Multiagent task allocation in social networks

Mathijs M. de Weerdt 0 Yingqian Zhang 0 Tomas Klos 0 0 Y. Zhang Department of Econometrics, Erasmus School of Economics , Rotterdam, The Netherlands This paper proposes a new variant of the task allocation problem, where the agents are connected in a social network and tasks arrive at the agents distributed over the network. We show that the complexity of this problem remains NP-complete. Moreover, it is not approximable within some factor. In contrast to this, we develop an efficient greedy algorithm for this problem. Our algorithm is completely distributed, and it assumes that agents have only local knowledge about tasks and resources. We conduct a broad set of experiments to evaluate the performance and scalability of the proposed algorithm in terms of solution quality and computation time. Three different types of networks, namely small-world, random and scalefree networks, are used to represent various social relationships among agents in realistic applications. The results demonstrate that our algorithm works well and also that it scales well to large-scale applications. In addition we consider the same problem in a setting where the agents holding the resources are self-interested. For this, we show how the optimal algorithm can be used to incentivize these agents to be truthful. However, the efficient greedy algorithm cannot be used in a truthful mechanism, therefore an alternative, cluster-based algorithm is proposed and evaluated. 1 Introduction Recent years have seen a significant amount of work on task and resource allocation methods, which can potentially be applied to many real-world applications. However, interesting applications where relations between agents play a role require a slightly more general model. Such situations appear very frequently in real-world scenarios, and recent technological developments are bringing more of them within the range of task allocation methods. Especially in business applications, preferential partner selection and interaction is very common, and this aspect becomes more important for task allocation research, to the extent that technological developments need to be able to support it. For example, the development of semantic web and grid technologies leads to increased and renewed attention for the potential of the web to support business processes [20,48]. As an example, virtual organizations (VOs) are being re-invented in the context of the grid, where they are composed of a number of autonomous entities (representing different individuals, departments and organizations), each of which has a range of problem-solving capabilities and resources at its disposal [48, p. 237]. The question is how VOs are to be dynamically composed and re-composed from individual agents, when different tasks and subtasks need to be performed. This would be done by allocating these subtasks to different agents who may each be capable of performing different subsets of these tasks. Similarly, supply chain formation (SCF) is concerned with the, possibly ad-hoc, allocation of services to providers in the supply chain, in such a way that overall profit is optimized [17,60]. Traditionally, such allocation decisions have been analyzed using transaction cost economics (TCE) [12], which takes the transaction between consecutive stages of development as its basic unit of analysis, and considers the firm and the market as alternative structural forms for organizing transactions. Transaction cost economics has traditionally built on analysis of comparative statics: the central problem of economic organization is considered to be the adaptation of organizational forms to the characteristics of transactions. More recently, TCEs founding father, Ronald Coase, acknowledged that this is too simplistic an approach [13, p. 245]: The analysis cannot be confined to what happens within a single firm. () What we are dealing with is a complex interrelated structure. In this paper, we study the problem of task allocation from the perspective of such a complex interrelated structure. In particular, the market cannot be considered as an organizational form without considering specific partners to interact with on the market [32]. Specifically, therefore, we consider agents to be connected to each other in a social network. Furthermore, this network is not fully connected: as informed by the business literature, firms typically have established working relations with limited numbers of preferred partners [27]; these are the ones they consider when new tasks arrive and they have to form supply chains to allocate those tasks [56]. Other than modeling the interrelated structure between business partners, the social network introduced in this paper can also be used to represent other types of connections or constraints among autonomous entities that arise from other application domains. Moreover, each agent in our model has a limited amount of resources of different types at its disposal. Agents may also have tasks to be completed. Each task, with a specified value on completion, requires some resources for execution. An agent with a task is called a manager, and only its neighboring agents are allowed to provide their resources to this task. These agents are called contractors. The social task allocation problem (STAP) is, given the set of tasks and the available resources of the agents, to decide which tasks to execute and which resources of which contractors to supply their resources, such that the total value of the allocated tasks is maximized. This simple framework is able to capture a variety of applications. For example, when each agent has some reputation in the eyes of other agents, agents may prefer to deal only with others whose reputation is good enough. Only these are then considered as neighbors in the agent network. Alternatively, consider a disaster rescue scenario, such as in RoboCup Rescue [19,43]. Emergency events occur in different parts of a city, and different types of emergency services can cooperate to perform rescue tasks. Geographical proximity determines which other agents are available for cooperation, while different types of equipment carried by these services are modeled by the resources in our model. The results presented in this paper improve and extend upon earlier work by the same authors [62]. This paper first studies the social task allocation problem in a cooperative setting, where the agents reveal their information truthfully to their neighboring partners. The main research question in this cooperative setting is the development of a computational model and efficient algorithm, and the effect of the structure of a social network on its performance. In the next section, we give a formal description of this cooperative social task allocation problem. Section 3 shows that the complexity of this problem is NP-hard. An exact method is put forward in Sect. 4.1. Since any exact algorithm is too computationally expensive in (...truncated)