Implementation in Adaptive Better-Response Dynamics

We study the classic implementation problem under the behavioral assumption that agents myopically adjust their actions in the direction of better-responses within a given institution. We offer results both under complete and incomplete information. First, we show that a necessary condition for assymptotically stable implementation is a small variation of (Maskin) monotonicity, which we call quasimonotonicity. Under standard assumptions in economic environments, we also provide a mechanism for Nash implementation which has good dynamic properties if the rule is quasimonotonic. Thus, quasimonotonicity is both necessary and almost sufficient for assymptotically stable implementation. Under incomplete information, incentive compatibility is necessary for any kind of stable implementation in our sense, while Bayesian quasimonotonicity is necessary for assymptotically stable implementation. Both conditions are also essentially sufficient for assymptotically stable implementation. We then tighten the assumptions on preferences and mutation processes and provide mechanisms for stochastically stable implementation under more permissive conditions on social choice rules.

The relation between implementability and the core

This paper proves a simple and general theorem on resource-allocation mechanisms that achieve Pareto efficiency. We say that a mechanism (game form) is normal if at any action profile, an agent who obtains his endowments neither pays nor receives a positive amount. In the context of auctions, this simply means that losers receive no bill. We prove that for any normal mechanism, if its Nash equilibrium allocations are Pareto efficient for all preference profiles, then the equilibrium allocations are necessarily in the core. The result holds for a large class of allocation problems in which monetary transfers are feasible and the consumption space is discrete except for the space of transfers. Examples include auctions with any number of objects, economies with indivisible public goods, marriage problems, and coalition formation

Incentives and Efficiency in Constrained Allocation Mechanisms

We study private-good allocation mechanisms where an arbitrary constraint delimits the set of feasible joint allocations. This generality provides a unified perspective over several prominent examples that can be parameterized as constraints in this model, including house allocation, roommate assignment, and social choice. We first characterize the set of two-agent strategy-proof and Pareto efficient mechanisms, showing that every mechanism is a "local dictatorship." For more than two agents, we leverage this result to provide a new characterization of group strategy-proofness. In particular, an N-agent mechanism is group strategy-proof if and only if all its two-agent marginal mechanisms (defined by holding fixed all but two agents' preferences) are individually strategy-proof and Pareto efficient. To illustrate their usefulness, we apply these results to the roommates problem to discover the novel finding that all group strategy-proof and Pareto efficient mechanisms are generalized serial dictatorships, a new class of mechanisms. Our results also yield a simple new proof of the Gibbard-Satterthwaite Theorem

Strategyproof Allocation of a Single Object

The problem of allocating a single indivisible object to one of several selfish agents is considered, where monetary payments are not allowed, and the object is not necessarily desirable to each agent. It is shown that ordinality and positive responsiveness together are necessary and sufficient conditions for strategyproofness, which implies that efficient social choice functions are not strategyproof. However, any Pareto-optimal, ordinal social choice function is strategyproof. A Gibbard-Satterthwaite-type impossibility result is established for nonbossy mechanisms. Thus, the best the planner can do without monetary transfers is to give the object to an agent who desires it, but whose valuation of the object may not be the highest among the agents, using a mechanism that is either dictatorial or bossy. It is also shown that all strategyproof, nonbossy, and Pareto-optimal social choice functions are serial dictatorships

Safe Implementation

We introduce Safe Implementation, a notion of implementation that adds to the stan-dard 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 stan-dard notions of implementation, and can accommodate a variety of considerations, including robustness concerns with respect to mistakes in play, model misspecification, behavioral con-siderations, 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 suf-ficient conditions (namely, Comonotonicity and safety-no veto) that restrict the joint behavior 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 in-divisible goods, but also that Safe Implementation can be very demanding in environments with ‘rich’ preferences, regardless of the underlying solution concept

Implementation in strong core by codes of rights

AbstractFollowing the seminal contribution of Koray and Yildiz (J Econ Theory 176:479–502, 2018), we re-examine the classical questions of implementation theory under complete information in a setting where coalitions are fundamental behavioral units, and the outcomes of their interactions are predicted by applying the solution concept of the strong core. The planner’s exercise includes designing a code of rights that specifies the collection of coalitions having the right to block one outcome by moving to another. We provide a complete characterization of the implementable social choice rules.</jats:p