We study a simple model of a decentralized market game in which firms make directed offers to workers. We focus on markets in which agents have aligned preferences. When agents have complete information or when there are no frictions in the economy, there exists an equilibrium that yields the stable match. In the presence of market frictions and preference uncertainty, harsher assumptions on the richness of the economy have to be made in order for decentralized markets to generate stable outcomes in equilibrium.

This book constitutes the conference proceedings of the 7th International Conference on Algorithmic Decision Theory, ADT 2021, held in Toulouse, France, in November 2021. The 27 full papers presented were carefully selected from 58 submissions. The papers focus on algorithmic decision theory broadly defined, seeking to bring together researchers and practitioners coming from diverse areas of computer science, economics and operations research in order to improve the theory and practice of modern decision support.

"In two-sided matching problems, there are two disjoint sets of agents, for instance, firms and workers, hospitals and interns. Each agent has a preference order over agents on the other side. An outcome of the problem is a match. Stability has been considered to be the main property that accounts for the success of many matching processes. It is a robustness property: no coalition has a good reason to disrupt the suggested match. A well-studied question is to what extent it is reasonable for agents to be truthful about their preferences. Agents may have an incentive to misrepresent their preferences. Therefore, procedures that produce stable matches with respect to the announced preferences may not produce stable matches with respect to the true preferences. Then, a natural question to ask is: What are Nash equilibria? A significant portion of this volume is devoted to full-fledged game theoretic analysis in one-to-one, many-to-one and many-to-many matching problems. In the first chapter, we study the problem of allocating indivisible goods to agents when monetary transfers are not allowed. Our main requirement is strategy-proofness. Our second goal is fairness. Fairness is incompatible with efficiency. We consider two instances of this problem: (1) the supply of each object is one; and (2) the supply of each object may be greater than one. For each instance, we identify a fair and strategy-proof rule that Pareto dominates any other rule satisfying the two properties. In the second chapter, we consider many-to-one and many-to-many matching problems where each agent has substitutable and separable preferences. We analyze the stochastic dominance (sd) Nash equilibria of the game induced by any vii probabilistic stable matching rule. In the third chapter, we model decentralized matching as a sequential game in which firms sequentially make job offers to workers. The complex and uncertain aspects of decentralized processes are represented by a randomly selected order according to which firms make offers. We study the sd-Nash and realization independent equilibria of the Decentralized Game we define. In the fourth chapter, we show that the so-called 'rural hospital theorem' generalizes to many-to-many matching problems where agents on both sides of the problem have substitutable and weakly separable preferences. We also show that this domain of preferences is maximal"--Page vi-vii.

The rich, multi-faceted and multi-disciplinary field of matching-based market design is an active and important one due to its highly successful applications with economic and sociological impact. Its home is economics, but with intimate connections to algorithm design and operations research. With chapters contributed by over fifty top researchers from all three disciplines, this volume is unique in its breadth and depth, while still being a cohesive and unified picture of the field, suitable for the uninitiated as well as the expert. It explains the dominant ideas from computer science and economics underlying the most important results on market design and introduces the main algorithmic questions and combinatorial structures. Methodologies and applications from both the pre-Internet and post-Internet eras are covered in detail. Key chapters discuss the basic notions of efficiency, fairness and incentives, and the way market design seeks solutions guided by normative criteria borrowed from social choice theory.

Handbook of Industrial Organization Volume 4 highlights new advances in the field, with this new volume presenting interesting chapters. Each chapter is written by an international board of authors. - Part of the renowned Handbooks in Economics series - Chapters are contributed by some of the leading experts in their fields - A source, reference and teaching supplement for industrial organizations or industrial economists