Recently, the problem of allocating one resource per agent with initial endowments () has seen a renewed interest: indeed, while in the general domain Top Trading Cycle is known to be the only procedure guaranteeing Pareto-optimality, individual rationality, and strategy proofness, the situation differs in single-peaked domains. Bade (2019) presented the Crawler, an alternative procedure enjoying the same properties (with the additional advantage of being implementable in obviously dominant strategies); while (2015) showed that allowing mutually beneficial swap-deals among the agents was already enough to guarantee Pareto-optimality. In this paper we significantly deepen our understanding of this decentralized procedures: we show in particular that the single-peaked domains happen to be maximal'' if one wishes to guarantee this convergence property. Interestingly, we also observe that the set of allocations reachable by swap-deals always contains the outcome of the Crawler. To further investigate how these different mechanisms compare, we pay special attention to the average and minimum rank of the resource obtained by the agents in the outcome allocation. We provide theoretical bounds on the loss potentially induced by these procedures with respect to these criteria, and complement these results with an extensive experimental study which shows how different variants of swap dynamics behave. In fact, even the simplest dynamics exhibit very good results, and it is possible to further guide the process towards our objectives, if one is ready to sacrifice a bit in terms of decentralization. On our way, we also show that a simple variant of the Crawler allows to check efficiently that an allocation is Pareto-optimal in single-peaked domains.
Following the development of multi-agent systems, fully decentralized procedures have been defined through the idea of local exchanges between agents in the idea of Pigou-Dalton deals . @cite_0 considered the problem of reallocating tasks among individually rational agents. @cite_10 and @cite_28 investigated different complexity problems in this setting. @cite_29 and @cite_8 respectively characterized the class of deals and the class of preferences required to reach socially optimal allocations. @cite_5 focused on reaching efficient and envy-free allocations. Similar procedures were also introduced in the area of two-sided matching .
@cite_8 @cite_28 @cite_29 @cite_0 @cite_5 @cite_10
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We investigate the properties of an abstract negotiation framework where agents autonomously negotiate over allocations of indivisible resources. In this framework, reaching an allocation that is optimal may require very complex multilateral deals. Therefore, we are interested in identifying classes of valuation functions such that any negotiation conducted by means of deals involving only a single resource at a time is bound to converge to an optimal allocation whenever all agents model their preferences using these functions. In the case of negotiation with monetary side payments amongst self-interested but myopic agents, the class of modular valuation functions turns out to be such a class. That is, modularity is a sufficient condition for convergence in this framework. We also show that modularity is not a necessary condition. Indeed, there can be no condition on individual valuation functions that would be both necessary and sufficient in this sense. Evaluating conditions formulated with respect to the whole profile of valuation functions used by the agents in the system would be possible in theory, but turns out to be computationally intractable in practice. Our main result shows that the class of modular functions is maximal in the sense that no strictly larger class of valuation functions would still guarantee an optimal outcome of negotiation, even when we permit more general bilateral deals. We also establish similar results in the context of negotiation without side payments. Reallocating resources to get mutually beneficial outcomes is a fundamental problem in various multi-agent settings. In the first part of the paper we focus on the setting in which agents express additive cardinal utilities over objects. We present computational hardness results as well as polynomial-time algorithms for testing Pareto optimality under different restrictions such as two utility values or lexicographic utilities. In the second part of the paper we assume that agents express only their (ordinal) preferences over single objects, and that their preferences are additively separable. In this setting, we present characterizations and polynomial-time algorithms for possible and necessary Pareto optimality. We analyze task reallocation where individually rational ([R) agents (re)contract tasks among themselves based on marginal costs. A task allocation graph is introduced as a tool for analyzing contract types. Traditional single task contracts always have a short path (sequence of contracts) to the optimal task allocation but an IR path may not exist, or it may not be short. We analyze an algorithm for finding the shortest IR path. Next we introduce cluster contracts, swaps, and multiagent contracts. Each of the four contract types avoids some local optima that the others do not. Even if the protocol is equipped with all four types, local optima exist. To attack this problem, we introduce OCSMcontracts which combine the ideas behind the four earlier types into an atomic contract type. If the protocol is equipped with OCSM-contracts, any sequence of IR contracts leads to the optimal task allocation in a finite number of steps: an oracle--or speculation--is not needed for choosing the path (no subset of OCSMcontracts suffices even with an oracle). This means that the multiagent search does not need to backtrack. This is a powerful result for small problem instances. For large ones, the anytime feature of our multicontract-type algorithm--with provably monotonic improvement of each agent’s solution--is more important. 1 Part 1 Machines that make deals: the premise machine encounters social engineering for machines scenarios how does this differ from Al? how does this differ from game theory? Part 2 Interaction mechanisms: the negotiation problem in different domains attributes of negotiation mechanisms assumptions incentive compatibility. Part 3 Task-oriented domains: domain definition attributes and examples a negotiation mechanism evaluation of the negotiation mechanism an alternative, one-step protocol mechanisms that maximize the product of utilities the bottom line. Part 4 Deception-free protocols: non-manipulable negotiation mechanisms probabilistic deals subadditive domains concave domains modular domains summary of incentive compatible mechanisms the bottom line. Part 5 State-oriented domains: side-effects in encounters domain definition attributes and examples a negotiation mechanism worth of a goal conflict resolution semi-co-operative deals in non-conflict situations unified negotiation protocols (UNP) multi-plan deals the hierarchy of deal types - summary unbounded worth of a goal - tidy agents the bottom line. Part 6 Strategic manipulation: negotiation with incomplete information incomplete information about worth of goals using the revelation principle to re-design the mechanisms the bottom line. Part 7 Worth-oriented domains: goal relaxation domain definition one agent best plan negotiation over sub-optimal states examples of worth functions the bottom line. Appendices: strict tolerant mechanisms some related work proofs. We study the complexity of a multilateral negotiation framework where autonomous agents agree on a sequence of deals to exchange sets of discrete resources in order to both further their own goals and to achieve a distribution of resources that is socially optimal. When analysing such a framework, we can distinguish different aspects of complexity: How many deals are required to reach an optimal allocation of resources? How many communicative exchanges are required to agree on one such deal? How complex a communication language do we require? And finally, how complex is the reasoning task faced by each agent? This paper presents a number of results pertaining, in particular, to the first of these questions.