Understanding how agents form beliefs is crucial to understand choices. I propose an equilibrium framework where players best-respond to their beliefs and where beliefs are formed through sequentially sampling from the population distribution of opponents’ actions at a cost. In equilibrium, beliefs are random, but closely tied to the primitives of the model: payoffs, sampling costs and priors. Relying on properties I establish for the sequential sampling problem in individual decision-making settings – collapsing bounds, speed-accuracy complementarity and comparative statics results – we illustrate the ability of our solution concept to rationalize well-known deviations from Nash equilibrium as the own-payoff effect (Goeree and Holt, 2001) as well as recent experimental evidence that relate gameplay and response times.

Do incentive levels matter in strategic environments? Existing models disagree not only on whether gameplay is affected by incentive levels, the overall stakes players face, but also on why. In this paper, we present experimental evidence establishing that the level of incentives affects both gameplay and beliefs. Holding fixed the actions of the other player, we find that, in the context of dominance-solvable games, higher incentives make subjects more likely to best-respond to their beliefs. Moreover, higher incentives result in more responsive beliefs but not necessarily less biased. We provide evidence that incentives affect effort and that it is effort, and not incentives directly, that accounts for the changes in belief formation. The results support models where, in addition to choice mistakes, players exhibit costly attention.

We study a model of strategic interaction between producers and a monopolist platform that employs a recommendation system. We characterize the consumer welfare implications of the platform’s entry into the production market. The platform’s entry induces the platform to bias recommendations to steer consumers towards its own goods, which leads to equilibrium investment adjustments by the producers and lower consumer welfare. Further, we find that a policy separating recommendation and production is not always welfare improving. Our results highlight the ability of integrated recommender systems to serve as tools of vertical foreclosure.

This note introduces a new class of dominance-solvable games called diagonal games with several theoretical interesting properties that make them particularly well-suited for experimental applications.