We study chip-strategy equilibria in two-player repeated games. Intuitively, in these equilibria, players exchange favors by taking individually suboptimal actions if these actions create a "gain" for the opponent larger than the player's "loss" from taking them. In exchange, the player who provides a favor implicitly obtains from the opponent a chip that entitles the player to receiving a favor at some future date. Players are initially endowed with a number of chips, and a player who runs out of chips is no longer entitled to receive any favors until she provides a favor to the opponent, in which case she receives one chip back.We show that such simple chip strategies approximate efficient outcomes in a class of repeated symmetric games with incomplete information, in which each player has two possible types, when discounting vanishes. This class includes many important applications, studied in numerous previous papers, such as the favor-exchange model of Möbius (2001), repeated auctions, and the repeated version of Spulber duopolies of Athey and Bagwell (2001), among others. We also show the limitation of chip strategies. For example, if players have more than two types, then such simple chip strategies may not approximate efficient outcomes even in symmetric games.

We study a class of chip strategies in repeated games of incomplete information. This class generalizes the strategies studied by Möbius (2001) in the context of a favor-exchange model and the strategies studied in our companion paper, Olszewski and Safronov (2017). In two-player games, if players have private values and their types evolve according to independent Markov chains, then under very mild conditions on the stage game, the efficient outcome can be approximated by chip-strategy equilibria when the discount factor tends to 1. We extend this result (assuming stronger conditions) to stage games with any number of players. Chip strategies can be viewed as a positive model of repeated interactions, and the insights from our analysis seem applicable in similar contexts, not covered by the present analysis.

We study the impact of deliberation rules on collective learning and decision making in committees. In contrast to much of the existing literature, this article makes a distinction between the final votes over policy proposals and the cloture votes that bring them about. We show how deliberation rules can cause Paretoinefficient outcomes and failures to bring good proposals to a final vote, and how they affect the distribution of power among committee members in the deliberative process. We further show that deliberation rules are dynamically stable, even when they generate Pareto-inefficient outcomes.

This paper explores potential inefficiencies of incomplete contracts in a dynamic career concerns context. In a firm-worker relationship, the worker performs public tasks that have trade-offs between productivity and informativeness. We show that the first-best outcome can be obtained with short-term contracts if the wage can depend on the task choice. This provides an explanation for wage jumps at promotions—the worker is assigned the more productive but less informative task after promotion. If task choice is not contractible, then inefficiency arises: the worker has an endogenous bias toward informativeness, while the firm is biased toward productivity. (JEL D82, D83, D86, J24, J31, M51)

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