Rent-Seeking Behavior in the War of Attrition

The object of this paper is to reexamine possible non-existence of Cournet-Nash equilibrium using the war of attrition, when there are increasing returns to rent-seeking expenditures. In our multi-person, multi-period model based on the war of attrition, each player, in addition to determining rent-seeking expenditures, plays a mixed strategy as to stay in or exit from rent-seeking competition in each period in a situation where his or her expected payoff from rent-seeking is negative. In such a setting the number of players is endogeneously determined over time so that surviving rent-seekers end up earning nonnegative expected payoffs in the long-run. We also conduct comparative statics analysis with respect to the degree of increasing returns to expenditures, the discount factor and the size of prize on the probability of exiting as well as on rent-seeking expenditures. In particular, we show that a decrease in the degree of increasing returns to expenditures on rent-seeking will increase social costs, contrary to the static Tullock model with a fixed number of players.