In many contests, players can influence their chances of winning through multiple activities or "arms". We develop a model of multi-armed contests and axiomatize its contest success function. We then analyze the outcomes of the multi-armed contest and the effects of allowing or restricting arms. Restricting an arm increases total effort directed to other arms if and only if restricting the arm balances the contest. Restricting an arm tends to reduce rent dissipation because it reduces the discriminatory power of the contest. But it also tends to increase rent dissipation if it balances the contest. Less rent is dissipated if an arm is restricted as long as no player is excessively stronger than the other with that arm. If players are sufficiently symmetric in an arm, both players are better off if that arm is restricted. Nevertheless, players cannot agree to restrict the arm if their costs of using the arm are sufficiently low.

We develop a model of dynamic multi‐activity contests. Players simultaneously choose efforts in long‐run activities, observe each other's efforts in these activities, and then simultaneously choose efforts in short‐run activities. A player's long‐run and short‐run efforts complement each other in determining the player's probability of winning. We compare the outcomes of this two‐stage model to those of the corresponding model in which players choose efforts in all activities simultaneously. Interestingly, effort expenditures are always lower in the sequential multi‐activity contest than in the simultaneous multi‐activity contest. The implications of this result for the organization of military, litigation, innovation, academic, and sporting contests are highlighted.

This paper compares the equilibrium outcomes in search markets with and without referrals. Although it seems clear that consumers would benefit from referrals, it is not at all clear whether firms would unilaterally provide information about competing offers since such information could encourage consumers to purchase the product elsewhere. In a model of a horizontally differentiated product market with sequential consumer search, we show that valuable referrals can arise in the equilibrium: a firm will give referrals to consumers whose ideal product is sufficiently far away from the firm's offering. We allow firms to price-discriminate among consumers, and consumers to misrepresent their tastes. We found that the equilibrium profits tend to be higher in markets with referrals than in markets without. Consumers tend to be better off in the presence of referrals when search costs are not too low, and under a certain parameter range, referrals lead to a Pareto improvement.

We compare equilibria in search markets with and without referrals.

We show that referrals can arise in horizontally differentiated product markets.

The equilibrium profits tend to be higher in markets with referrals.

Consumers tend to be better off under referrals when search costs are not too low.

Referrals can lead to a Pareto improvement.