Matchings with Externalities and Attitudes Simina Brânzei, Tomasz Michalak,Talal Rahwan, Kate Larson and Nicholas Jennings

Matchings

Stability

Intensely studied class of combinatorial problems:

One-to-One: The stable marriage problem

Stability is a central question in game theoretic analyses of matchings Which matchings are such that the agents don't have incentives to (i) cut existing matches or (ii) form new matches?

One-to-Many: House allocation problems, assigning medical interns to hospitals

The stable outcomes depend on the solution concept used

This work: pairwise stability and the core

Many-to-Many: Most labor markets, friendships

Deviation: Each member of a deviating coalition B must either sever a match with a player in N, or form a new match with a player in B

Externalities

Response to a deviation: Given matching A and deviation A' of coalition B, the response Γ(B, A, A') defines the reaction of the players outside B upon the deviation

Also known as transaction spillovers Third parties are influenced by transactions they did not agree to

Stability: A matching is stable if no coalition can deviate and improve the utility of at least one member while not degrading the other members in the response of N \ B

Positive externalities: Education, immunization, environmental remediation, research

How will society react to a deviation?

Negative externalities: Environmental pollution, smoking, alcohol consumption and car accidents

Externalities in Matchings Matchings are a natural model for studying externalities: Agents are influenced not only by their own choices (matches), but also by the transactions that others make In general, agents can have a different utility for every different state of the world

This work: Succinct model of externalities in matchings (polynomial-size preferences in the number of agents)

Model Matching game: G = (M, W, Π), where M andW are agents on the two sides of the market Denote by Π(m, w | z) the influence of match (m, w) on agent z (if the match forms)

m

The agents need to compute the response (possibly intractable)

Attitudes (Heuristics) Optimism: Deviators assume the best case reaction from the rest of the agents (attitude à la “All is for the best in the best of all the possible worlds”) Neutrality: No reaction (the deviators assume the others are not going to do anything about it) Pessimism: Worst case reaction (deviators assume the remaining agents will retaliate in the worst possible way Many others possible: Contractual: Assume retaliation from players hurt by the deviation, and no reaction from the rest

Many-to-Many Matchings Core

Optimism

Neutrality

Membership

P

Nonemptiness

NP-complete

coNP-complete coNP-complete NP-hard

NP-hard Pessimistic Core

The cores are included in each other:

Neutral Core Optimistic Core

w Π(m,w|x)

Π(m,w|y)

y

x Π(z,t|x)

Π(z,t|y)

z

t

The utility of an agent z in matching A is:

u(z, A) = ∑(m,w) ∈ A Π(m, w | z)

Pessimism

One-to-One Matchings Pairwise Stable Set

Optimism

Neutrality Pessimism

Membership

P

P

P

Nonemptiness

NP-complete

P

P

Core

Optimism

Neutrality

Pessimism

Membership

P

coNP-complete

coNP-complete

Nonemptiness

NP-complete

NP-hard

NP-hard

Matchings with Externalities and Attitudes Simina ...

Pessimistic. Core. The cores are included in each other: Core. Optimism. Neutrality. Pessimism. Membership. P. coNP-complete coNP-complete. Nonemptiness NP-complete. NP-hard. NP-hard. One-to-One Matchings. Pairwise Stable Set Optimism Neutrality Pessimism. Membership. P. P. P. Nonemptiness. NP-complete. P.
Download PDF
107KB Sizes 1 Downloads 179 Views
Report

Recommend Documents

Matchings with Externalities and Attitudes
Optimism: Deviators assume the best case reaction from the rest of ... matches good for the deviators and removal of all bad .... Externalities in social networks.
Matchings with Externalities and Attitudes
the search for compact representations of externalities. One of the central questions in matching games is stabil- ity [14], which informally means that no group .... Neutrality, optimism and pessimism are heuristics used by agents in blocking coalit
Matching with Aggregate Externalities
Feb 23, 2016 - Hafalir: Tepper School of Business, Carnegie Mellon University, ... to move to Flagstaff, Arizona, for a new, higher-paying job. .... more important than the small externality change brought about by their deviation, so they.
Attitudes and Evaluations - Martel Press
2001; Olson & Parayitam, 2007; Peterson & Behfar, 2003;. Simons & Peterson, 2000) or else the .... 10:1-6, James 5:16,. Prov. 9:8,9). There are many positive consequences of accountability that have been demonstrated empirically. (Lerner & Tetlock, 1
Vertical Exclusion with Endogenous Competiton Externalities
May 9, 2012 - Tel: (44 20) 7183 8801, Fax: (44 20) 7183 8820. Email: [email protected], Website: www.cepr.org. This Discussion Paper is ... reasoning exclusion is also optimal with downstream wealth constraints. Thus exclusion arises when ...
Contracting with Externalities and Outside Options
Oct 15, 2004 - and the contract imposes externalities on non-trading agents. We focus on ..... Exiting would then be a strict best response at some action phase ...... Our analysis only deals with the case where there is a unique player with the.
Attitudes and Evaluations - Martel Press
David R. Dunaetz. Azusa Pacific University. Abstract. “Co-operation and the Promotion of Unity” was one the major themes addressed at Edinburgh 1910. ... of Unity.” Five Group Processes that Influence Cooperation and. Unity. Since the end of th
Stable Matchings and Preferences of Couples
Abstract: Couples looking for jobs in the same labor market may cause instabilities. ... stable matchings.1 In order to explain stability, let us assume for the moment that one side ... the couple can still live together, then the couple is better of
Risk and attitudes towards it
Insurance companies. Banks. Building societies. Funds or similar. Unit trust providers. Table 4.3 Medium-risk products. Financial need. Product. Provider(s). Product that invests in a spread of shares or bonds. (or a mix). Used to invest for medium t
Islamization of Attitudes and Practices
ultimate salvation of man. ... man's attaining knowledge from life and the universe is contingent upon three ... and nature as manifested in the natural universe.
Network Externalities, Competition, and Compatibility
American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The .... amine the private and social incentives for.
Information and Crowding Externalities
Nov 16, 2009 - information is better) is optimal. However, if the desired degree of coordination is suffi ciently low, then the other type of equilibrium in which agents always heed their private information is optimal. Finally, we analyze the effect
Capital Flows, Crises and Externalities
Capital flows to emerging market economies create externalities that make the ... For contact information visit http: ... Capital. Outflows. Falling. Exchange Rates. Figure 2: Balance sheet crises and financial amplification in emerging economies. Th
Pecuniary Externalities in Economies with Financial ... - of Anton Korinek
Unpacking the optimal tax rates for distributive and collateral externalities into three sufficient statistics each is also helpful in spelling out explicit conditions ...
Externalities in Economies with Endogenous Sharing ...
Jan 17, 2017 - A3: The graph of E, defined by Γ := {(x, v) : v ∈ U(x) and xi ∈ Bi(x−i) for ... It is then standard to define a generalized Nash equilibrium of E as a ...
Coase Theorem with Identity-Dependent Externalities
Mar 11, 2004 - concept of IDE operates in business world. In the recent bidding war for AT&T Wireless, if Vodafone were to win the auction, the ..... number is positive, we say player i s consumption is socially desirable; otherwise, it is ..... “g
Externalities, Information Processing and ... - Semantic Scholar
C. Athena Aktipis. Reed College. Box 25. 3203 SE Woodstock Blvd. ... It is unclear exactly how groups of this nature fit within the framework of group selection.
Externalities, Information Processing and ... - Semantic Scholar
for the coupling of utility functions of agents in dyads or larger groups. Computer .... probably lies in the co-evolution of the capacity to detect individuals who are ...
Residents' Attitudes toward Existing and Future Tourism ...
Residents' Attitudes toward Existing and Future Tourism Development in Rural Communities.pdf. Residents' Attitudes toward Existing and Future Tourism ...
Externalities in economies with endogenous sharing rules
Apr 18, 2017 - In this note, we prove existence of a Simon and Zame “solution” in ... For example, in exchange economies, consumers are limited by their.
Pecuniary Externalities in Economies with Financial ... - of Anton Korinek
There are two types of goods, a homogeneous consumption good, which serves as numeraire, and a capital good. We denote by L ∈ o the state of nature realized at date 1, where o is the set of possible states. Preferences/endowments. Each agent i valu
Pecuniary Externalities in Economies with Financial ...
interaction and feedback with credit frictions. → suggests ... externalities can generally take on either sign. ▷ illustrate which factors cause sign to ip. ▷ Bonus: ...
Coase Theorem with Identity-Dependent Externalities
Mar 11, 2004 - asymmetrical impacts on the firms. In the proceeding ... This paper asks if allowing resale can mitigate/internalize identity-dependent externalities. ... The firm that employs the license increases its profits by $2. Mean- while, the