M-DPOP: Faithful Distributed Implementation of Efficient Social Choice Problems

Abstract

In the efficient social choice problem, the goal is to assign values, subject to side constraints, to a set of variables to maximize the total utility across a population of agents, where each agent has private information about its utility function. In this paper we model the social choice problem as a distributed constraint optimization problem (DCOP), in which each agent can communicate with other agents that share an interest in one or more variables. Whereas existing DCOP algorithms can be easily manipulated by an agent, either by misreporting private information or deviating from the algorithm, we introduce M-DPOP, the first DCOP algorithm that provides a faithful distributed implementation for efficient social choice. This provides a concrete example of how the methods of mechanism design can be unified with those of distributed optimization. Faithfulness ensures that no agent can benefit by unilaterally deviating from any aspect of the protocol, neither informationrevelation, computation, nor communication, and whatever the private information of other agents. We allow for payments by agents to a central bank, which is the only central authority that we require. To achieve faithfulness, we carefully integrate the Vickrey-Clarke-Groves (VCG) mechanism with the DPOP algorithm, such that each agent is only asked to perform computation, report information, and send messages that is in its own best interest. Determining agent i's payment requires solving the social choice problem without agent i. Here, we present a method to reuse computation performed in solving the main problem in a way that is robust against manipulation by the excluded agent. Experimental results on structured problems show that as much as 87% of the computation required for solving the marginal problems can be avoided by re-use, providing very good scalability in the number of agents. On unstructured problems, we observe a sensitivity of M-DPOP to the density of the problem, and we show that reusability decreases from almost 100% for very sparse problems to around 20% for highly connected problems. We close with a discussion of the features of DCOP that enable faithful implementations in this problem, the challenge of reusing computation from the main problem to marginal problems in other algorithms such as ADOPT and OptAPO, and the prospect of methods to avoid the welfare loss that can occur because of the transfer of payments to the bank.

A Tutorial on Optimization for Multi-Agent Systems

“…While auctions are deemed appropriate for competitive settings where each agent is vying for some resource and is unlikely to reveal its private information to gain an advantage, DCOPs are more appropriate when the agents aim at maximising a system wide objective and might be willing to exchange messages containing some of their private information to do so. Nonetheless, privacy is considered as a crucial issue in DCOP solution techniques and there are approaches that analyse the privacy-eciency tradeo (e.g., [112]) or propose the use of DCOPs for issues related to mechanism design, such as devising a faithful distributed implementation for ecient social choice (e.g., [113]). These approaches lead toward interesting research directions where DCOPs could be used as ecient tools for resource allocation problems that are typically solved by using auctions.…”

Simple negotiation schemes for agents with simple preferences: sufficiency, necessity and maximality

“…In this case, the system designer will typically seek to set up the system in such way that it nevertheless guarantees certain desirable properties, but without directly interfering in the negotiation process itself. Similar considerations have led to research areas such as distributed constraint optimisation [14] or distributed mechanism design [25,26]. In this paper, we further analyse a framework for distributed negotiation over indivisible resources recently investigated by a number of authors [4,12,13,29,30].…”

Protecting Privacy through Distributed Computation in Multi-agent Decision Making

“…Note that this honesty assumption does not mean that all agents are assumed to faithfully report their true constraints to the algorithm; they may be tempted to strategize by reporting slightly different constraints, hoping that this would lead the algorithm to select a solution to the problem that they deem preferable to them. This issue of incentive-compatibility has been addressed in related work such as by Petcu, Faltings, and Parkes (2008), and is orthogonal to the issue of privacy addressed in this paper. Furthermore, an agent would take a risk in reporting constraints different from its true constraints: reporting relaxed constraints could yield a solution that violates its true constraints and would therefore not be viable, while reporting tighter constraints could make the overall problem infeasible and the algorithm fail to find any solution at all.…”