Abstract: I study binding agreements over play in a game. I propose a negotiation protocol where, in each round, agents propose actions from the underlying game. The protocol terminates when proposals are confirmed. I study the outcomes of Negotiated Binding Agreements of the negotiation protocol, a refinement of Subgame Perfect Equilibrium. A full characterisation is provided for two-player games, relying on appropriate individual punishments. These individual punishments are used for sufficiency in n-player games and a necessary iterative rationality constraint is introduced. I extend the solution concept to allow cooperative agreements within the negotiation game. Generalisations of the main results hold.

Abstract: We introduce Safe Implementation, a notion of implementation that adds to the standard requirements the restriction that deviations from the baseline solution concept induce outcomes that are acceptable. The primitives of Safe Implementation, therefore, include both a Social Choice Correspondence, as standard, and an Acceptability Correspondence, each mapping every state of the world to a subset of allocations. This framework generalizes standard notions of implementation and can accommodate a variety of considerations, including robustness concerns with respect to mistakes in play, model misspecification, behavioural considerations, state-dependent feasibility restrictions, limited commitment, etc.

We provide results both for general solution concepts and for the case in which agents’ interaction is modelled by Nash Equilibrium. In the latter case, we identify necessary and sufficient conditions (namely, Comonotonicity and safety-no veto) that restrict the joint behaviour of the Social Choice and Acceptability Correspondences. These conditions are more stringent than Maskin’s (1978) but coincide with them when the safety requirements are vacuous. We also show that these conditions are quite permissive in important economic applications, such as environments with single-crossing preferences and in problems of efficient allocation of indivisible goods, but also that Safe Implementation can be very demanding in environments with ‘rich’ preferences, regardless of the underlying solution concept.

Abstract: I consider Ray and Vohra (1997)’s Coalitional Equilibrium and show the methodological advantage of taking the notion of “an improvement for a group” to mean that there is a joint action of the group that induces a strict improvement in utility for all its members. This is opposed to assuming no agent in the group is worse off while one is strictly better off. I show that, when this interpretation is taken, the sufficient conditions for existence of Ray and Vohra (1997)’s Coalitional Equilibrium can be weakened. I do so by showing that the existence of Coalitional Equilibrium is implied by the existence of a Nash Equilibrium of an auxiliary game. Further to this, I show that the proof of existence can be extended to a generalisation of the concept, where groups may overlap but do not necessarily include the grand coalition.