Combinatorial Civic Crowdfunding with Budgeted Agents: Welfare Optimality at Equilibrium and Optimal Deviation

Civic Crowdfunding (CC) uses the ``power of the crowd'' to garner contributions towards public projects. As these projects are non-excludable, agents may prefer to ``free-ride,'' resulting in the project not being funded. For single project CC, researchers propose to provide refunds to incentivize agents to contribute, thereby guaranteeing the project's funding. These funding guarantees are applicable only when agents have an unlimited budget. This work focuses on a combinatorial setting, where multiple projects are available for CC and agents have a limited budget. We study certain specific conditions where funding can be guaranteed. Further, funding the optimal social welfare subset of projects is desirable when every available project cannot be funded due to budget restrictions. We prove the impossibility of achieving optimal welfare at equilibrium for any monotone refund scheme. We then study different heuristics that the agents can use to contribute to the projects in practice. Through simulations, we demonstrate the heuristics' performance as the average-case trade-off between welfare obtained and agent utility.Comment: To appear in the Proceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence (AAAI '23). A preliminary version of this paper titled "Welfare Optimal Combinatorial Civic Crowdfunding with Budgeted Agents" also appeared at GAIW@AAMAS '2

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

A Shapley-value Mechanism for Bandwidth On Demand between Datacenters

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Cost Sharing Games for Energy-Efficient Multi-Hop Broadcast in Wireless Networks

We study multi-hop broadcast in wireless networks with one source node and multiple receiving nodes. The message flow from the source to the receivers can be modeled as a tree-graph, called broadcast-tree. The problem of finding the minimum-power broadcast-tree (MPBT) is NP-complete. Unlike most of the existing centralized approaches, we propose a decentralized algorithm, based on a non-cooperative cost-sharing game. In this game, every receiving node, as a player, chooses another node of the network as its respective transmitting node for receiving the message. Consequently, a cost is assigned to the receiving node based on the power imposed on its chosen transmitting node. In our model, the total required power at a transmitting node consists of (i) the transmit power and (ii) the circuitry power needed for communication hardware modules. We develop our algorithm using the marginal contribution (MC) cost-sharing scheme and show that the optimum broadcast-tree is always a Nash equilibrium (NE) of the game. Simulation results demonstrate that our proposed algorithm outperforms conventional algorithms for the MPBT problem. Besides, we show that the circuitry power, which is usually ignored by existing algorithms, significantly impacts the energy-efficiency of the network.Comment: 33 pages including references, figures, and table

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]

Public exludable goods and how to finance them: a literature review

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2024, Director: Bruno Mazorra i Mikel Álvarez-Mozos[en] Since the transition of Ethereum from a Proof-of-Work to a Proof-of-Stake consensus protocol back in September 2022, the Proposer Buider Separation schema, or PBS, arose as the methodology for block producing. This protocol runs at a deficit for the relays, the trusted third party between the proposers and builders, fact that motivated our intrest in studying the properties of the protocol. In this work we review the theoretical background needed to takle this analysis from a mechanism design perspective, we heavily relayand sumarise the the work of Roughgarden et al., providing the tools we need for it. Our main goal is to expose the basic notions of mechanism design theory and build a model capable of explaining the financing of public excludable goods, trying to provide a self sufficient and coherent thesis, even if disregarding problem that motivated this line of research. To achieve our goal we start by introducing several basic concepts of different aspects of applied mathematics and economics, opening the way to the development of those ideas into more sophisticated concepts. This theoretical approach peaks with the exposition of a selection of mechanisms and models and a review of their properties

La Moderna teoria de l'elecció social: de la impossibilitat a la possibilitat

Es presenten els dos teoremes d'impossibilitat més importants de la moderna teoria de l'elecció social: el teorema d'Arrow per a funcions de benestar social no dictatorials que satisfan el principi de Pareto i la propietat de la independència d'alternatives irrellevants, i el teorema de Gibbard-Satterthwaite per a funcions d'elecció social no trivials i no manipulables. Es descriuen set exemples de problemes concrets d'elecció social en què l'estructura particular del conjunt d'alternatives socials permet restringir el domini de preferències individuals i dissenyar, per a cada un d'aquests, funcions d'elecció social no manipulables en els corresponents dominis de preferències restringits.We present the two most important impossibility theorems of the modern social choice theory: Arrow’s theorem for social welfare functions satisfying the Pareto principle and the independence of irrelevant alternatives property, and Gibbard-Satterthwaite’s theorem for non-trivial and strategy-proof social choice functions. We describe seven examples of specific social choice problems where the particular structure of the set of social alternatives allows to restrict the domain of individual preferences and to design for each of them strategy-proof social choice functions on the corresponding restricted preference domains