Distributed Mechanisms for Multi-Agent Systems: Analysis and Design

Abstract

There is an increasing need for multi-agent systems to operate under decentralised control regimes that support openness (individual components can enter and leave at will) and enable components representing distinct stakeholders with different aims and objectives to interact effectively. To this end, this thesis explores issues associated with using techniques from Game Theory and Mechanism Design to organise and analyse such systems. In particular, emphasis is given to distributed mechanisms in which there is distributed allocation (no single centre determines the allocation of the resources or the tasks) and distributed information (agents require information privately known by other agents in order to determine their own valuation or cost). Such mechanisms are important because, in comparison to their centralised counterparts, they are robust to a single-point failure, the computational burden can be potentially shared amongst many agents, and there is a reduction in bottlenecks since not all communication need pass through a single point. As a result, distributed mechanisms are better suited to many types of multi-agent application. To provide a grounding for the mechanisms we develop, the thesis contains a running example of a multi-sensor network scenario. In these systems, distributed allocation mechanisms are desirable since they are robust and reduce bottlenecks in the communication system. Furthermore, we show that distributed information naturally arises by deriving an information-theoretic valuation function. This scenario also gives rise to two additional requirements that are addressed within this thesis: (i) constrained capacity, whereby suppliers can only provide a limited amount of goods or services at any given time and (ii) uncertainty in task completion, whereby sensors potentially fail after they have been assigned tasks. Specifically, we focus on the \ac{vcg} mechanisms and investigate ways of extending it so as to address the requirements that arise within distributed setting in general and sensor networks. In particular, we choose the VCG as our point of departure since it is a mechanism that is efficient, individually rational and incentive compatible. Unfortunately, it is brittle in the sense that it does not conserve these desirable properties when considering the requirements that we outlined above. Therefore, we develop novel mechanisms that do. In more detail, the first part of this thesis considers two distributed allocation mechanisms --- a simultaneous auction environment and \ac{cda}. In the former, bidders place sealed bids in a number of selling auctions which are concurrently offering items. This results in a distributed allocation whereby the winner at each auction is determined by the seller conducting it. For this case, we derive the optimal strategy of the bidders using a game-theoretic approach. In the \acs{cda}, buyers and sellers, respectively, submit bids and asks continuously and the market clears when a bid is higher than an ask; meaning that the allocation is again determined in a distributed way. Furthermore, CDAs are known to yield close to efficient allocations, under certain conditions, even when utilising very simple strategies. However, in our case, we need to modify their format in order to deal with the requirement of constrained capacity. In both of these mechanisms, we study the system's loss in efficiency that ensues from distributing the allocation and find that it is $\frac{1}{e}$ in the simultaneous auction case and upto $35 \%$ in the continuous double auction case. The second part of this thesis is concerned with designing mechanisms when agents have distributed information within the system. Such settings are more general than those more traditionally studied in that they encompass the fact that agents can potentially change their valuation or cost upon knowing a signal about the system (which they have not observed) that was hitherto unknown to them. Specifically, we first show that interdependent valuations arise naturally within a sensor network when we develop an information-theoretic valuation function. To account for this, we significantly extend the VCG mechanism in order to deal with these interdependent valuations. We then go on to develop a mechanism that can deal with uncertainty in task allocation. In both of these cases, our mechanisms are shown to be efficient, individually rational and incentive compatible. Moreover, their computational properties are studied and efficient algorithms are designed (based on linear and dynamic programming) in order to speed up the computation of the allocation problem which is generally $\mathcal{NP}$-hard.

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