Contest success function with the possibility of a draw: Axiomatization

Abstract

Abstract:In imperfectly discriminating contests the contestants contribute effort to win a prize but the highest contributed effort does not necessarily secure a win. The contest success function (CSF) is the technology that translates an individual's effort into his or her probability of winning. This paper provides an axiomatization of CSF when there is the possibility of a draw (the sum of winning probabilities across all contestants is non-additive).

On the Existence of Nash Equilibrium in Bayesian Games

“…To see this, it suffices to set each h i equal to zero and define f i (t, b) as the profit of a monopolist i at price b i given a type profile t ∈ T. 15 Observe that implicit in this interpretation of (5) is the assumption that individual cost functions are identical across firms.…”

“…In an imperfectly discriminating contest, the agent who expends the greatest effort has the highest probability of winning but this probability may be less than one. For examples and analyses of imperfectly discriminating contests with complete information, see, e.g., Blavatskyy [15], Szymanski [73], Nitzan [54,55], Nti [57], and Rosen [65]. For a model of an imperfectly discriminating contest with incomplete information and continuous payoffs, see Wasser [78], which proves the existence of a monotone pure strategy equilibrium using the results of Athey [5].…”

Contest Success Functions: The Common-Pool Perspective

“…This aspect of the common-pool approach should be welcomed because numerous applications of contest theory work with two-person contests as a main building block. 17 Relatedly, as we discussed, the common-pool approach to the axiomatic foundation of CSF resolves an important issue recently identi…ed by Blavatskyy (2010). However, based upon a novel induction argument, the common-pool perspective delivers concise axiom sets also for contests with more than two players.…”

The Lottery Contest is a Best-Response Potential Game

“…In the …rst part, we show that the n-player lottery contest admits a BR-potential. This holds true regardless of whether the contest allocates the prize with probability one (Haavelmo, 1954;Tullock, 1975;Bell et al, 1975;Baron, 1994) or there is a probability of a draw (Loury, 1979;Dasgupta and Nti, 1998;Blavatskyy, 2010;Jia, 2012). 1 In the second part of the paper, we exploit the useful strategic equivalence between contests and zero-sum games, 2 so as to derive a perplexing implication of our result.…”