Distributed Mechanisms for Multi-Agent Systems: Analysis and Design

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

Computational Mechanism Design: A Call to Arms

Game theory has developed powerful tools for analyzing decision making in systems with multiple autonomous actors. These tools, when tailored to computational settings, provide a foundation for building multiagent software systems. This tailoring gives rise to the field of computational mechanism design, which applies economic principles to computer systems design

Sellers Competing for Buyers in Online Markets

We consider competition between sellers offering similar items in concurrent online auctions, where each seller must set its individual auction parameters (such as the reserve price) in such a way as to attract buyers. We show that there exists a pure Nash equilibrium in the case of two sellers with asymmetric production costs. In addition, we show that, rather than setting a reserve price, a seller can further improve its utility by shill bidding (i.e., pretending to be a buyer in order to bid in its own auction). But, using an evolutionary simulation, we show that this shill bidding introduces inefficiencies within the market. However, we then go on to show that these inefficiencies can be reduced when the mediating auction institution uses appropriate auction fees that deter sellers from submitting shill bids

Sellers Competing for Buyers in Online Markets: Reserve Prices, Shill Bids, and Auction Fees

We consider competition between sellers offering similar items in concurrent online auctions through a mediating auction institution, where each seller must set its individual auction parameters (such as the reserve price) in such a way as to attract buyers. We show that in the case of two sellers with asymmetric production costs, there exists a pure Nash equilibrium in which both sellers set reserve prices above their production costs. In addition, we show that, rather than setting a reserve price, a seller can further improve its utility by shill bidding (i.e., bidding as a buyer in its own auction). This shill bidding is undesirable as it introduces inefficiencies within the market. However, through the use of an evolutionary simulation, we extend the analytical results beyond the two seller case, and we then show that these inefficiencies can be effectively reduced when the mediating auction institution uses auction fees based on the difference between the auction closing and reserve prices

Overlapping Coalition Formation for Efficient Data Fusion in Multi-Sensor Networks

This paper develops new algorithms for coalition formation within multi-sensor networks tasked with performing wide-area surveillance. Specifically, we cast this application as an instance of coalition formation, with overlapping coalitions. We show that within this application area sub-additive coalition valuations are typical, and we thus use this structural property of the problem to we derive two novel algorithms (an approximate greedy one that operates in polynomial time and has a calculated bound to the optimum, and an optimal branch-and-bound one) to find the optimal coalition structure in this instance. We empirically evaluate the performance of these algorithms within a generic model of a multi-sensor network performing wide area surveillance. These results show that the polynomial algorithm typically generated solutions much closer the optimal than the theoretical bound, and prove the effectiveness of our pruning procedure

Market-Based Task Allocation Mechanisms for Limited Capacity Suppliers

This paper reports on the design and comparison of two economically-inspired mechanisms for task allocation in environments where sellers have finite production capacities and a cost structure composed of a fixed overhead cost and a constant marginal cost. Such mechanisms are required when a system consists of multiple self-interested stakeholders that each possess private information that is relevant to solving a system-wide problem. Against this background, we first develop a computationally tractable centralised mechanism that finds the set of producers that have the lowest total cost in providing a certain demand (i.e. it is efficient). We achieve this by extending the standard Vickrey-Clarke-Groves mechanism to allow for multi-attribute bids and by introducing a novel penalty scheme such that producers are incentivised to truthfully report their capacities and their costs. Furthermore our extended mechanism is able to handle sellers' uncertainty about their production capacity and ensures that individual agents find it profitable to participate in the mechanism. However, since this first mechanism is centralised, we also develop a complementary decentralised mechanism based around the continuous double auction. Again because of the characteristics of our domain, we need to extend the standard form of this protocol by introducing a novel clearing rule based around an order book. With this modified protocol, we empirically demonstrate (with simple trading strategies) that the mechanism achieves high efficiency. In particular, despite this simplicity, the traders can still derive a profit from the market which makes our mechanism attractive since these results are a likely lower bound on their expected returns

On Similarities between Inference in Game Theory and Machine Learning

In this paper, we elucidate the equivalence between inference in game theory and machine learning. Our aim in so doing is to establish an equivalent vocabulary between the two domains so as to facilitate developments at the intersection of both fields, and as proof of the usefulness of this approach, we use recent developments in each field to make useful improvements to the other. More specifically, we consider the analogies between smooth best responses in fictitious play and Bayesian inference methods. Initially, we use these insights to develop and demonstrate an improved algorithm for learning in games based on probabilistic moderation. That is, by integrating over the distribution of opponent strategies (a Bayesian approach within machine learning) rather than taking a simple empirical average (the approach used in standard fictitious play) we derive a novel moderated fictitious play algorithm and show that it is more likely than standard fictitious play to converge to a payoff-dominant but risk-dominated Nash equilibrium in a simple coordination game. Furthermore we consider the converse case, and show how insights from game theory can be used to derive two improved mean field variational learning algorithms. We first show that the standard update rule of mean field variational learning is analogous to a Cournot adjustment within game theory. By analogy with fictitious play, we then suggest an improved update rule, and show that this results in fictitious variational play, an improved mean field variational learning algorithm that exhibits better convergence in highly or strongly connected graphical models. Second, we use a recent advance in fictitious play, namely dynamic fictitious play, to derive a derivative action variational learning algorithm, that exhibits superior convergence properties on a canonical machine learning problem (clustering a mixture distribution)

Computational-Mechanism Design: A Call to Arms

Game theory has developed several powerful tools for analyzing decision making in systems composed of multiple autonomous actors. Given this fact, AI practitioners would like to exploit these tools when building software systems containing multiple agents. However, to do this, the tools must be tailored to computational settings. To this end, the authors provide an overview of computational-mechanism design, which deals with the application of economic principles in computer systems design. Moreover, because many complex systems are inherently distributed, they also present initial results from the relatively new field of distributed-computational-mechanism design and outline the key challenges involved in making the ideas practicable.Engineering and Applied Science

Trust-Based Mechanisms for Robust and Efficient Task Allocation in the Presence of Execution Uncertainty

Vickrey-Clarke-Groves (VCG) mechanisms are often used to allocate tasks to selfish and rational agents. VCG mechanisms are incentive-compatible, direct mechanisms that are efficient (i.e. maximise social utility) and individually rational (i.e. agents prefer to join rather than opt out). However, an important assumption of these mechanisms is that the agents will always successfully complete their allocated tasks. Clearly, this assumption is unrealistic in many real-world applications where agents can, and often do, fail in their endeavours. Moreover, whether an agent is deemed to have failed may be perceived differently by different agents. Such subjective perceptions about an agent’s probability of succeeding at a given task are often captured and reasoned about using the notion of trust. Given this background, in this paper, we investigate the design of novel mechanisms that take into account the trust between agents when allocating tasks. Specifically, we develop a new class of mechanisms, called trust-based mechanisms, that can take into account multiple subjective measures of the probability of an agent succeeding at a given task and produce allocations that maximise social utility, whilst ensuring that no agent obtains a negative utility. We then show that such mechanisms pose a challenging new combinatorial optimisation problem (that is NP-complete), devise a novel representation for solving the problem, and develop an effective integer programming solution (that can solve instances with about 2×105 possible allocations in 40 seconds).

Optimal Bidding Strategies for Simultaneous Vickrey Auctions with Perfect Substitutes

We derive optimal bidding strategies for a global bidder who participates in multiple, simultaneous second-price auctions with perfect substitutes. We prove that, if everyone else bids locally in a single auction, the global bidder should always place non-zero bids in all available auctions, provided there are no budget constraints. With a budget, however, the optimal strategy is to bid locally if this budget is equal or less than the valuation. Furthermore, for a wide range of valuation distributions, we prove that the problem of finding the optimal bids reduces to two dimensions if all auctions are identical. Moreoever, we address markets with both sequential and simultaneous auctions, non-identical auctions, and the allocative efficiency of the market. Finally, by combining analystical and simulation results, we analyse equilibrium strategies in case of several global bidders. However, a stable solution is then only found if there are local bidders as well