Abstract: I study the binding agreements that may result from players negotiating over their behaviour in an underlying strategic environment. To do so, I propose a negotiation protocol where, in each round of negotiation, agents make public proposals of the action they will take in the underlying game. The protocol terminates when these proposals are confirmed. Confirmation results in a binding agreement over the action profile and payoffs are the corresponding ones in the underlying game. I study the outcomes of Negotiated Binding Agreements of the negotiation protocol, which is a refinement of Subgame Perfect Equilibrium that I introduce in this context to obtain both credibility and tractability. The main results show that any outcome of the underlying game that is agreed upon must satisfy an iterative individual rationality constraint. Additionally, an outcome of the underlying game can be agreed upon if appropriate individual punishments in the underlying game can be found. A full characterisation is provided for two-player games. Finally, to allow for the possibility that agents make binding agreements over how they will negotiate, I extend the solution concept to allow for cooperative agreements within the negotiation game. Generalisations of the main results hold and refine the set of agreement outcomes.

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.