Abstract: We consider a two-player game of war of attrition under complete information. Our main result shows that if the players' payoffs whilst fighting for the prize vary stochastically, and their exit payoffs are heterogeneous, then the game admits Markov Perfect equilibria in pure strategies only. This result holds irrespective of the degree of randomness and heterogeneity, thus highlighting the fragility of mixed-strategy equilibria to a natural perturbation of the canonical model. In contrast, when the players' flow payoffs are deterministic or their exit payoffs are homogeneous, we show that the game admits equilibria in pure, as well as in mixed strategies.
Abstract: Consider an agent who can costlessly add mean-preserving noise to his output. To deter such risk-taking, the principal optimally offers a contract that makes the agent's utility concave in output. If the agent is risk-neutral and protected by limited liability, optimal incentives are strikingly simple: linear contracts maximize profit. If the agent is risk averse, we characterize the unique profit-maximizing contract and show how deterring risk-taking affects the insurance-incentive tradeoff. We extend our model to analyze costly risk-taking and alternative timings, and reinterpret our model as a dynamic setting in which the agent can manipulate the timing of output.
Abstract: Two heterogeneous agents contribute over time to a joint project, and collectively decide its scope. A larger scope requires greater cumulative effort and delivers higher benefits upon completion. We show that the efficient agent prefers a smaller scope, and preferences are time-inconsistent: as the project progresses, the efficient (inefficient) agent's preferred scope shrinks (expands). We characterize the equilibrium outcomes under dictatorship and unanimity, with and without commitment. We find that an agent's degree of efficiency is a key determinant of control over project scopes. From a welfare perspective, it may be desirable to allocate decision rights to the inefficient agent.