Cost Sharing over Combinatorial Domains: Complement-Free Cost Functions and Beyond

We study mechanism design for combinatorial cost sharing models. Imagine that multiple items or services are available to be shared among a set of interested agents. The outcome of a mechanism in this setting consists of an assignment, determining for each item the set of players who are granted service, together with respective payments. Although there are several works studying specialized versions of such problems, there has been almost no progress for general combinatorial cost sharing domains until recently [S. Dobzinski and S. Ovadia, 2017]. Still, many questions about the interplay between strategyproofness, cost recovery and economic efficiency remain unanswered. The main goal of our work is to further understand this interplay in terms of budget balance and social cost approximation. Towards this, we provide a refinement of cross-monotonicity (which we term trace-monotonicity) that is applicable to iterative mechanisms. The trace here refers to the order in which players become finalized. On top of this, we also provide two parameterizations (complementary to a certain extent) of cost functions which capture the behavior of their average cost-shares. Based on our trace-monotonicity property, we design a scheme of ascending cost sharing mechanisms which is applicable to the combinatorial cost sharing setting with symmetric submodular valuations. Using our first cost function parameterization, we identify conditions under which our mechanism is weakly group-strategyproof, O(1)-budget-balanced and O(H_n)-approximate with respect to the social cost. Further, we show that our mechanism is budget-balanced and H_n-approximate if both the valuations and the cost functions are symmetric submodular; given existing impossibility results, this is best possible. Finally, we consider general valuation functions and exploit our second parameterization to derive a more fine-grained analysis of the Sequential Mechanism introduced by Moulin. This mechanism is budget balanced by construction, but in general only guarantees a poor social cost approximation of n. We identify conditions under which the mechanism achieves improved social cost approximation guarantees. In particular, we derive improved mechanisms for fundamental cost sharing problems, including Vertex Cover and Set Cover

07271 Abstracts Collection -- Computational Social Systems and the Internet

From 01.07. to 06.07.2007, the Dagstuhl Seminar 07271 ``Computational Social Systems and the Internet\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

On Proportionate and Truthful International Alliance Contributions: An Analysis of Incentive Compatible Cost Sharing Mechanisms to Burden Sharing

Burden sharing within an international alliance is a contentious topic, especially in the current geopolitical environment, that in practice is generally imposed by a central authority\u27s perception of its members\u27 abilities to contribute. Instead, we propose a cost sharing mechanism such that burden shares are allocated to nations based on their honest declarations of the alliance\u27s worth. Specifically, we develop a set of multiobjective nonlinear optimization problem formulations that respectively impose Bayesian Incentive Compatible (BIC), Strategyproof (SP), and Group Strategyproof (GSP) mechanisms based on probabilistic inspection efforts and deception penalties that are budget balanced and in the core. Any feasible solution to these problems corresponds to a single stage Bayesian stochastic game wherein a collectively honest declaration is a Bayes-Nash equilibrium, a Nash Equilibrium in dominant strategies, or a collusion resistant Nash equilibrium, respectively, but the optimal solution considers the alliance\u27s central authority preferences. Each formulation is shown to be a nonconvex optimization problem. The solution quality and computational effort required for three heuristic algorithms as well as the BARON global solver are analyzed to determine the superlative solution methodology for each problem. The Pareto fronts associated with each multiobjective optimization problem are examined to determine the tradeoff between inspection frequency and penalty severity required to obtain truthfulness under stronger assumptions. Memory limitations are examined to ascertain the size of alliances for which the proposed methodology can be utilized. Finally, a full block design experiment considering the clustering of available alliance valuations and the member nations\u27 probability distributions therein is executed on an intermediate-sized alliance motivated by the South American alliance UNASUR

Cost sharing over combinatorial domains: Complement-free cost functions and beyond

We study mechanism design for combinatorial cost sharing models. Imagine that multiple items or services are available to be shared among a set of interested agents. The outcome of a mechanism in this setting consists of an assignment, determining for each item the set of players who are granted service, together with respective payments. Although there are several works studying specialized versions of such problems, there has been almost no progress for general combinatorial cost sharing domains until recently [7]. Still, many questions about the interplay between strategyproofness, cost recovery and economic efficiency remain unanswered. The main goal of our work is to further understand this interplay in terms of budget balance and social cost approximation. Towards this, we provide a refinement of cross-monotonicity (which we term trace-monotonicity) that is applicable to iterative mechanisms. The trace here refers to the order in which players become finalized. On top of this, we also provide two parameterizations (complementary to a certain extent) of cost functions which capture the behavior of their average cost-shares. Based on our trace-monotonicity property, we design a scheme of ascending cost sharing mechanisms which is applicable to the combinatorial cost sharing setting with symmetric submodular valuations. Using our first cost function parameterization, we identify conditions under which our mechanism is weakly group-strategyproof, O(1)-budget-balanced and O(Hn)-approximate with respect to the social cost. Further, we show that our mechanism is budget-balanced and Hn-approximate if both the valuations and the cost functions are symmetric submodular; given existing impossibility results, this is best possible. Finally, we consider general valuation functions and exploit our second parameterization to derive a more fine-grained analysis of the Sequential Mechanism introduced by Moulin. This mechanism is budget balanced by construction, but in general only guarantees a poor social cost approximation of n. We identify conditions under which the mechanism achieves improved social cost approximation guarantees. In particular, we derive improved mechanisms for fundamental cost sharing problems, including Vertex Cover and Set Cover

On cost sharing in the provision of a binary and excludable public good

Jordi Massó acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centers of Excellence in R&D (SEV-2011-0075) and FEDER grant ECO2008-04756 (Grupo Consilidado-C), and from the Generalitat de Catalunya, through the prize "ICREA Academia" for excellence in research and grant SGR2009-419. Antonio Nicolò's work is partially supported by the project "Intelligent preference reasoning for multi-agent decision making" (Univ. of Padova).Altres ajuts: FEDER/ECO2008-04756We study efficiency and fairness properties of the equal cost sharing with maximal participation (ECSMP) mechanism in the provision of a binary and excludable public good. According to the maximal welfare loss criterion, the ECSMP is optimal within the class of strategyproof, individually rational and no-deficit mechanisms only when there are two agents. In general the ECSMP mechanism is not optimal: we provide a class of mechanisms obtained by symmetric perturbations of ECSMP with strictly lower maximal welfare loss. We show that if one of two possible fairness conditions is additionally imposed, the ECSMP mechanism becomes optimal

Designing efficient and incentive compatible mechanisms is almost impossible in quasi-linear environments

In quasi-linear environments, classic theories state that it is possible to design efficient and incentive-compatible mechanisms, such as Vickrey, Clarke and Groves (VCG) mechanisms. However, once financial constraints are taken into account, we find that almost no financial constraint is compatible with efficiency and individual incentives over unrestricted domains and some restricted domains. Therefore, our results imply that even in quasi-linear environments, it is still impossible to design an efficient and incentive compatible mechanism because of financial constraints

Generalized Incremental Mechanisms for Scheduling Games

We study the problem of devising truthful mechanisms for cooperative cost sharing games that realize (approximate) budget balance and social cost. Recent negative results show that group-strategyproof mechanisms can only achieve very poor approximation guarantees for several fundamental cost sharing games. Driven by these limitations, we consider cost sharing mechanisms that realize the weaker notion of weak groupstrategyproofness. Mehta et al. [Games and Economic Behavior, 67:125–155, 2009] recently introduced the broad class of weakly group-strategyproof acyclic mechanisms and show that several primal-dual approximation algorithms naturally give rise to such mechanisms with attractive approximation guarantees. In this paper, we provide a simple yet powerful approach that enables us to turn any r-approximation algorithm into a r-budget balanced acyclic mechanism. We demonstrate the applicability of our approach by deriving weakly group-strategyproof mechanisms for several fundamental scheduling problems that outperform the best possible approximation guarantees of Moulin mechanisms. The mechanisms that we develop for completion time scheduling problems are the first mechanisms that achieve constant budget balance and social cost approximation factors. Interestingly, our mechanisms belong to the class of generalized incremental mechanisms proposed by Moulin [Social Choice and Welfare, 16:279–320, 1999]

Cost sharing over combinatorial domains

We study the problem of designing cost-sharing mechanisms for combinatorial domains. Suppose that multiple items or services are available to be shared among a set of interested agents. The outcome of a mechanism in this setting consists of an assignment, determining for each item the set of players who are granted service, together with respective payments. Although there are several works studying specialized versions of such problems, there has been almost no progress for general combinatorial cost-sharing domains until recently [9]. Still, many questions about the interplay between strategyproofness, cost recovery, and economic efficiency remain unanswered.The main goal of our work is to further understand this interplay in terms of budget balance and social cost approximation. Towards this, we provide a refinement of cross-monotonicity (which we term trace-monotonicity) that is applicable to iterative mechanisms. The trace here refers to the order in which players become finalized. On top of this, we also provide two parameterizations (complementary to a certain extent) of cost functions, which capture the behavior of their average cost-shares.Based on our trace-monotonicity property, we design an Iterative Ascending Cost-Sharing Mechanism, which is applicable to the combinatorial cost-sharing setting with symmetric submodular valuations. Using our first cost function parameterization, we identify conditions under which our mechanism is weakly group-strategyproof, O(1)-budget-balanced, and O(Hn)-approximate with respect to the social cost. Furthermore, we show that our mechanism is budget-balanced and Hn-approximate if both the valuations and the cost functions are symmetric submodular; given existing impossibility results, this is best possible.Finally, we consider general valuation functions and exploit our second parameterization to derive a more fine-grained analysis of the Sequential Mechanism introduced by Moulin. This mechanism is budget balanced by construction, but in general, only guarantees a poor social cost approximation of n. We identify conditions under which the mechanism achieves improved social cost approximation guarantees. In particular, we derive improved mechanisms for fundamental cost-sharing problems, including Vertex Cover and Set Cover