Maximizing Social Welfare in Fractional Hedonic Games using Shapley Value

2019 ◽  
Author(s):  
Siyuan Chen ◽  
Wei Liu ◽  
Jiamou Liu ◽  
Khi-Ui Soo ◽  
Wu Chen
Keyword(s):  
Social Welfare ◽  
Shapley Value ◽  
Hedonic Games

DON and Shapley Value for Allocation among Cooperating Agents in a Network: Conditions for Equivalence

2017 ◽  
Vol 5 (2) ◽  
pp. 143-161 ◽  
Author(s):  
Sridhar Mandyam ◽  
Usha Sridhar
Keyword(s):  
Social Welfare ◽  
Shapley Value ◽  
Centrality Measures ◽  
Pareto Optimal ◽  
Undirected Network ◽  
Social Welfare Maximization ◽  
Optimal Allocations ◽  
Game Theoretic ◽  
Cooperating Agents ◽  
Pareto Optimal Allocations

In a paper appearing in a recent issue of this journal ( Studies in Microeconomics), the authors explored a new method to allocate a divisible resource efficiently among cooperating agents located at the vertices of a connected undirected network. It was shown in that article that maximizing social welfare of the agents produces Pareto optimal allocations, referred to as dominance over neighbourhood (DON), capturing the notion of dominance over neighbourhood in terms of network degree. In this article, we show that the allocation suggested by the method competes well with current cooperative game-theoretic power centrality measures. We discuss the conditions under which DON turns exactly equivalent to a recent ‘fringe-based’ Shapley Value formulation for fixed networks, raising the possibility of such solutions being both Pareto optimal in a utilitarian social welfare maximization sense as well as fair in the Shapley value sense.

scholarly journals Nash Stable Outcomes in Fractional Hedonic Games: Existence, Efficiency and Computation

2018 ◽  
Vol 62 ◽  
pp. 315-371 ◽  
Author(s):  
Vittorio Bilò ◽  
Angelo Fanelli ◽  
Michele Flammini ◽  
Gianpiero Monaco ◽  
Luca Moscardelli
Keyword(s):  
Social Welfare ◽  
Optimal Solution ◽  
Solution Concept ◽  
Coalition Structure ◽  
Upper And Lower Bounds ◽  
Price Of Stability ◽  
Average Value ◽  
Tree Graphs ◽  
Hedonic Games ◽  
Stable Outcome

We consider fractional hedonic games, a subclass of coalition formation games that can be succinctly modeled by means of a graph in which nodes represent agents and edge weights the degree of preference of the corresponding endpoints. The happiness or utility of an agent for being in a coalition is the average value she ascribes to its members. We adopt Nash stable outcomes as the target solution concept; that is we focus on states in which no agent can improve her utility by unilaterally changing her own group. We provide existence, efficiency and complexity results for games played on both general and specific graph topologies. As to the efficiency results, we mainly study the quality of the best Nash stable outcome and refer to the ratio between the social welfare of an optimal coalition structure and the one of such an equilibrium as to the price of stability. In this respect, we remark that a best Nash stable outcome has a natural meaning of stability, since it is the optimal solution among the ones which can be accepted by selfish agents. We provide upper and lower bounds on the price of stability for different topologies, both in case of weighted and unweighted edges. Beside the results for general graphs, we give refined bounds for various specific cases, such as triangle-free, bipartite graphs and tree graphs. For these families, we also show how to efficiently compute Nash stable outcomes with provable good social welfare.

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.

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