Nash and dominant strategy implementation in economic environments

When environments are ‘rich’, single-valued social choice functions which are implementable in Nash strategies are implementable in dominant strategies. Moreover the Gibbard–Satterthwaite impossibility theorem of implementation in dominant strategies has been extended to differential economic environments. Therefore it is important to study implementation for non-rich environments. We characterize for quasi-linear utility functions mechanisms which are implementable in dominant strategies (providing a generalization of the Groves–Clarke mechanisms) and in Nash strategies. This second type of mechanisms differ from the first only by the types of transfers they allow. Properties of these mechanisms such as balancedness, individual rationality and robustness with respect to coalitions are then studied.