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On Pareto optimality in social distance games
Artificial Intelligence ( IF 14.4 ) Pub Date : 2022-08-02 , DOI: 10.1016/j.artint.2022.103768
Alkida Balliu , Michele Flammini , Giovanna Melideo , Dennis Olivetti

We investigate Pareto stability in Social Distance Games (SDGs), which are coalition formation games where agents utilities are proportional to their harmonic centralities in the respective coalitions, i.e., to the average inverse distance from the other agents. Pareto optimal solutions have already been considered in the literature as outcomes arising from the strategic interaction of the self-interested agents. In particular, they are stable under the deviation of the grand coalition, as they do not permit a simultaneous deviation by all the agents making all of them weakly better off and some strictly better off. First, by providing a polynomial-time reduction from the NP-complete Restricted Exact 3-Cover by 3-Sets problem, we prove that computing a Pareto stable solution for a SDG maximizing the social welfare is NP-hard also in bounded degree graphs. Then, we show that a 2min(Δ,n)-approximating solution can be determined in polynomial time, where n is the number of agents and Δ the maximum node degree. Moreover, we provide asymptotically tight bounds on the price of Pareto optimality for several classes of social graphs arising from the following combinations: unbounded and bounded node degree, undirected and directed arcs, unweighted and weighted arcs.



中文翻译:

社交距离博弈中的帕累托最优

我们调查社交距离博弈中的帕累托稳定性(可持续发展目标s),这是联盟形成博弈,其中代理效用与其在各自联盟中的调和中心性成正比,即与其他代理的平均反距离成正比。帕累托最优解已经在文献中被认为是自利代理人战略互动产生的结果。特别是,它们在大联盟的偏离下是稳定的,因为它们不允许所有代理人同时偏离,从而使他们所有人的境况都变得微弱地好一些,而一些人的境况则严格地好一些。首先,通过从 NP-complete Restricted Exact 3-Cover by 3-Sets 问题中提供多项式时间缩减,我们证明计算一个 Pareto 稳定解可持续发展目标在有界度图中,最大化社会福利也是 NP 难的。然后,我们证明一个2分钟(Δ,n)-近似解可以在多项式时间内确定,其中n是代理的数量,Δ 是最大节点度。此外,我们为由以下组合产生的几类社会图提供了帕累托最优价格的渐近紧密界限:无界和有界节点度、无向和有向弧、未加权和加权弧。

更新日期:2022-08-02
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