The Price of Anarchy of Self-Selection in Tullock Contests

Crowdsourcing platforms operate by offering their clients the ability to obtain cost-effective solutions for their problems through contests. The top contestants with the best solutions are rewarded, and the submitted solutions are provided to the clients. Within the platforms, the contestants can self-select which contest they compete in. In this paper, we measure crowdsourcing efficiency induces by the strategic behavior of contestants. We first propose a game-theoretic model of self-selection in Tullock contests (SSTC). To study the efficiency of SSTC, we establish the existence of a pure-strategy Nash equilibrium (PSNE). We then study the efficiency, via the price of anarchy (PoA), that comes from the worst-case equilibria of SSTC. We develop general efficiency PoA bounds with respect to PSNE, fully mixed NE, and general equilibrium concepts. For the case of identical contestants, we show that the pure and fully mixed PoA are one when the number of contestants is large -- implying self-selection is efficient. In simulations, we show that an empirical bound well approximates the pure PoA, and the bound goes to one as the number of contestants becomes large.