16. Acceptable Points in General Cooperative n-Person Games

Aumann, Robert J.

doi:10.1515/9781400882168-018

Cited by 597 publications

(590 citation statements)

References 5 publications

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“…We study the social cost (sum of individual agents' costs) of stable network infrastructures, represented by pure Nash equilibria and strong equilibria of the game. Strong equilibriaintroduced by Aumann in [3] -extend pure equilibria by being resilient to pure coalitional deviations: no subset of agents can deviate so that all of its members are better off. We prove bounds on the Price of Stability (PoS) of pure equilibria, i.e.…”

Section: Introductionmentioning

confidence: 99%

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On Pure and (Approximate) Strong Equilibria of Facility Location Games

Hansen

Telelis

2008

Lecture Notes in Computer Science

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Abstract. We study social cost losses in Facility Location games, where n selfish agents install facilities over a network and connect to them, so as to forward their local demand (expressed by a non-negative weight per agent). Agents using the same facility share fairly its installation cost, but every agent pays individually a (weighted) connection cost to the chosen location. We study the Price of Stability (PoS) of pure Nash equilibria and the Price of Anarchy of strong equilibria (SPoA), that generalize pure equilibria by being resilient to coalitional deviations. For unweighted agents on metric networks we prove upper and lower bounds on P oS, while an O(ln n) upper bound implied by previous work is tight for nonmetric networks. We also prove a constant upper bound for the SPoA of metric networks when strong equilibria exist. For the weighted game on general networks we prove existence of e-approximate (e = 2.718 . . .) strong equilibria and an upper bound of O(ln W ) on SPoA (W is the sum of agents' weights), which becomes tight Θ(ln n) for unweighted agents.

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Section: Introductionmentioning

confidence: 99%

“…For α ≥ 1, a strategy profile s is an α-approximate strong equilibrium if no subset of agents can perform a pure deviation, and each of its members be better off by a factor more than α. If α = 1, s is a strong equilibrium [3,8].…”

Section: Introductionmentioning

confidence: 99%

On Pure and (Approximate) Strong Equilibria of Facility Location Games

Hansen

Telelis

2008

Lecture Notes in Computer Science

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“…SE of network design games were first studied by Epstein et al [6]. The notion of SE is due to Aumann [11]. Metric Facility Location with unweighted players is the only case of the model of [1], in which tight constant bounds are known for the Price of Stability [2].…”

Section: Introductionmentioning

confidence: 99%

Improved Bounds for Facility Location Games with Fair Cost Allocation

Hansen

Telelis

2009

Combinatorial Optimization and Applications

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Abstract. We study Facility Location games played by n agents situated on the nodes of a graph. Each agent orders installation of a facility at a node of the graph and pays connection cost to the chosen node, and shares fairly facility installation cost with other agents having chosen the same location. This game has pure strategy Nash equilibria, that can be found by simple improvements performed by the agents iteratively. We show that this algorithm may need super-polynomial Ω(2 n 1 2 ) steps to converge. For metric graphs we show that approximate pure equilibria can be found in polynomial time. On metric graphs we consider additionally strong equilibria; previous work had shown that they do not always exist. We upper bound the overall (social) cost of α-approximate strong equilibria within a factor O(α ln α) of the optimum, for every α ≥ 1.

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“…As for cooperative game theory, the need of a strategic-form foundation has been persistently felt. One suggestion was provided for the transferable-utility ("TU") case by the founders (von Neumann and Morgenstern, 1944, proposed to define what a coalition could reach as the maximin level for the sum of the payoffs of the members of the coalition), and later generalized (Aumann, 1959) to the non-transferable-utility ("NTU") case in the guise of the "alpha" and "beta" coalitional forms. Dissatisfaction with these definitions drew attention to particular classes of games where the determination of the coalitional form appeared uncontroversial (the "c-games" of Shapley-Shubik, a leading example of which is exchange economies; see Shubik, 1983, Section 6.2.2), and thus the theory of bargaining could be nicely factored through the coalitional form.…”

Section: Introductionmentioning

confidence: 99%

Cooperative Games in Strategic Form

Hart

Mas-Colell

2008

SSRN Journal

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In this paper we view bargaining and cooperation as an interaction superimposed on a strategic form game. A multistage bargaining procedure for N players, the "proposer commitment" procedure, is presented. It is inspired by Nash's two-player variable-threat model; a key feature is the commitment to "threats." We establish links to classical cooperative game theory solutions, such as the Shapley value in the transferable utility case. However, we show that even in standard pure exchange economies the traditional coalitional function may not be adequate when utilities are not transferable.

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16. Acceptable Points in General Cooperative n-Person Games

Cited by 597 publications

References 5 publications

On Pure and (Approximate) Strong Equilibria of Facility Location Games

On Pure and (Approximate) Strong Equilibria of Facility Location Games

Improved Bounds for Facility Location Games with Fair Cost Allocation

Cooperative Games in Strategic Form

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