Optimal reimbursement schemes in contests

Many contests, such as innovation races or sport competitions, often involve reimbursement of expenses. This study examines optimal reimbursement schemes in two-player Tullock contests, analyzing six reimbursement structures: external versus internal funding source each targeting the contest winner, the loser, or both of them. We assess the implications on effort, winning probabilities, and designer payoff under three key conditions: full-reimbursement, neutrality (preserving initial win chances) and viability (positive efforts from players). We find that all the schemes can satisfy viability; and all the schemes except for external reimbursement to the winner can satisfy neutrality. Additionally, all the schemes except internal reimbursement to the winner, and internal or external reimbursement to both players can satisfy full-reimbursement. These findings indicate that optimal reimbursement structures and rates vary depending on the contest structure, and the designer's objectives, such as maximizing effort or maximizing personal payoff.