Author: James W. BoudreauPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Preference Structure and Random Paths to Stability in Matching Markets
Author: James W. BoudreauRandom Paths to Pairwise Stability in Many-to-Many Matching Problems
Author: Fuhito KojimaPublisher:
ISBN:
Category :
Languages : en
Pages : 20
Book Description
This paper considers a decentralized process in many-to-many matching problems. We show that if agents on one side of the market have substitutable preferences and those on the other side have responsive preferences, then, from an arbitrary matching, there exists a finite path of matchings such that each matching on the path is formed by satisfying a blocking individual or a blocking pair for the previous matching, and the final matching is pairwise-stable. This implies that an associated stochastic process converges to a pairwise-stable matching in finite time with probability one, if each blocking individual or pair is satisfied with a positive probability at each period along the process.
Web and Internet Economics
Author: Yiling ChenPublisher: Springer
ISBN: 3642450466
Category : Computers
Languages : en
Pages : 450
Book Description
This book constitutes the thoroughly refereed conference proceedings of the 9th International Conference on Web and Internet Economics, WINE 2013, held in Cambridge, MA, USA, in December 2013. The 36 revised full papers were carefully reviewed and selected from 150 submissions and cover research in theoretical computer science, artificial intelligence and microeconomics.
Algorithmic Game Theory
Author: Market Structure and Dynamics
Author: Qingyun Wu (Researcher in game theory and market design)Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
This thesis consists of three self-contained essays that investigate the algebraic structure of matching markets and the stabilization dynamics in decentralized markets. Chapter 2 is based on Wu and Roth (2018). It studies envy-free matchings that naturally arise from workers retiring or companies expanding. We show that the set of envy-free matchings forms a lattice that has a Conway-like join, but not a Conway-like meet. Furthermore, a job hopping process in which companies make offers to their favorite blocking workers, and workers accept their favorite offers, producing a sequence of vacancy chains, is a Tarski operator on this lattice. The fixed points of this Tarski operator correspond to the set of stable matchings; and the steady state matching starting from any given initial state is derived analytically. Chapter 3 is based on Wu (2020). The goal of this chapter, is to provide a systematic approach for analyzing entering classes in the college admissions model. When dealing with a many-to-one matching model, we often convert it into a one-to-one matching problem by assigning each seat of a college to a single student, instead of matching each college to multiple students. The preferences in this new model are significantly correlated and severely restrict the possible changes to entering classes. Through the so-called "rotations" that correspond to the join-irreducible elements in the lattice of stable matchings, we present a unified treatment for several results on entering classes, including the famous "Rural Hospital Theorem". We also show that, the least preferred student in an entering class appears to play a very interesting role. For example, each entering class can be completely characterized by its worst student. Chapter 4 is based on Gu, Roth, and Wu (2020). The motivating question is that, how come some black markets, such as the market for hitmen are well-regulated, but many others like the market for drugs are far from being under our control, even though we try very hard to eliminate them. To understand this, we build a three-dimensional discrete time Markov chain to study how black markets evolve over time, focusing on social repugnance and search frictions. We borrow tools from Markov jump processes, random walks, exponential martingales and optional sampling theory to analyze both the steady state limit and the realizations along the way. In the first part of the chapter, we identify conditions that lead to market survival or extinction. And the second part studies speed of convergence. We show that if a market is going to die eventually, then it dies exponentially fast. This further implies if a market has survived for a long time, then it is likely to survive forever.
Algorithmics of Matching Under Preferences
Author: David F. ManlovePublisher: World Scientific
ISBN: 9814425257
Category : Mathematics
Languages : en
Pages : 524
Book Description
Matching problems with preferences are all around us OCo they arise when agents seek to be allocated to one another on the basis of ranked preferences over potential outcomes. Efficient algorithms are needed for producing matchings that optimise the satisfaction of the agents according to their preference lists.In recent years there has been a sharp increase in the study of algorithmic aspects of matching problems with preferences, partly reflecting the growing number of applications of these problems worldwide. This book describes the most important results in this area, providing a timely update to The Stable Marriage Problem: Structure and Algorithms (D Gusfield and R W Irving, MIT Press, 1989) in connection with stable matching problems, whilst also broadening the scope to include matching problems with preferences under a range of alternative optimality criteria."
Two-Sided Matching
Author: Alvin E. RothPublisher: Cambridge University Press
ISBN: 1107782430
Category : Business & Economics
Languages : en
Pages : 288
Book Description
Two-sided matching provides a model of search processes such as those between firms and workers in labor markets or between buyers and sellers in auctions. This book gives a comprehensive account of recent results concerning the game-theoretic analysis of two-sided matching. The focus of the book is on the stability of outcomes, on the incentives that different rules of organization give to agents, and on the constraints that these incentives impose on the ways such markets can be organized. The results for this wide range of related models and matching situations help clarify which conclusions depend on particular modeling assumptions and market conditions, and which are robust over a wide range of conditions. 'This book chronicles one of the outstanding success stories of the theory of games, a story in which the authors have played a major role: the theory and practice of matching markets ... The authors are to be warmly congratulated for this fine piece of work, which is quite unique in the game-theoretic literature.' From the Foreword by Robert Aumann
Automata, Languages and Programming
Author: Luca AcetoPublisher: Springer Science & Business Media
ISBN: 3642220118
Category : Computers
Languages : en
Pages : 689
Book Description
The two-volume set LNCS 6755 and LNCS 6756 constitutes the refereed proceedings of the 38th International Colloquium on Automata, Languages and Programming, ICALP 2011, held in Zürich, Switzerland, in July 2011. The 114 revised full papers (68 papers for track A, 29 for track B, and 17 for track C) presented together with 4 invited talks, 3 best student papers, and 3 best papers were carefully reviewed and selected from a total of 398 submissions. The papers are grouped in three major tracks on algorithms, complexity and games; on logic, semantics, automata, and theory of programming; as well as on foundations of networked computation: models, algorithms and information management.
Algorithmics Of Matching Under Preferences
Author: David ManlovePublisher: World Scientific
ISBN: 9814425265
Category : Computers
Languages : en
Pages : 524
Book Description
Matching problems with preferences are all around us: they arise when agents seek to be allocated to one another on the basis of ranked preferences over potential outcomes. Efficient algorithms are needed for producing matchings that optimise the satisfaction of the agents according to their preference lists.In recent years there has been a sharp increase in the study of algorithmic aspects of matching problems with preferences, partly reflecting the growing number of applications of these problems worldwide. The importance of the research area was recognised in 2012 through the award of the Nobel Prize in Economic Sciences to Alvin Roth and Lloyd Shapley.This book describes the most important results in this area, providing a timely update to The Stable Marriage Problem: Structure and Algorithms (D Gusfield and R W Irving, MIT Press, 1989) in connection with stable matching problems, whilst also broadening the scope to include matching problems with preferences under a range of alternative optimality criteria.
Algorithmic Game Theory
Author: Ron LaviPublisher: Springer
ISBN: 3662448033
Category : Computers
Languages : en
Pages : 307
Book Description
This book constitutes the refereed proceedings of the 7th International Symposium on Algorithmic Game Theory, SAGT 2014, held in Haifa, Israel, in October 2014. The 24 full papers and 5 short papers presented were carefully reviewed and selected from 65 submissions. They cover various important aspects of algorithmic game theory, such as matching theory, game dynamics, games of coordination, networks and social choice, markets and auctions, price of anarchy, computational aspects of games, mechanism design and auctions.