<経済学部優秀卒業論文賞受賞論文>Effort Allocations in Elimination Tournaments with Different Fatigue Parameters for Each Stage

Abstract

In this paper, we study an elimination tournament with n stages by 2n symmetric players, generalizing Sela's [2022] model. The probability that a player will win in a race against an opponent is determined by the amount of effort invested by each player (Tullock 1980). Each player has a common amount of effort budget: the budget constraint for a given stage is the budget constraint for the preceding stage, discounted by the fatigue parameter specific to each stage of the effort spent in that stage. We analyze the optimal allocation of effort for each player, and show that the optimal allocation of effort at a stage maximizes the expected payoff independent of the fatigue parameters at earlier stages and dependent only on the budget constraint at that stage. Also, if there is regularity in the fatigue parameters, ensure that the fatigue parameters should always be constant in order to make the tournament more exciting.