In this paper we investigate the implementation problem arising when some of the players are “faulty” in the sense that they fail to act optimally. The planner and the non-faulty players only know that there can be at most k faulty players in the population. However, they know neither the identity of the faulty players, their exact number nor how faulty players behave. We define a solution concept which requires a player to optimally respond to the non-faulty players regardless of the identity and actions of the faulty players. We introduce a notion of fault tolerant implementation, which unlike standard notions of full implementation, also requires robustness to deviations from the equilibrium. The main result of this paper establishes that under symmetric information any choice rule that satisfies two properties—k-monotonicity and no veto power—can be implemented by a strategic game form if there are at least three players and the number of faulty players is less than 1\2n−1. As an application of our result we present examples of simple mechanisms that implement the constrained Walrasian function and a choice rule for the efficient allocation of an indivisible good.

The phenomenon of choice shifts in group decision-making has received attention in the social psychology literature. Faced with a risky group decision, individuals appear to support more extreme choices relative to those they would make on their own. This paper demonstrates that from a decision-theoretic perspective, choice shifts are intimately connected to failures of expected utility theory. In the model studied here, the Allais paradox is equivalent to a well-studied configuration of choice shifts. Thus, our results marry two well-known behavioral regularities, one in individual decision theory and another in the social psychology of groups.

In standard contract-theoretic models, the underlying assumption is that agent types differ in their preference or cost parameters, and the principal's objective is to design contracts in order to screen this type. We study a contract-theoretic model in which the heterogeneity among agent types is of a “cognitive” nature. In our model, the agent has dynamically inconsistent preferences. Agent types differ only in their degree of “sophistication”, that is, their ability to forecast the change in their future tastes. We fully characterize the menu of contracts which the principal offers in order to screen the agent's sophistication. The menu does not exclude any type: it provides a perfect commitment device for relatively sophisticated types, and “exploitative” contracts which involve speculation with relatively naive types. More naive types are more heavily exploited and generate a greater profit for the principal. Our results allow us to interpret real-life contractual arrangements in a variety of industries.

When two parties have different prior beliefs about some future event, they can realize gains through speculative trade. Can these gains be realized when the parties' prior beliefs are not common knowledge? We examine a simple example in which two parties having heterogeneous prior beliefs, independently drawn from some distribution, bet on what future action one of them will choose. We define a notion of "constrained interim-efficient" best and ask whether they can be implemented in Bayesian equilibrium by some mechanism. Our main result establishes that as the costs of unilaterally manipulating the bet's outcome become more symmetric across states, implementation becomes easier. In particular, when these costs are equal in both states, implementation is possible for any distribution.

Consumers purchase multiple types of goods but may be able to examine only a limited number of markets for the best price. We propose a simple model that captures these features, conveying new insights. A firm’s price can deflect or draw attention to its market, and consequently, limited attention introduces a new dimension of cross-market competition. We characterize the equilibrium and show that having partially attentive consumers improves consumer welfare. With less attention, consumers are more likely to miss the best offers; but enhanced cross-market competition decreases average price paid, as leading firms try to stay under the consumers’ radar.

We formalize the argument that political disagreements can be traced to a “clash of narratives.” Drawing on the “Bayesian Networks” literature, we represent a narrative by a causal model that maps actions into consequences, weaving a selection of other random variables into the story. Narratives generate beliefs by interpreting long-run correlations between these variables. An equilibrium is defined as a probability distribution over narrative-policy pairs that maximize a representative agent's anticipatory utility, capturing the idea that people are drawn to hopeful narratives. Our equilibrium analysis sheds light on the structure of prevailing narratives, the variables they involve, the policies they sustain, and their contribution to political polarization.

We study decentralized mechanisms for allocating firms into search pools. The pools are created in response to noisy preference signals provided by consumers, who then browse the pools via costly random sequential search. Surplus-maximizing search pools are implementable in symmetric Nash equilibrium. Full extraction of the maximal surplus is implementable if and only if the distribution of consumer types satisfies a set of simple inequalities, which involve the relative fractions of consumers who like different products and the Bhattacharyya coefficient of similarity between their conditional signal distributions. The optimal mechanism can be simulated by a keyword auction with broad matching.

A key feature of arbitration is the possibility for conflicting parties to participate in the selection of the arbitrator, the individual who will rule the case. We analyze this problem of the selection of arbitrators from the perspective of implementation theory. In particular, theoretical analyses document problems with veto-rank—a simultaneous procedure commonly used in practice—and develop a new sequential procedure—shortlisting—with better properties. Experimental results are consistent with the theoretical predictions, highlighting both the disadvantages associated with the veto-rank procedure and the advantages associated with the shortlisting procedure.