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 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 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 Algorithms for Closed Under Rational Behavior (CURB) Sets

2010 ◽  
Vol 38 ◽  
pp. 513-534 ◽  
Author(s):  
M. Benisch ◽  
G. B. Davis ◽  
T. Sandholm
Keyword(s):  
Nash Equilibrium ◽  
Polynomial Time ◽  
Solution Concept ◽  
Rational Behavior ◽  
Strategy Space ◽  
Normal Form Games ◽  
Polynomial Time Algorithms ◽  
Game Theoretic ◽  
Theoretic Solution ◽  
Best Responses

We provide a series of algorithms demonstrating that solutions according to the fundamental game-theoretic solution concept of closed under rational behavior (CURB) sets in two-player, normal-form games can be computed in polynomial time (we also discuss extensions to n-player games). First, we describe an algorithm that identifies all of a player’s best responses conditioned on the belief that the other player will play from within a given subset of its strategy space. This algorithm serves as a subroutine in a series of polynomial-time algorithms for finding all minimal CURB sets, one minimal CURB set, and the smallest minimal CURB set in a game. We then show that the complexity of finding a Nash equilibrium can be exponential only in the size of a game’s smallest CURB set. Related to this, we show that the smallest CURB set can be an arbitrarily small portion of the game, but it can also be arbitrarily larger than the supports of its only enclosed Nash equilibrium. We test our algorithms empirically and find that most commonly studied academic games tend to have either very large or very small minimal CURB sets.

scholarly journals On the Nash equilibrium in the inspector problem

2014 ◽  
Vol 55 ◽  
Author(s):  
Martynas Sabaliauskas ◽  
Jonas Mockus
Keyword(s):  
Nash Equilibrium ◽  
Polynomial Time ◽  
Explicit Solution ◽  
Security Systems ◽  
Bimatrix Game ◽  
Complete Problem ◽  
Elimination Algorithm ◽  
Np Complete ◽  
Special Case

Inspector problem represents an economic duel of inspector and law violator and is formulated as a bimatrix game. In general, bimatrix game is NP-complete problem. The inspector problem is a special case where the equilibrium can be found in polynomial time. In this paper, a generalized version of the Inspector Problem is described with the aim to represent broader family of applied problems, including the optimization of security systems. The explicit solution is provided and the Modified Strategy Elimination algorithm is introduced.

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.

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.

scholarly journals Machine load balancing game with linear externalities

2021 ◽  
Vol 13 (2) ◽  
pp. 62-79
Author(s):  
Юлия Васильевна Чиркова ◽  
Julia Chirkova
Keyword(s):  
Nash Equilibrium ◽  
Load Balancing ◽  
Social Cost ◽  
Price Of Anarchy ◽  
Equilibrium Existence ◽  
Machine Load ◽  
Maximum Delay ◽  
The Social ◽  
Two Machines

The Machine Load Balancing Game with linear externalities is considered. A set of jobs is to be assigned to a set of machines with different latencies depending on their own loads and also loads on other machines. Jobs choose machines to minimize their own latencies. The social cost of a schedule is the maximum delay among all machines, i.e. {\it makespan. For the case of two machines in this model an Nash equilibrium existence is proven and of the expression for the Price of Anarchy is obtained.

scholarly journals Distance Polymatrix Coordination Games

2021 ◽  
Author(s):  
Alessandro Aloisio ◽  
Michele Flammini ◽  
Bojana Kodric ◽  
Cosimo Vinci
Keyword(s):  
Price Of Anarchy ◽  
Threshold Value ◽  
Natural Generalization ◽  
Coordination Games ◽  
Upper And Lower Bounds ◽  
Price Of Stability ◽  
Community Interactions ◽  
Bounded Degree ◽  
New Class ◽  
The Social

In polymatrix coordination games, each player x is a node of a graph and must select an action in her strategy set. Nodes are playing separate bimatrix games with their neighbors in the graph. Namely, the utility of x is given by the preference she has for her action plus, for each neighbor y, a payoff which strictly depends on the mutual actions played by x and y. We propose the new class of distance polymatrix coordination games, properly generalizing polymatrix coordination games, in which the overall utility of player x further depends on the payoffs arising by mutual actions of players v,z that are the endpoints of edges at any distance h<d from x, for a fixed threshold value d≤n. In particular, the overall utility of player x is the sum of all the above payoffs, where each payoff is proportionally discounted by a factor depending on the distance h of the corresponding edge. Under the above framework, which is a natural generalization that is well-suited for capturing positive community interactions, we study the social inefficiency of equilibria resorting to standard measures of Price of Anarchy and Price of Stability. Namely, we provide suitable upper and lower bounds for the aforementioned quantities, both for bounded-degree and general graphs.

Seeing Similarity or Distance?

2014 ◽  
Vol 45 (2) ◽  
pp. 127-134 ◽  
Author(s):  
Leigh Wilton ◽  
Diana T. Sanchez ◽  
Lisa Giamo
Keyword(s):  
Social Distance ◽  
Mixed Race ◽  
Racial Groups ◽  
Perceived Similarity ◽  
The Social ◽  
Intergroup Perception ◽  
Intergroup Perceptions ◽  
Racially Ambiguous ◽  
Ambiguous Faces

Biracial individuals threaten the distinctiveness of racial groups because they have mixed-race ancestry, but recent findings suggest that exposure to biracial-labeled, racially ambiguous faces may positively influence intergroup perception by reducing essentialist thinking among Whites ( Young, Sanchez, & Wilton, 2013 ). However, biracial exposure may not lead to positive intergroup perceptions for Whites who are highly racially identified and thus motivated to preserve the social distance between racial groups. We exposed Whites to racially ambiguous Asian/White biracial faces and measured the perceived similarity between Asians and Whites. We found that exposure to racially ambiguous, biracial-labeled targets may improve perceptions of intergroup similarity, but only for Whites who are less racially identified. Results are discussed in terms of motivated intergroup perception.

People represent their own mental states more distinctly than others’

2018 ◽  
Author(s):  
Mark Allen Thornton ◽  
Miriam E. Weaverdyck ◽  
Judith Mildner ◽  
Diana Tamir
Keyword(s):  
Mental State ◽  
Social Distance ◽  
Activity Patterns ◽  
Mental States ◽  
Direct Access ◽  
Social Brain ◽  
Privileged Access ◽  
Behavioral Studies ◽  
The Social ◽  
External Cues

One can never know the internal workings of another person – one can only infer others’ mental states based on external cues. In contrast, each person has direct access to the contents of their own mind. Here we test the hypothesis that this privileged access shapes the way people represent internal mental experiences, such that they represent their own mental states more distinctly than the states of others. Across four studies, participants considered their own and others’ mental states; analyses measured the distinctiveness of mental state representations. Two neuroimaging studies used representational similarity analyses to demonstrate that the social brain manifests more distinct activity patterns when thinking about one’s own states versus others’. Two behavioral studies support these findings. Further, they demonstrate that people differentiate between states less as social distance increases. Together these results suggest that we represent our own mind with greater granularity than the minds of others.

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