This paper considers rent-seeking games in which a small percentage change in a player's bid has a large percentage impact on her odds of winning, i.e., on the ratio of her respective probabilities of winning and losing. An example is the Tullock contest with a high R. The analysis provides a fairly complete characterization of the equilibrium set. In particular, for "sufficiently generic" valuations, any equilibrium of the rent-seeking game is shown to be both payoff- and revenue-equivalent to the first-price all-pay auction. For general valuations, the analysis establishes a robustness property of the all-pay auction.
Rent-seeking games mixed-strategy Nash equilibrium robustness of the all-pay auction Tullock contest