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.
The idea of using swap deals was explored for instance by @cite_31 , who studied barter exchange networks. @cite_34 and @cite_12 studied dynamics of swap-deals by considering an underlying social network constraining the possible interactions of the agents, and focusing on complexity issues. These results were recently extended by @cite_19 .
@cite_19 @cite_31 @cite_34 @cite_12
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Of late online social networks have become popular, with interest spanning various aspects including search, analysis mining, and their potential use for item barter exchange markets. The idea is that users can leverage their social network for exchanging items they possess with other users. The problem of generating recommendations for item exchanges between users, consisting of synchronous exchange cycles has been investigated[2]. In this paper, we identify the shortcomings of the above exchange model and propose an asynchronous model that makes use of credit points. Rather than insist on exchanging items synchronously, we award points to users whenever they give items to other users, which can be redeemed later. Points and their redemption raise an issue of fairness which intuitively means users who contribute more should have a greater priority over others for receiving items they wish for. We focus on fairness maximization and prove that it is NPhard and cannot be approximated within any factor in polynomial time unless P=NP. We then develop efficient heuristic algorithms, and experimentally demonstrate their effectiveness and scalability on both synthetic data and a real dataset from readitswapit.co.uk. We examine a resource allocation problem where each agent is to be assigned exactly one object. Agents are initially endowed with a resource that they can swap with one another. However, not all exchanges are plausible: we represent required connections between agents with a social network. Agents may only perform pairwise exchanges with their neighbors and only if it brings them preferred objects. We analyze this distributed process through two dual questions. Could an agent obtain a certain object if the swaps occurred favourably? Can an agent be guaranteed a certain level of satisfaction regardless of the actual exchanges? These questions are investigated through parameterized complexity, focusing on budget constraints such as the number of exchanges an agent may be involved in or the total duration of the process. The study of bargaining has a long history, but many basic settings are still rich with unresolved questions. In particular, consider a set of agents who engage in bargaining with one another,but instead of pairs of agents interacting in isolation,agents have the opportunity to choose whom they want to negotiate with, along the edges of a graph representing social-network relations. The area of network exchange theory in sociology has developed a large body of experimental evidence for the way in which people behave in such network-constrained bargaining situations, and it is a challenging problem to develop models that are both mathematically tractable and in general agreement with the results of these experiments. We analyze a natural theoretical model arising in network exchange theory, which can be viewed as a direct extension of the well-known Nash bargaining solution to the case of multiple agents interacting on a graph. While this generalized Nash bargaining solution is surprisingly effective at picking up even subtle differences in bargaining power that have been observed experimentally on small examples, it has remained an open question to characterize the values taken by this solution on general graphs, or to find an efficient means to compute it. Here we resolve these questions, characterizing the possible values of this bargaining solution, and giving an efficient algorithm to compute the set of possible values. Our result exploits connections to the structure of matchings in graphs, including decomposition theorems for graphs with perfect matchings, and also involves the development of new techniques. In particular, the values we are seeking turn out to correspond to a novel combinatorially defined point in the interior of a fractional relaxation of the matching problem. Why and to what extent do people make significant purchases from people with whom they have prior noncommercial relationships ? Using data from the economic sociology module of the 1996 General Social Survey, the authors document high levels of within-network exchanges. They argue that transacting with social contacts is effective because it embeds commercial exchanges in a web of obligations and holds the seller's network hostage to appropriate role performance in the economic transaction. It follows that within-network exchanges will be more common in risky transactions that are unlikely to be repeated and in which uncertainty is high. The data support this view. Self-reports about major purchases are consistent with the expectation that exchange frequency reduces the extent of within-network exchanges. Responses to questions about preferences for in-group exchanges support the argument that uncertainty about product and performance quality leads people to prefer sellers with whom they have noncommercial ties. Moreover, people prefer to avoid selling to social contacts under the same conditions that lead buyers to seek such transactions; and people who transact with friends and relatives report greater satisfaction with the results than do people who transact with strangers, especially for risk-laden exchanges