Full Implementation of Rank Dependent Prizes

Abstract

A manager/mechanism designer must allocate a set of money prizes ($1, $2, .., $n) between n agents working in a team. The agents know the state i.e. who contributed most, second most, etc. The agents' preferences over prizes are state independent. We incorporate the possibility that the manager knows the state with a tiny probability and present a simple mechanism that uniquely implement prizes that respects the true state.

Mechanism Design When Player's Preferences and Information Coincide

“…the expected value of the distance between the true state and the one chosen by the regulator; 1 We make the cost k explicit, but others have introduced forms of inspections where the information comes "for free" to the mechanism designer (see for example Midjord, 2013; in that paper the designer may learn the true state with some probability; here the true state is never revealed to the designer). 2 The cost k being small also helps in the sense that if the planner did not have the commitment power to implement the inspection if the cost was high, and players knew this, the mechanism wouldn't work.…”

“…In these interesting papers, players know the state of the world and can either provide "evidence"or have a lexicographic preference for telling the truth. As noted by Midjord (2013), whose planner could learn the true state with some (possibly small probability), the way all these mechanisms work is similar: the planner uses his/her small edge to break ties, and pitch players against each other. In every case, a player has a slight incentive to deviate from a "lying" equilibrium by providing di¤erent evidence (which may not change the outcome), or telling the truth (again without changing the outcome), but still breaking the proposed equilibrium.…”