Monotone Equilibria in Games with Maxmin Expected Utility
(Job Market Paper)
I introduce ambiguity aversion to a class of games that includes the all-pay auction and war of attrition. The main result is a characterization of the set of increasing equilibria. Unlike with subjective expected utility, even when beliefs are independent of type, an increasing equilibrium may not exist. Sufficient conditions are provided for such an equilibrium to exist. The games are compared in terms of the expected sum of expenditures.
Elimination Contests with Endogenous Budgets With Gagan Ghosh
We model budgets in a contest where player's compete with one another in preliminary rounds and the winners of the preliminary rounds then compete in a final to determine the winner of a prize. Such a format is common in political competitions, sports, and labor promotion tournaments. Each contestant's budget is endogenously determined by a set of strategic players called backers. Total spending is increasing in the fraction of unused funds that are returned to backers; however, the backers expected payoff is increasing in the fraction returned. When backers cannot provide more resources in the final stage the total expenditure is higher than when backer can provide resources throughout the game. This suggests that in political contests sufficient time, between the preliminary and general election, should be provided to replenish budgets.
Sequential Contests with Endogenous Budgets With Gagan Ghosh
We model contests such as political campaigns, research and development contests, war, and sports competitions. The dynamic aspect is modeled by a series. We show that if the two backers are symmetric, in equilibrium the backers will replicate the expenditure of a game in which backers directly control the timing of expenditure. Spending is highest when the backer is only permitted to provide resources at the beginning of the game. When backers are asymmetric, if the stronger campaign falls behind, the backer can use the budget as a commitment tool.