Multi-Dimensional All-Pay Contests

Abstract

In many real-world contest scenarios, contestants compete in multiple dimensions. In the context of all-pay contests, we examine two prevalent methods of organizing such competitions: a grand multi-dimensional (MD) contest, where a single winner is selected based on an aggregated performance measure across all dimensions, and a set of independent single-dimensional (SD) contests, where winners are determined based on their performance in each dimension. Our analysis demonstrates that the grand MD contest, with an optimal aggregated performance evaluation measure, outperforms a set of SD contests with optimally allocated SD prizes. When multiplicative handicaps are applied to contestants, this result continues to hold, with each contestant's expected payoff being zero in all optimally designed MD and SD contests.

Keywords: All-pay contests, Multi-dimensional contests, Single-dimensional contests, Optimal contest design.