INTRODUCTION AND SUMMARY OF RESULTS

A social choice rule (SCR) is best seen as a conflict resolution device. The most common interpretation goes as follows. The players agree on some general principles: say, some criteria of efficiency and symmetry. Then they identify an SCR that meets such criteria. Finally, they agree to use it as a collective decision device in all relevant circumstances. Two major game-theoretic problems arise in this connection:

1. (1) Are the socially best outcomes likely to be selected when the players, and their coalitions as well, behave strategically?

This is the implementation problem. An SCR is implementable with respect to (w.r.t) a suitable equilibrium concept if and only if a game form exists such that, for any relevant profile of players' characteristics, the SCR-optimal outcomes at that profile arise as the equilibrium outcomes of the induced game.

1. (2) To what extent are the socially best outcomes robust w.r.t changes in the agenda – that is, in the set of actually feasible alternatives?

This is a subtle question, because in a sense socially best outcomes do obviously depend on the specification of the set of feasible alternatives. However, one would like to rule out any change in the optimal set due to mere addition or deletion of suboptimal alternatives. The main reason for this requirement is, again, a strategic one. If it is the case that such “suboptimal” changes in the agenda do modify the optimal set, then the choice of the agenda may be a source of conflict (perhaps of a conflict stronger than the one over the final choice).