In economic theory, the concept of externality refers to any indirect effect resulting from an interaction between players that affects the social welfare. Most of the models within which externality has been studied assume that agents have perfect knowledge of their environment and preferences. This is a major hindrance to the practical implementation of many proposed solutions. To address this issue, we consider a two-player bandit setting where the actions of one of the players affect the other player and we extend the Coase theorem [Coase, 1960]. This result shows that the optimal approach for maximizing the social welfare in the presence of externality is to establish property rights, i.e., enable transfers and bargaining between the players. Our work removes the classical assumption that bargainers possess perfect knowledge of the underlying game. We first demonstrate that in the absence of property rights, the social welfare breaks down. We then design a policy for the players which allows them to learn a bargaining strategy which maximizes the total welfare, recovering the Coase theorem under uncertainty.

翻译：在经济学理论中，外部性概念指的是玩家间互动所产生的、影响社会福利的任何间接效应。现有研究外部性的大多数模型均假设参与者对其环境与偏好具备完全知识。这一假设是许多已提出方案在实际应用中的主要障碍。为解决此问题，我们考虑一个双玩家赌博机场景，其中一位玩家的行动会影响另一位玩家，并由此拓展了科斯定理[Coase, 1960]。该定理表明，在存在外部性的情况下，最大化社会福利的最优途径是建立产权，即允许玩家之间进行转移支付与议价。我们的研究摒弃了传统模型中议价者完全了解底层博弈的假设。我们首先证明，在缺乏产权的情况下，社会福利将出现崩溃。随后，我们为玩家设计了一种策略，使其能够学习最大化总福利的议价策略，从而在不确定性条件下重新验证科斯定理。