Multi-activity contests

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.