Limitations of cross-monotonic cost-sharing schemes

Immorlica, Nicole; Mahdian, Mohammad; Mirrokni, Vahab

doi:10.1145/1361192.1361201

Cited by 79 publications

(141 citation statements)

References 23 publications

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“…In these games the underlying assumption is that a central authority designs and maintains the solution and dictates cost shares for each player. This is close to assumptions that are made in the area of cost sharing mechanisms, which have received a lot of attention [27,29,30,34]. Designing cost shares, e.g., using Shapley value cost sharing [1,6,15,31], can yield favorable properties on the existence and cost of Nash equilibria.…”

Section: Introductionsupporting

confidence: 62%

Strategic cooperation in cost sharing games

Hoefer

2011

Int J Game Theory

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In this paper we consider strategic cost sharing games with so-called arbitrary sharing based on various combinatorial optimization problems, such as vertex and set cover, facility location, and network design problems. We concentrate on the existence and computational complexity of strong equilibria, in which no coalition can improve the cost of each of its members.Our main result reveals a connection between strong equilibrium in strategic games and the core in traditional coalitional cost sharing games studied in economics. For set cover and facility location games this results in a tight characterization of the existence of strong equilibrium using the integrality gap of suitable linear programming formulations. Furthermore, it allows to derive all existing results for strong equilibria in network design cost sharing games with arbitrary sharing via a unified approach. In addition, we are able to show that in general the strong price of anarchy is always 1. This should be contrasted with the price of anarchy of Θ(n) for Nash equilibria. Finally, we indicate that the LP-approach can also be used to compute near-optimal and near-stable approximate strong equilibria.

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Section: Introductionsupporting

confidence: 62%

Strategic cooperation in cost sharing games

Hoefer

2011

Int J Game Theory

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“…2. The construction of this example is inspired by the example presented in Immorlica et al (2008) for lower bounding the budget-balance factor of any cross-monotonic cost-sharing scheme for metric uncapacitated facility location. 3.…”

Section: Endnotesmentioning

confidence: 99%

Price of Correlations in Stochastic Optimization

Agrawal

Ding

Saberi

et al. 2012

Operations Research

119

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When decisions are made in the presence of large-scale stochastic data, it is common to pay more attention to the easy-to-see statistics (e.g., mean) instead of the underlying correlations. One reason is that it is often much easier to solve a stochastic optimization problem by assuming independence across the random data. In this paper, we study the possible loss incurred by ignoring these correlations through a distributionally-robust stochastic programming model, and propose a new concept called Price of Correlations (POC) to quantify that loss. We show that the POC has a small upper bound for a wide class of cost functions, including uncapacitated facility location, Steiner tree and submodular functions, suggesting that the intuitive approach of assuming independent distribution may actually work well for these stochastic optimization problems. On the other hand, we demonstrate that for some cost functions, POC can be particularly large, e.g., the supermodular functions. We propose alternative ways to solve the corresponding distributionally robust models for these functions. As a byproduct, our analysis yields new results on social welfare maximization and the existence of Walrasian equilibria, which may be of independent interest.

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“…The bound 1 ln dmax is tight. We also present a cost sharing method that is 1 2n -budget-balanced core and cross-monotone, which is almost the optimum [4].…”

Section: Our Resultsmentioning

confidence: 99%

Cost sharing and strategyproof mechanisms for set cover games

Sun

Wang

et al. 2009

J Comb Optim

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Abstract. We develop for set cover games several general cost-sharing methods that are approximately budget-balanced, core, and/or group-strategyproof. We first study the cost sharing for a single set cover game, which does not have a budget-balanced core. We show that there is no cost allocation method that can always recover more than 1 ln n of the total cost if we require the cost sharing being a core. Here n is the number of all players to be served. We give an efficient cost allocation method that always recovers 1 ln dmax of the total cost, where dmax is the maximum size of all sets. We then study the cost allocation scheme for all induced subgames. It is known that no cost sharing scheme can always recover more than 1 n of the total cost for every subset of players. We give an efficient cost sharing scheme that always recovers at least 1 2n of the total cost for every subset of players and furthermore, our scheme is cross-monotone. When the elements to be covered are selfish agents with privately known valuations, we present a strategyproof charging mechanism, under the assumption that all sets are simple sets, such that each element maximizes its profit when it reports its valuation truthfully; further, the total cost of the set cover is no more than ln dmax times that of an optimal solution. When the sets are selfish agents with privately known costs, we present a strategyproof payment mechanism in which each set maximizes its profit when it reports its cost truthfully. We also show how to fairly share the payments to all sets among the elements.

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Limitations of cross-monotonic cost-sharing schemes

Cited by 79 publications

References 23 publications

Strategic cooperation in cost sharing games

Strategic cooperation in cost sharing games

Price of Correlations in Stochastic Optimization

Cost sharing and strategyproof mechanisms for set cover games

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