Abstract: Implementation theory is concerned with the existence of mechanisms in which, at each state of the world, all equilibria result in outcomes that are within a given Social Choice Correspondence (SCC). But if agents make mistakes, if their preferences or the solution concept are misspecified, or if the designer is limited in what can be used as punishments, then it may be desirable to insist that also deviations result in ‘acceptable’ outcomes. Safe Implementation adds this extra requirement to standard implementation. Our primitives therefore also include an Acceptability Correspondence, which like the SCC maps states of the world to sets of allocations. When the underlying solution concept is Nash Equilibrium, We identify necessary and sufficient conditions (namely, Comonotonicity and Safe No-Veto) that restrict the joint behavior of the SCC and of the Acceptability Correspondence, and that generalize Maskin’s (1977) conditions. In relevant economic applications, these conditions can be quite permissive. But in ‘rich’ preference domains, Safe Implementation is impossible, regardless of the solution concept.

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: This paper shows that stability-based equilibrium refinements may not be well defined when taken to the infinite horizon. To do so, we extend the concept of Asheim (1997)’s dynamically consistent partition to allow for incomplete information. We provide a concrete example where in the infinite horizon the set of dynamically consistent equilibria is not well defined.

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.