Optimal reimbursement schemes in contests

Many contests, such as innovation races or litigation, often involve reimbursement of expenses. This study examines optimal reimbursement schemes in two-player Tullock contests, analyzing four reimbursement structures: external and internal mechanisms targeting the contest winner or loser. We assess the implications on participant effort, winning probabilities, and designer payoff, under two key conditions: fairness (preserving initial win chances) and viability (positive efforts from players). We find that while external reimbursement for the loser ensures both fairness and viability, full reimbursement to the winner fails to meet these criteria. Additionally, the findings indicate that optimal reimbursement structures and proportions vary depending on the contest designer's objectives, such as maximizing effort or personal payoff.