Anonymous implementation

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Official URL: https://dx.doi.org/10.1007/s00355-025-01635-5

This paper investigates full implementation under complete information, incorporating fairness considerations when designing mechanisms. In particular, we propose two notions of full implementation: anonymous implementation and no-envy implementation. Anonymous implementation requires that for any state, all socially optimal alternatives are attainable via a Nash equilibrium (NE) offering identical opportunity sets to all individuals, and that any such NE is itself socially optimal. No-envy implementation requires socially optimal alternatives to be achievable via NE, adding the condition that each individual weakly prefers the socially desirable alternative to any alternative in others’ opportunity sets. We identify necessary and (almost) sufficient conditions for both anonymous and no-envy implementation. We also demonstrate the existence of social choice rules that are anonymously and no-envy implementable but not implementable in NE, revealing that fairness considerations may enlarge the set of implementable social choice rules. Finally, we establish the equivalence of anonymous and no-envy implementation in rational environments with at least three individuals and no-veto social goals, but show that this equivalence fails in behavioral environments.