Alexander Wolitzky

Reputational Bargaining With Minimal Knowledge of Rationality

Two players announce bargaining postures to which they may become committed and then bargain over the division of a surplus. The share of the surplus that a player can guarantee herself under first-order knowledge of rationality is determined (as a function of her probability of becoming committed), as is the bargaining posture that she must announce in order to guarantee herself this much. This “maxmin” share of the surplus is large relative to the probability of becoming committed (e.g., it equals 30% if the commitment probability is 1 in 10 and equals 13% if the commitment probability is 1 in 1000), and the corresponding bargaining posture simply demands this share plus compensation for any delay in reaching agreement.

Communication with tokens in repeated games on networks

A key obstacle to coordination and cooperation in many networked environments is that behavior in each bilateral relationship is not observable to individuals outside that relationship: that is, information is local. This paper investigates when players can use communication to replicate any outcome that would have been sustainable were this information public. A benchmark result is that if only cheap talk communication is possible then public information can only be replicated if the network is 2-connected: that is, if no player can prevent the flow of information to another. In contrast, the main result is that public information can always be replicated if in addition to cheap talk the players have access to undifferentiated tokens that can be freely transferred among neighbors (which bear some resemblance to certain models of fiat money). Sufficient conditions are provided for such tokens to expand the equilibrium payoff set, relative to what would be achievable without explicit communication or with cheap talk communication only.

Sustaining Cooperation: Community Enforcement vs. Specialized Enforcement

We introduce the possibility of direct punishment by specialized enforcers into a model of community enforcement. Specialized enforcers need to be given incentives to carry out costly punishments. Our main result shows that, when the specialized enforcement technology is sufficiently effective, cooperation is best sustained by a “single enforcer punishment equilibrium,” where any deviation by a regular agent is punished only once, and only by enforcers. In contrast, enforcers themselves are disciplined (at least in part) by community enforcement. The reason why there is no community enforcement following deviations by regular agent is that such actions, by reducing future cooperation, would decrease the amount of punishment that enforcers are willing to impose on deviators. Conversely, when the specialized enforcement technology is ineffective, optimal equilibria do punish deviations by regular agents with community enforcement. The model thus predicts that societies with more advanced enforcement technologies should rely on specialized enforcement, while less technologically advanced societies should rely on community enforcement. Our results hold both under perfect monitoring of actions and under various types of private monitoring.

Indeterminacy of reputation effects in repeated games with contracts

We study whether allowing players to sign binding contracts governing future play leads to reputation effects in repeated games with long-run players. We proceed by extending the analysis of Abreu and Pearce (2007) by allowing for the possibility that different behavioral types may not be immediately distinguishable from each other. Given any prior over behavioral types, we construct a modified prior with the same total weight on behavioral types and a larger support under which almost all efficient, feasible, and individually rational payoffs are attainable in perfect Bayesian equilibrium. Thus, whether reputation effects emerge in repeated games with contracts depends on details of the prior distribution over behavioral types other than its support.

Dynamic monopoly with relational incentives

This paper studies the price-setting problem of a monopoly that in each time period has the option of failing to deliver its good after receiving payment. The monopoly may be induced to deliver the good if consumers expect that the monopoly will not deliver in the future if it does not deliver today. If the good is non-durable and consumers are anonymous, the monopolys optimal strategy is to set price equal to the static monopoly price each period if the discount factor is high enough, and otherwise to set the lowest price at which it can credibly promise to deliver the good. If the good is durable, we derive an intuitive lower bound on the monopolys optimal profit for any discount factor and show that it converges to the optimal static monopoly profit as the discount factor converges to one, in contrast to the Coase conjecture. We also show that rationing the good is never optimal for the monopoly if there is an efficient resale market and that the best equilibrium in which the monopoly always delivers involves a strictly decreasing price path that asymptotes to a level weakly above the ratio of the monopolys marginal cost to the discount factor.

Bounding equilibrium payoffs in repeated games with private monitoring: Bounding equilibrium payoffs

We provide a simple sufficient condition for the existence of a recursive upper bound on (the Pareto frontier of) the sequential equilibrium payoff set at a fixed discount factor in two-player repeated games with imperfect private monitoring. The bounding set is the sequential equilibrium payoff set with perfect monitoring and a mediator. We show that this bounding set admits a simple recursive characterization, which nonetheless necessarily involves the use of private strategies. Under our condition, this set describes precisely those payoff vectors that arise in equilibrium for some private monitoring structure, if either non-stationary monitoring or communication is allowed.

Endogenous institutions and political extremism

The election of extreme political leaders is often associated with changes in political institutions. This paper studies these phenomena through a model in which the median voter elects a leader anticipating that he will impose institutional constraints—such as constitutional amendments, judicial appointments, or the implicit threat of a coup—that influence the behavior of future political challengers. It is typically optimal for the median voter to elect an extreme incumbent when democracy is less fully consolidated, when the costs of imposing institutional constraints are intermediate, and when the distribution of potential challengers is asymmetric. The median voter typically elects a more right-wing incumbent when the distribution of potential challengers shifts to the left. Implications of the model for the consolidation of democracy and institutional constraints are discussed, as are several related mechanisms through which politiciansʼ ability to affect institutions may lead voters to optimally elect extremists.

Maintaining Privacy in Cartels

It is conventional wisdom that transparency in cartels—monitoring of competitors’ prices, sales, and profits—facilitates collusion. However, in several recent cases cartels have instead worked to preserve the privacy of their participants’ actions and outcomes. Toward explaining this behavior, we show that cartels can sometimes sustain higher profits when actions and outcomes are observed only privately, because better information can hinder collusion by helping firms devise more profitable deviations from the collusive agreement. We provide conditions under which maintaining privacy is optimal for cartels that follow a market-segmentation strategy.