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Safety in Mechanism Design and Implementation Theory

A mechanism is unsafe if a small number of agents deviating unexpectedly can make the mechanism deliver an outcome regarded as bad by a large number of other agents. Under Nash behavior, the direct approach of designing mechanisms with only safe Nash equilibria is impossible in many environments. A weaker approach (double implementation in Nash and safe equilibria) making just some Nash equilibria safe is enough to guarantee the safety of players in equilibrium with mild behavioral assumptions. In general, to be safe, a mechanism must restrict the set of outcomes that agents can achieve by deviating, introducing a trade-off between safety and individual autonomy. Also, requiring a mechanism to have safe equilibria implement a social choice rule may require that other equilibria deliver outcomes that are socially undesirable.