Evolutionary equilibrium in contests with stochastic participation: Entry, effort and overdissipation

Abstract

This paper examines the evolutionary stability of behaviour in contests where players' participation can be stochastic. We find, for exogenously given participation probabilities, players exert more effort under the concept of a finite-population evolutionarily stable strategy (FPESS) than under Nash equilibrium (NE). We show that there is exante overdissipation under FPESS for sufficiently large participation probabilities, if, and only if, the impact function is convex. With costly endogenous entry, players enter the contest with a higher probability and exert more effort under FPESS than under NE. Importantly, under endogenous entry, overdissipation can occur for all (Tullock) contest success functions, in particular those with concave impact functions.

Optimal Price of Entry Into a Competition

“…2. Gu, Hehenkamp, and Leininger (2019) also consider endogenous entry, but at a fixed, rather than endogenously determined, cost. value and mass of prizes on the price and intensity of entry.…”

“…In addition, a number of studies have looked at contests with a stochastic number of players (Boosey, Brookins, and Ryvkin 2017, 2019; Fu, Jiao, and Lu 2011; Gu, Hehenkamp, and Leininger 2019; Kahana and Klunover 2015, 2016; Lim and Matros 2009; Münster 2006; Myerson and Wärneryd 2006). In that literature, nature exogenously draws the number of players, who then all participate in a contest 2 .…”

“…22 Gu, Hehenkamp, and Leininger (2019) also consider endogenous entry, but at a fixed, rather than endogenously determined, cost. …”