Monotonicity and Nash implementation in matching markets with contracts

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (2005) and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable (Theorems 1 and 3). Furthermore, any solution that is Pareto efficient, individually rational, and monotonic is a supersolution of the stable correspondence (Theorem 2). In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.matching with contracts, (Maskin) monotonicity, Nash implementation, stability.

Nash Implementation Using Undominated Strategies

We study the problem of implementing social choice correspondences using the concept of undominated Nash equilibrium, i.e. Nash equilibrium in which no one uses a weakly dominated strategy. We show that this mild refinement of Nash equilibrium has a dramatic impact on the set of implementable correspondences. Our main result is that if there are at least three agents in the society, then any correspondence which satisfies the usual no veto power condition is implementable unless some agents are completely indifferent over all possible outcomes. Many common welfare criteria, such as the Pareto correspondence, and several familiar voting rules, such as majority and plurality rules, satisfy our conditions. This possibility result stands in sharp contrast to the more restrictive findings with implementation in either Nash equilibrium or subgame perfect equilibrium. We present several examples to illustrate the difference between undominated Nash implementation and implementation with alternative solution concepts

Equilibrium Participation in Public Goods Allocations

An alternative notion of individual rationality for mechanism design is studied in which mechanisms suggest public goods allocations and individuals then choose whether or not to submit their requested transfer to the central planner. The set of allocations such that unanimous participation is a Nash equilibrium is shown to be sub-optimal in a wide variety of environments and shrinks to the endowment as the economy is replicated. Therefore, any non-trivial mechanism suffers from non-participation in the selected outcome when agents cannot be coerced to contribute.

Implementation Theory

This surveys the branch of implementation theory initiated by Maskin (1977). Results for both complete and incomplete information environments are covered

Implementation in Bayesian Equilibrium: The Multiple Equilibrium Problem in Mechanism Design

This paper surveys the literature on implementation in Bayesian Equilibrium

Mechanism Design with Incomplete Information: A Solution to the Implementation Problem

The main result of this paper is that the multiple equilibrium problem in mechanism design can be avoided in private-value models if agents do not use weakly dominated strategies in equilibrium. We show that in such settings, any incentive-compatible allocation rule can be made the unique equilibrium outcome to a mechanism. We derive a general necessary condition for unique implementation that implies that the positive result for private-value models applies. with considerably less generality to the common-value settings

Epsilon bayesian implementation

Ankara : Department of Economics İhsan Doğramacı Bilkent University, 2014.Thesis (Master's) -- Bilkent University, 2014.Includes bibliographical references leaves 19-20.Ergin, EmreM.S

Implementation in Bayesian Equilibrium: The Multiple Equilibrium Problem in Mechanism Design

This paper surveys the literature on implementation in Bayesian Equilibrium