally, we revisit a large class of global games, and we illustrate that their Nash equilibrium policies may be less coordination efficient then certainty equivalent policies, despite of them providing better expected utility. This counter-intuitive result, establishes the existence of a nontrivial trade-offs between coordination efficiency and expected utility in coordination games.

翻译：我们研究了在随机设置下，由一组决策者选择参与或不参与任务来实现去中心化协调的问题。首先，我们定义了一个对称效用博弈类，包括广泛的协调博弈，包括已知为全局博弈框架的一类。为了研究代理人参与随机协调博弈的程度，我们提出了一种新的概率化协调效率度量方法。然后，我们提供了一个通用的信息论上界来衡量协调效率，该上界是观察通道中噪声量的函数。最后，我们重新审视了一大类全局博弈，并说明了它们的纳什均衡策略在协调效率上可能不如等价策略，尽管它们提供了更好的预期效用。这一令人反感的结果确立了协调博弈中协调效率和预期效用之间存在着非平凡的权衡。