Thomas Wiseman

Reputation and impermanent types

I consider a version of the chain store game where the incumbent firm’s type evolves according to a Markov process with two states: a “tough†type who always fights entry, and a “weak†type who prefers to accommodate. There exists a minimal level of persistence necessary for the incumbent to be able to sustain any reputation for being tough. Above that level, as the number of markets T increases, in equilibrium play alternates between intervals of entry by competitors and intervals of deterrence. When T is infinite, then regardless of the discount factor there exists a sequential equilibrium in which the incumbent’s payoff is bounded below her Stackelberg payoff. Both results are in contrast to the outcome when the incumbent’s type is fixed. One interpretation is that reputation is not permanent, but must be renewed occasionally

A partial folk theorem for games with private learning

The payoff matrix of a finite stage game is realized randomly, and then the stage game is repeated infinitely. The distribution over states of the world (a state corresponds to a payoff matrix) is commonly known, but players do not observe nature’s choice. Over time, they can learn the state in two ways. After each round, each player observes his own realized payoff (which may be stochastic, conditional on the state), and he observes a noisy public signal of the state (whose informativeness may vary with the actions chosen). Actions are perfectly observable. The result is that for any function that maps each state to a payoff vector that is feasible and individually rational in that state, there is a sequential equilibrium in which patient players learn the realized state with arbitrary precision and achieve a payoff close to the one specified for that state. That result extends to the case where there is no public signal, but instead players receive very closely correlated private signals of the vector of realized payoffs.

Reputation and Exogenous Private Learning

Short-run competitors in the chain store game receive noisy signals of the long-run incumbent firms type. The history of signals, which in the limit is fully revealing, is observable to the competitors but possibly not to the incumbent. As long as there is sufficient noise in the signals, then in any equilibrium a patient weak incumbent obtains a payoff strictly higher than her minmax payoff.

The impact of gun laws: A model of crime and self-defense

We develop a model of crime and self-defense that provides a rationale both for the right to bear arms and for regulating this right. It also suggests that a severe punishment for gun crime might best guarantee both the security and freedom of potential victims.

A Simple Model Of Optimal Hate Crime Legislation

We present a simple model of the effects of hate crime legislation. It shows that even if the direct harm to victims of hate crime is the same as for other crimes, because of other differences in the effects it may still be optimal to exert more law-enforcement effort to deter or prevent hate crime. These differences also have previously unrecognized effects on the optimal level of effort by potential hate crime victims to avoid being victimized, thus affecting the efficiency of government policies that encourage or discourage such effort. We discuss the implications of these results for optimal hate-crime policy, as well as for policy toward other similar crimes, such as terrorism.

War and Stability in Dynamic International Systems

We present a dynamic, complete-information bargaining model of war with N countries. The analysis of a network with more than two countries significantly generalizes previous work. We consider an environment where a country’s military strength varies stochastically over time as a function of endogenous consumption. If countries are sufficiently patient, then war is inevitable and will quickly spread throughout the network. We leverage insights from the limiting case to identify two key factors that promote peace among countries with limited patience: peace is easier to sustain when countries have equal military strength or when mechanisms exist to preserve any existing inequalities. Varying the number of countries does not have a consistent effect.

When Does Predation Dominate Collusion

I study repeated competition among oligopolists. The only novelty is that firms may go bankrupt and permanently exit: the probability that a firm survives a price war depends on its financial strength, which varies stochastically over time. Under some conditions including no entry, an anti‐folk theorem holds: when firms are patient, so that strength levels change relatively quickly, every Nash equilibrium involves an immediate price war that lasts until at most one firm remains. Surprisingly, the possibility of entry may facilitate collusion, as may impatience. The model can explain some observed patterns of collusion and predation.