Strategy-Proof Resource Allocation with Punishment

A planner chooses an allocation of a divisible resource and charges agents based on their reported type. We discover and describe the set of dominant-strategy incentive-compatible (strategy-proof) mechanisms when the planner has the ability to observe the true type of agents ex-post and punish those agents who misreported their type. This class of mechanisms depends on the punishment function available for the planner to use and expands previous characterizations of incentive-compatible mechanisms when punishment was not available. For any punishment function, an optimal mechanism for the planner is characterized as the convex combination of two mechanisms resembling the first-price and second-price mechanisms. When the planner has the ability to select the punishment function, the minimal punishment necessary to achieve incentive compatibility and first-best efficiency is provided