We consider rent-seeking contests between and within two equal-sized groups. Each group adopts one of three sequences: first internal then external contest, first external then internal contest, and simultaneous internal and external contests. Groups cannot unilaterally postpone a contest...

The n-player Tullock contest with complete information is known to admit explicit solutions in special cases, such as (i) homogeneous valuations, (ii) constant returns, and (iii) two contestants. But can that model be solved more generally? In this paper, we show that key characteristics of the...

Any symmetric mixed-strategy equilibrium in a Tullock contest with intermediate values of the decisiveness parameter ("2 R É") has countably infinitely many mass points. All probability weight is concentrated on those mass points, which have the zero bid as their sole point of accumulation....

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...

I examine the impact of risk preferences on efforts and winning probabilities in generalised Tullock contests between two players. The theoretical analysis yields two main results. First, I specify a sufficient condition on the agents’ comparative prudence under which a higher common level of...

I examine sequential round-robin tournaments with three and four symmetric players. Each player is matched once with each other player. If the matches are organized as Tullock contests (all-pay auctions), the tournament will be almost fair (highly discriminatory): subject to the position of...

It is shown that the n-player lottery contest admits a best-response potential (Voorneveld, 2000, Economics Letters). This is true also when the contest technology reflects the possibility of a draw. The result implies, in particular, the existence of a nontrivial example of a strictly...

It is shown that the equilibrium in the asymmetric Tullock contest is unique for parameter values r È 2. This allows proving a revenue ranking result saying that a revenue-maximizing designer capable of biasing the contest always prefers a contest technology with higher accuracy.

We examine the fairness and intensity of sequential round-robin tournaments with multiple prizes. With three symmetric players and two prizes, the tournament is completely fair if and only if the second prize is valued half of the first prize, regardless of whether matches are organized as...

I characterize the optimal accuracy level r of an unbiased Tullock contest between two players with heterogeneous prize valuations. The designer maximizes the winning probability of the strong player or the winner's expected valuation by choosing a contest with an all-pay auction equilibrium (r...