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：我们研究了在随机环境中，一群战略决策者选择参与或不参与任务时实现去中心化协调的问题。首先，我们定义了一类包含广泛协调博弈的对称效用博弈，其中包括被称为“全局博弈”的流行框架。为了研究参与随机协调博弈的智能体实际协调的程度，我们提出了一种新的协调效率概率度量方法。随后，我们给出了基于观测通道噪声量的协调效率的通用信息论上界。最后，我们重新审视了一大类全局博弈，并说明其纳什均衡策略在协调效率上可能低于确定性等价策略，尽管前者能提供更好的期望效用。这一反直觉结果揭示了协调博弈中协调效率与期望效用之间存在非平凡的权衡关系。