4 research outputs found
Maximizing Social Welfare in Score-Based Social Distance Games
Social distance games have been extensively studied as a coalition formation
model where the utilities of agents in each coalition were captured using a
utility function that took into account distances in a given social
network. In this paper, we consider a non-normalized score-based definition of
social distance games where the utility function depends on a generic
scoring vector , which may be customized to match the specifics of each
individual application scenario.
As our main technical contribution, we establish the tractability of
computing a welfare-maximizing partitioning of the agents into coalitions on
tree-like networks, for every score-based function . We provide more
efficient algorithms when dealing with specific choices of or simpler
networks, and also extend all of these results to computing coalitions that are
Nash stable or individually rational. We view these results as a further strong
indication of the usefulness of the proposed score-based utility function: even
on very simple networks, the problem of computing a welfare-maximizing
partitioning into coalitions remains open for the originally considered
canonical function .Comment: Short version appeared at TARK 2023. arXiv admin note: substantial
text overlap with arXiv:2307.0506
On Non-Cooperativeness in Social Distance Games
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.Peer reviewe
On Non-Cooperativeness in Social Distance Games
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.Peer reviewe