scholarly journals Additively Separable Hedonic Games with Social Context

Games ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 71
Author(s):  
Gianpiero Monaco ◽  
Luca Moscardelli ◽  
Yllka Velaj
Keyword(s):  
Nash Equilibrium ◽  
Social Context ◽  
Nash Equilibria ◽  
Price Of Anarchy ◽  
Strategic Interaction ◽  
Price Of Stability ◽  
Fundamental Class ◽  
New Model ◽  
Hedonic Games ◽  
And Performance

In hedonic games, coalitions are created as a result of the strategic interaction of independent players. In particular, in additively separable hedonic games, every player has valuations for all other ones, and the utility for belonging to a coalition is given by the sum of the valuations for all other players belonging to it. So far, non-cooperative hedonic games have been considered in the literature only with respect to totally selfish players. Starting from the fundamental class of additively separable hedonic games, we define and study a new model in which, given a social graph, players also care about the happiness of their friends: we call this class of games social context additively separable hedonic games (SCASHGs). We focus on the fundamental stability notion of Nash equilibrium, and study the existence, convergence and performance of stable outcomes (with respect to the classical notions of price of anarchy and price of stability) in SCASHGs. In particular, we show that SCASHGs are potential games, and therefore Nash equilibria always exist and can be reached after a sequence of Nash moves of the players. Finally, we provide tight or asymptotically tight bounds on the price of anarchy and the price of stability of SCASHGs.

THE PRICE OF NASH EQUILIBRIA IN MULTICAST TRANSMISSION GAMES

2010 ◽  
Vol 11 (03n04) ◽  
pp. 97-120 ◽  
Author(s):  
VITTORIO BILÒ
Keyword(s):  
Nash Equilibrium ◽  
Cost Sharing ◽  
Price Of Anarchy ◽  
Optimal Solution ◽  
Minimum Cost ◽  
Price Of Stability ◽  
Common Source ◽  
Cost Share ◽  
Worst Case ◽  
The Cost

We consider the problem of sharing the cost of multicast transmissions in non-cooperative undirected networks where a set of receivers R wants to be connected to a common source s. The set of choices available to each receiver r ∈ R is represented by the set of all (s, r)-paths in the network. Given the choices performed by all the receivers, a public known cost sharing method determines the cost share to be charged to each of them. Receivers are selfish agents aiming to obtain the transmission at the minimum cost share and their interactions create a non-cooperative game. Devising cost sharing methods yielding games whose price of anarchy (price of stability), defined as the worst-case (best-case) ratio between the cost of a Nash equilibrium and that of an optimal solution, is not too high is thus of fundamental importance in non-cooperative network design. Moreover, since cost sharing games naturally arise in socio-economical contests, it is convenient for a cost sharing method to meet some constraining properties. In this paper, we first define several such properties and analyze their impact on the prices of anarchy and stability. We also reconsider all the methods known so far by classifying them according to which properties they satisfy and giving the first non-trivial lower bounds on their price of stability. Finally, we propose a new method, namely the free-riders method, which admits a polynomial time algorithm for computing a pure Nash equilibrium whose cost is at most twice the optimal one. Some of the ideas characterizing our approach have been independently proposed in Ref. 10.

scholarly journals Selfishness Level of Strategic Games

2014 ◽  
Vol 49 ◽  
pp. 207-240 ◽  
Author(s):  
K. R. Apt ◽  
G. Schaefer
Keyword(s):  
Nash Equilibrium ◽  
Social Welfare ◽  
Price Of Anarchy ◽  
Congestion Games ◽  
Price Of Stability ◽  
Social Optimum ◽  
Potential Game ◽  
Strategic Games ◽  
The Social ◽  
The Impact

We introduce a new measure of the discrepancy in strategic games between the social welfare in a Nash equilibrium and in a social optimum, that we call selfishness level. It is the smallest fraction of the social welfare that needs to be offered to each player to achieve that a social optimum is realized in a pure Nash equilibrium. The selfishness level is unrelated to the price of stability and the price of anarchy and is invariant under positive linear transformations of the payoff functions. Also, it naturally applies to other solution concepts and other forms of games. We study the selfishness level of several well-known strategic games. This allows us to quantify the implicit tension within a game between players' individual interests and the impact of their decisions on the society as a whole. Our analyses reveal that the selfishness level often provides a deeper understanding of the characteristics of the underlying game that influence the players' willingness to cooperate. In particular, the selfishness level of finite ordinal potential games is finite, while that of weakly acyclic games can be infinite. We derive explicit bounds on the selfishness level of fair cost sharing games and linear congestion games, which depend on specific parameters of the underlying game but are independent of the number of players. Further, we show that the selfishness level of the $n$-players Prisoner's Dilemma is c/(b(n-1)-c), where b and c are the benefit and cost for cooperation, respectively, that of the n-players public goods game is (1-c/n)/(c-1), where c is the public good multiplier, and that of the Traveler's Dilemma game is (b-1)/2, where b is the bonus. Finally, the selfishness level of Cournot competition (an example of an infinite ordinal potential game), Tragedy of the Commons, and Bertrand competition is infinite.

THE PRICE OF ANARCHY FOR RESTRICTED PARALLEL LINKS

2006 ◽  
Vol 16 (01) ◽  
pp. 117-131 ◽  
Author(s):  
MARTIN GAIRING ◽  
THOMAS LÜCKING ◽  
MARIOS MAVRONICOLAS ◽  
BURKHARD MONIEN
Keyword(s):  
Nash Equilibrium ◽  
System Performance ◽  
Nash Equilibria ◽  
Price Of Anarchy ◽  
Pure Nash Equilibrium ◽  
Worst Case ◽  
Comprehensive Collection ◽  
Parallel Links ◽  
Special Case

In the model of restricted parallel links, n users must be routed on m parallel links under the restriction that the link for each user be chosen from a certain set of allowed links for the user. In a (pure) Nash equilibrium, no user may improve its own Individual Cost (latency) by unilaterally switching to another link from its set of allowed links. The Price of Anarchy is a widely adopted measure of the worst-case loss (relative to optimum) in system performance (maximum latency) incurred in a Nash equilibrium. In this work, we present a comprehensive collection of bounds on Price of Anarchy for the model of restricted parallel links and for the special case of pure Nash equilibria. Specifically, we prove: • For the case of identical users and identical links, the Price of Anarchy is [Formula: see text]. • For the case of identical users, the Price of Anarchy is [Formula: see text]. • For the case of identical links, the Price of Anarchy is [Formula: see text], which is asymptotically tight. • For the most general case of arbitrary users and related links, the Price of Anarchy is at least m – 1 and less than m. The shown bounds reveal the dependence of the Price of Anarchy on n and m for all possible assumptions on users and links.

scholarly journals On Non-Cooperativeness in Social Distance Games

2019 ◽  
Vol 66 ◽  
pp. 625-653
Author(s):  
Alkida Balliu ◽  
Michele Flammini ◽  
Giovanna Melideo ◽  
Dennis Olivetti
Keyword(s):  
Nash Equilibrium ◽  
Polynomial Time ◽  
Social Distance ◽  
Price Of Anarchy ◽  
Cluster Formation ◽  
Solution Concept ◽  
Price Of Stability ◽  
The Social ◽  
Np Complete ◽  
Inverse Distance

We consider Social Distance Games (SDGs), that is cluster formation games in which the utility of each agent only depends on the composition of the cluster she belongs to, proportionally to her harmonic centrality, i.e., to the average inverse distance from the other agents in the cluster. Under a non-cooperative perspective, we adopt Nash stable outcomes, in which no agent can improve her utility by unilaterally changing her coalition, as the target solution concept. Although a Nash equilibrium for a SDG can always be computed in polynomial time, we obtain a negative result concerning the game convergence and we prove that computing a Nash equilibrium that maximizes the social welfare is NP-hard by a polynomial time reduction from the NP-complete Restricted Exact Cover by 3-Sets problem. We then focus on the performance of Nash equilibria and provide matching upper bound and lower bounds on the price of anarchy of Θ(n), where n is the number of nodes of the underlying graph. Moreover, we show that there exists a class of SDGs having a lower bound on the price of stability of 6/5 − ε, for any ε > 0. Finally, we characterize the price of stability 5 of SDGs for graphs with girth 4 and girth at least 5, the girth being the length of the shortest cycle in the graph.

scholarly journals Synthesis of Controllable Nash Equilibria in Quantitative Objective Game

2018 ◽  
Author(s):  
Shaull Almagor ◽  
Orna Kupferman ◽  
Giuseppe Perelli
Keyword(s):  
Social Choice ◽  
Nash Equilibria ◽  
Price Of Anarchy ◽  
Decision Procedures ◽  
Price Of Stability ◽  
Multi Agent System ◽  
Agent System ◽  
Multi Agent ◽  
Real Value ◽  
Strategy Logic

In Rational Synthesis, we consider a multi-agent system in which some of the agents are controllable and some are not. All agents have objectives, and the goal is to synthesize strategies for the controllable agents so that their objectives are satisfied, assuming rationality of the uncontrollable agents. Previous work on rational synthesis considers objectives in LTL, namely ones that describe on-going behaviors, and in Objective-LTL, which allows ranking of LTL formulas. In this paper, we extend rational synthesis to LTL[F] -- an extension of LTL by quality operators. The satisfaction value of an LTL[F] formula is a real value in [0,1], where the higher the value is, the higher is the quality in which the computation satisfies the specification. The extension significantly strengthens the framework of rational synthesis and enables a study its game- and social-choice theoretic aspects. In particular, we study the price of stability and price of anarchy of the rational-synthesis game and use them to explain the cooperative and non-cooperative settings of rational synthesis. Our algorithms make use of strategy logic and decision procedures for it. Thus, we are able to handle the richer quantitative setting using existing tools. In particular, we show that the cooperative and non-cooperative versions of quantitative rational synthesis are 2EXPTIME-complete and in 3EXPTIME, respectively -- not harder than the complexity known for their Boolean analogues.

scholarly journals Why You Should Charge Your Friends for Borrowing Your Stuff

2017 ◽  
Author(s):  
Kijung Shin ◽  
Euiwoong Lee ◽  
Dhivya Eswaran ◽  
Ariel D. Procaccia
Keyword(s):  
Social Networks ◽  
Social Network ◽  
Theoretical Analysis ◽  
Nash Equilibria ◽  
Price Of Anarchy ◽  
Price Of Stability ◽  
Free Riders ◽  
The Social ◽  
Access Cost ◽  
Game Theoretic

We consider goods that can be shared with k-hop neighbors (i.e., the set of nodes within k hops from an owner) on a social network. We examine incentives to buy such a good by devising game-theoretic models where each node decides whether to buy the good or free ride. First, we find that social inefficiency, specifically excessive purchase of the good, occurs in Nash equilibria. Second, the social inefficiency decreases as k increases and thus a good can be shared with more nodes. Third, and most importantly, the social inefficiency can also be significantly reduced by charging free riders an access cost and paying it to owners, leading to the conclusion that organizations and system designers should impose such a cost. These findings are supported by our theoretical analysis in terms of the price of anarchy and the price of stability; and by simulations based on synthetic and real social networks.

A Theory of Patronized Goods: Inefficient and Efficient Equilibria

2011 ◽  
pp. 65-87 ◽  
Author(s):  
A. Rubinstein
Keyword(s):  
Nash Equilibrium ◽  
Social Policy ◽  
Nash Equilibria ◽  
Institutional Environment ◽  
Social Motivation ◽  
Pareto Optimal ◽  
Market Failures ◽  
Equilibrium Conditions ◽  
Policy Issues

The article considers some aspects of the patronized goods theory with respect to efficient and inefficient equilibria. The author analyzes specific features of patronized goods as well as their connection with market failures, and conjectures that they are related to the emergence of Pareto-inefficient Nash equilibria. The key problem is the analysis of the opportunities for transforming inefficient Nash equilibrium into Pareto-optimal Nash equilibrium for patronized goods by modifying the institutional environment. The paper analyzes social motivation for institutional modernization and equilibrium conditions in the generalized Wicksell-Lindahl model for patronized goods. The author also considers some applications of patronized goods theory to social policy issues.

Revelation

2019 ◽  
pp. 348-369
Author(s):  
Lynn R. Huber
Keyword(s):  
Social Context ◽  
Gender Identity ◽  
Limited Attention ◽  
Gender Expectations ◽  
New Model

Despite much scholarship on Revelation’s feminine imagery, there has been limited attention to how the narrative as a whole participates in constructing the gender identity of its audience(s). Situated within a historical and social context in which ideal personhood was imagined in masculine terms, however, this gender identity is best understood in terms of masculinity, albeit a complexly imagined and anti-imperial masculinity, and as John’s attempt at “making men.” Revelation’s appropriation of the dominant culture’s discourses about masculinity serve as a tool for resisting that culture’s portrayal of the true man as one who succeeds in competition and who finds success in marrying and bearing children. Therefore, John undoes the gender expectations of his context, as he presents his audience a new model for being ideal men, ideal followers of the Lamb.

scholarly journals Expressiveness and Nash Equilibrium in Iterated Boolean Games

2021 ◽  
Vol 22 (2) ◽  
pp. 1-38
Author(s):  
Julian Gutierrez ◽  
Paul Harrenstein ◽  
Giuseppe Perelli ◽  
Michael Wooldridge
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Infinite Sequence ◽  
Multi Agent Systems ◽  
Temporal Logics ◽  
Agent Systems ◽  
Temporal Properties ◽  
Multi Agent ◽  
Game Theoretic ◽  
Boolean Games

We define and investigate a novel notion of expressiveness for temporal logics that is based on game theoretic equilibria of multi-agent systems. We use iterated Boolean games as our abstract model of multi-agent systems [Gutierrez et al. 2013, 2015a]. In such a game, each agent  has a goal  , represented using (a fragment of) Linear Temporal Logic ( ) . The goal  captures agent  ’s preferences, in the sense that the models of  represent system behaviours that would satisfy  . Each player controls a subset of Boolean variables , and at each round in the game, player is at liberty to choose values for variables in any way that she sees fit. Play continues for an infinite sequence of rounds, and so as players act they collectively trace out a model for , which for every player will either satisfy or fail to satisfy their goal. Players are assumed to act strategically, taking into account the goals of other players, in an attempt to bring about computations satisfying their goal. In this setting, we apply the standard game-theoretic concept of (pure) Nash equilibria. The (possibly empty) set of Nash equilibria of an iterated Boolean game can be understood as inducing a set of computations, each computation representing one way the system could evolve if players chose strategies that together constitute a Nash equilibrium. Such a set of equilibrium computations expresses a temporal property—which may or may not be expressible within a particular fragment. The new notion of expressiveness that we formally define and investigate is then as follows: What temporal properties are characterised by the Nash equilibria of games in which agent goals are expressed in specific fragments of  ? We formally define and investigate this notion of expressiveness for a range of fragments. For example, a very natural question is the following: Suppose we have an iterated Boolean game in which every goal is represented using a particular fragment of : is it then always the case that the equilibria of the game can be characterised within ? We show that this is not true in general.

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