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 consider the problem of reallocating indivisible objects amongst a set of agents when the preference ordering of each agent may contain indifferences. The same model, but with strict preferences, goes back to the seminal work of Shapley and Scarf in 1974. When preferences are strict, we now know that the Top-Trading Cycles (TTC) mechanism invented by Gale is Pareto efficient, strategy-proof, and finds a core allocation, and that it is the only mechanism satisfying these properties. In the extensive literature on this problem since then, the TTC mechanism has been characterized in multiple ways, establishing its central role within the class of all allocation mechanisms. The question motivating our work is the extent to which these results can be generalized to the setting with indifferences. Our main contribution is a general framework to design strategyproof mechanisms that find a Pareto optimal allocation in the weak-core. Along the way, we establish a sufficient condition for a mechanism (within a broad class of mechanisms) to be strategyproof and use this condition to design fast algorithms for finding a "good" reallocation. Our results generalize and unify two (different) mechanisms for the reallocation problem derived, independently of each other, by Manjunath and Jaramillo, and Alcalde-Unzu and Molis. Decentralised coordination in multi-agent systems is typically achieved using communication. However, in many cases, communication is expensive to utilise because there is limited bandwidth, it may be dangerous to communicate, or communication may simply be unavailable at times. In this context, we argue for a rational approach to communication --- if it has a cost, the agents should be able to calculate a value of communicating. By doing this, the agents can balance the need to communicate with the cost of doing so. In this research, we present a novel model of rational communication, that uses reward shaping to value communications, and employ this valuation in decentralised POMDP policy generation. In this context, reward shaping is the process by which expectations over joint actions are adjusted based on how coordinated the agent team is. An empirical evaluation of the benefits of this approach is presented in two domains. First, in the context of an idealised bench-mark problem, the multiagent Tiger problem, our method is shown to require significantly less communication (up to 30 fewer messages) and still achieves a 30 performance improvement over the current state of the art. Second, in the context of a larger-scale problem, RoboCupRescue, our method is shown to scale well, and operate without recourse to significant amounts of domain knowledge. Abstract We study the problem of fairly allocating indivisible goods to groups of agents. Agents in the same group share the same set of goods even though they may have different preferences. Previous work has focused on unanimous fairness, in which all agents in each group must agree that their group's share is fair. Under this strict requirement, fair allocations exist only for small groups. We introduce the concept of democratic fairness, which aims to satisfy a certain fraction of the agents in each group. This concept is better suited to large groups such as cities or countries. We present protocols for democratic fair allocation among two or more arbitrarily large groups of agents with monotonic, additive, or binary valuations. For two groups with arbitrary monotonic valuations, we give an efficient protocol that guarantees envy-freeness up to one good for at least 1 2 of the agents in each group, and prove that the 1 2 fraction is optimal. We also present other protocols that make weaker fairness guarantees to more agents in each group, or to more groups. Our protocols combine techniques from different fields, including combinatorial game theory, cake cutting, and voting. Optimal mechanisms for agents with multi-dimensional preferences are generally complex. This complexity makes them challenging to solve for and impractical to run. In a typical mechanism design approach, a model is posited and then the optimal mechanism is designed for the model. Successful mechanism design gives mechanisms that one could at least imagine running. By this measure, multi-dimensional mechanism design has had only limited success. In this paper we take the opposite approach, which we term reverse mechanism design. We start by hypothesizing the optimality of a particular form of mechanism that is simple and reasonable to run, then we solve for sufficient conditions for the mechanism to be optimal (among all mechanisms). This paper has two main contributions. The first is in codifying the method of virtual values from single-dimensional auction theory and extending it to agents with multidimensional preferences. The second is in applying this method to two paradigmatic classes of multi-dimensional preferences. The first class is unit-demand preferences (e.g., a homebuyer who wishes to buy at most one house); for this class we give sufficient conditions under which posting a uniform price for each item is optimal. This result generalizes one of [2013] for a consumer with values uniform on interval [0; 1], and contrasts with an example of Thanassoulis [2004] for a consumer with values uniform on interval [5; 6] where uniform pricing is not optimal. The second class is additive preferences, for this class we give sufficient conditions under which posting a price for the grand bundle is optimal. This result generalizes a recent result of Hart and Nisan [2012] and relates to work of Armstrong [1999]. Similarly to an approach of [2013], these results for single-agent pricing problems can be generalized naturally to multi-agent auction problems.