Correlated equilibria arise naturally when agents communicate or rely on intermediaries such as recommendation systems.We study when a given Nash equilibrium can be improved within the set of correlated equilibria for general objectives.Our key insight is a detail-free criterion: any Nash equilibrium with three or more randomizing agents is generically improvable.We refine this insight to specific classes of games and objectives, including Pareto and utilitarian welfare, and provide constructive methods to obtain improvements.Our findings underscore the ubiquity of improvable Nash equilibria and the crucial role of correlation in enhancing strategic outcomes.

The search for good outcomes-be it government policies, technological breakthroughs, or a lasting purchase-takes time and effort. In this paper, we consider a continuous-time search setting. Discoveries beget discoveries and their observations are correlated over time, which we model using a Brownian motion. A searching agent makes two critical decisions: how ambitiously or broadly to search at any point, and when to cease search. Once search stops, the agent is rewarded for the best outcome observed throughout her search. We call this search process retrospective search.

A key tension in the study of experimentation revolves around the exploration of new possibilities and the exploitation of prior discoveries. Starting from Robbins (1952), a large literature in economics and statistics has married the two: Agents experiment by selecting potentially risky options and observing their resulting payoffs. This framework has been used in many applications, ranging from pricing decisions to labor market search. Nonetheless, in many applications, agents' exploration and exploitation need not be intertwined. An investor may study stocks she is not invested in, an employee may explore alternative jobs while working, etc. The current paper focuses on the consequences of disentangling exploration from exploitation.