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.

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.

scholarly journals The Impact of Selfishness in Hypergraph Hedonic Games

2020 ◽  
Vol 34 (02) ◽  
pp. 1766-1773
Author(s):  
Alessandro Aloisio ◽  
Michele Flammini ◽  
Cosimo Vinci
Keyword(s):  
Social Welfare ◽  
Price Of Anarchy ◽  
Maximum Size ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
The Social ◽  
Worst Case Ratio ◽  
Distinct Node ◽  
Hedonic Games ◽  
The Impact

We consider a class of coalition formation games that can be succinctly represented by means of hypergraphs and properly generalizes symmetric additively separable hedonic games. More precisely, an instance of hypegraph hedonic game consists of a weighted hypergraph, in which each agent is associated to a distinct node and her utility for being in a given coalition is equal to the sum of the weights of all the hyperedges included in the coalition. We study the performance of stable outcomes in such games, investigating the degradation of their social welfare under two different metrics, the k-Nash price of anarchy and k-core price of anarchy, where k is the maximum size of a deviating coalition. Such prices are defined as the worst-case ratio between the optimal social welfare and the social welfare obtained when the agents reach an outcome satisfying the respective stability criteria. We provide asymptotically tight upper and lower bounds on the values of these metrics for several classes of hypergraph hedonic games, parametrized according to the integer k, the hypergraph arity r and the number of agents n. Furthermore, we show that the problem of computing the exact value of such prices for a given instance is computationally hard, even in case of non-negative hyperedge weights.

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 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 A Lower Bound for the Query Phase of Contraction Hierarchies and Hub Labels and a Provably Optimal Instance-Based Schema

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 164
Author(s):  
Tobias Rupp ◽  
Stefan Funke
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Real World ◽  
Road Network ◽  
Upper And Lower Bounds ◽  
Bounded Degree ◽  
Shortest Path Routing ◽  
Graph Classes ◽  
Speed Up ◽  
To Come

We prove a Ω(n) lower bound on the query time for contraction hierarchies (CH) as well as hub labels, two popular speed-up techniques for shortest path routing. Our construction is based on a graph family not too far from subgraphs that occur in real-world road networks, in particular, it is planar and has a bounded degree. Additionally, we borrow ideas from our lower bound proof to come up with instance-based lower bounds for concrete road network instances of moderate size, reaching up to 96% of an upper bound given by a constructed CH. For a variant of our instance-based schema applied to some special graph classes, we can even show matching upper and lower bounds.

Green Politics and the New Class: Selfishness or Virtue?

1989 ◽  
Vol 37 (2) ◽  
pp. 205-223 ◽  
Author(s):  
Robyn Eckersley
Keyword(s):  
Middle Class ◽  
Production Process ◽  
Green Movement ◽  
New Class ◽  
Green Parties ◽  
New Middle Class ◽  
Social Composition ◽  
The Social ◽  
Green Politics ◽  
Material Values

The predominantly new middle-class social composition of the green movement has become a matter of increasing interest in the wake of the success of green parties and the growth of an international green movement. This paper considers the concept of the ‘new class' in relation to two explanations for the social composition of the green movement. The class-interest argument seeks to show that green politics is a means of furthering either middle-class or new-class interests while the ‘new childhood’ argument claims that the development of the green movement is the result of the spread of post-material values, the main bearers of which are the new class. Against these arguments a more comprehensive explanation is presented, which focuses on the education of the new class and its relative structural autonomy from the production process.

A Novel Method to Dynamically Fix Threshold for Node Neighbourhood Based Link Prediction Techniques

2020 ◽  
Vol 15 (1) ◽  
pp. 17-34
Author(s):  
Anand Kumar Gupta ◽  
Neetu Sardana
Keyword(s):  
Social Network ◽  
Link Prediction ◽  
Binary Classification ◽  
Online Social Network ◽  
Threshold Value ◽  
Classification Problem ◽  
Similarity Score ◽  
The Social ◽  
Comparative Results ◽  
Prediction Techniques

The objective of an online social network is to amplify the stream of information among the users. This goal can be accomplished by maximizing interconnectivity among users using link prediction techniques. Existing link prediction techniques uses varied heuristics such as similarity score to predict possible connections. Link prediction can be considered a binary classification problem where probable class outcomes are presence and absence of connections. One of the challenges in classification is to decide threshold value. Since the social network is exceptionally dynamic in nature and each user possess different features, it is difficult to choose a static, common threshold which decides whether two non-connected users will form interconnectivity. This article proposes a novel technique, FIXT, that dynamically decides the threshold value for predicting the possibility of new link formation. The article evaluates the performance of FIXT with six baseline techniques. The comparative results depict that FIXT achieves accuracy up to 93% and outperforms baseline techniques.

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 Box-Cox Gamma-G Family of Distributions: Theory and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1801
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Christophe Chesneau ◽  
Farrukh Jamal
Keyword(s):  
Maximum Likelihood ◽  
Statistical Model ◽  
Cauchy Distribution ◽  
Natural Generalization ◽  
Power Parameter ◽  
New Class ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
Box Cox Transformation ◽  
Family Of Distributions

This paper is devoted to a new class of distributions called the Box-Cox gamma-G family. It is a natural generalization of the useful Ristić–Balakrishnan-G family of distributions, containing a wide variety of power gamma-G distributions, including the odd gamma-G distributions. The key tool for this generalization is the use of the Box-Cox transformation involving a tuning power parameter. Diverse mathematical properties of interest are derived. Then a specific member with three parameters based on the half-Cauchy distribution is studied and considered as a statistical model. The method of maximum likelihood is used to estimate the related parameters, along with a simulation study illustrating the theoretical convergence of the estimators. Finally, two different real datasets are analyzed to show the fitting power of the new model compared to other appropriate models.

scholarly journals The representations of LGBTQ themes and individuals in non-fiction young adult literature

2017 ◽  
Vol 12 (2) ◽  
pp. 182-198 ◽  
Author(s):  
John H. Bickford
Keyword(s):  
Secondary Students ◽  
Publication Date ◽  
Trade Books ◽  
Community Interactions ◽  
Intended Audience ◽  
Content Type ◽  
White American ◽  
Non Fiction ◽  
The Social ◽  
Current Events

Purpose Social justice themes permeate the social studies, history, civics, and current events curricula. The purpose of this paper is to examine how non-fiction trade books represented lesbian, gay, bisexual, transsexual, transgender, and queer (LGBTQ) individuals and issues. Design/methodology/approach Trade books published after 2000 and intended for middle grades (5-8) and high school (9-12) students were analyzed. Findings Findings included main characters’ demography, sexuality, and various ancillary elements, such as connection to LGBTQ community, interactions with non-LGBTQ individuals, the challenges and contested terrain that LGBTQ individuals must traverse, and a range of responses to these challenges. Publication date, intended audience, and subgenre of non-fiction – specifically, memoir, expository, and historical text – added nuance to findings. Viewed broadly, the books generally engaged in exceptionalism, a historical misrepresentation, of one singular character who was a gay or lesbian white American. Diverse sexualities, races, ethnicities, and contexts were largely absent. Complex resistance structures were frequent and detailed. Originality/value This research contributes to previous scholarship exploring LGBTQ-themed fiction for secondary students and close readings of secondary level non-fiction trade books.

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