In this section we have given a brief overview of the economic principles involved in mechanism design. We provided a generic model of a mechanism and discussed some of the different solution concepts under which a mechanism may be implemented. We then studied a number of desiderata which we might wish a SCF to be endowed with while explaining which particular set can or cannot be achieved under the respective solution concepts. While discussing the theories in this chapter, we have implicitly made three assumptions (which are also common to most work in these areas):
1. There is always a trusted centre that can gather the necessary data from the agents nd can compute and enforce the outcome.
2. In a reverse auction, an agent has the capacity to fulfill the demand required by the auc- tioneer.
3. An agent’s valuation or cost is derived from a private observation of its type only.
4. Once an agent has been allocated a task in a reverse auction, it will complete it to the predefined specifications which have been agreed with the allocator.
However, as we argued chapter 1, these assumptions do not always hold in MASs. Thus,in the next four chapters, we deal with the challenges posed by removing each assumption. Specifi- cally, we study the case where there is no trusted centre in Chapter 3 by analysing a simultaneous auction scenario. We then remove the assumption of unconstrained capacity in Chapter 4 and design a centralised mechanism with desirable SCFs for this case. Within this chapter, we also design a distributed mechanism and compare its performance with that of the centralised one. We then address the third assumption by designing a mechanism for multiple goods and in- terdependent valuations in Chapter 5. Finally, we remove the last assumption in Chapter 6 by considering agents that have a certain failure rate and we go on to design a mechanism with desirable SCFs for this case.
Distributed Allocation Mechanisms
The first part of this thesis will consider issues associated with distributed allocation mecha- nisms. This is a core challenge within distributed mechanisms (as highlighted in red in figure I.1). Specifically, this challenge considers how to design mechanisms when there is no trusted centre who collects data from all the agents and determines the allocation of resources and pay- ments within the system.
Distributed Mechanism Employing Simultaneous Auctions (Chapter 3) Distributed Allocation (Part I) Distributed Information (Part II) Design of Protocol Strategy Design and Analysis Computational Mechanism Design Mechanism for Interdependent Valuations (Chapter 5) Mechanism with Uncertainty in Task Allocation (Chapter 6) Mechanism with Constrained Capacity Suppliers(Chapter 4)
Design Perspective Design Challenge
FIGUREI.1: The challenges addressed and the design perspective of part I of the thesis
Within distributed allocation mechanisms, the allocation of resources and payments must be determined via the interactions of each agent rather than at a central point. Such mechanisms are very attractive for sensor networks since they have the advantages of tractability, robust- ness, trustworthiness and reduction of bottlenecks (see Chapter 1 for a more detailed discus- sion). Now, within a cooperative setting, distributed task allocation has been extensively studied [Lesser and Corkill, 1981; Jennings and Bussmann, 2003; Pynadath and Tambe, 2003; Kraus et al., 1998]. However, the implementation of these mechanisms remain a challenge when con- sidering selfish agents since these agents act to maximise their own utilities and therefore would not collaborate unless there is an incentive to do so. As a result, the distributed allocation mechanisms we study in this thesis all show a certain loss of efficiency when compared to their centralised counterparts.
In more detail, Chapter 3 reports on the optimal strategies that should be adopted by agents within a simultaneous auction environment. Here the distributed allocation occurs since each of the seller agents independently determine which buyer agent will be allocated their service. We then analyse another distributed mechanism based on the CDA in Chapter 4 whilst considering
constrained capacity suppliers. In this case, the distributed allocation emerges out of the interac- tions between buyers and sellers. In order to benchmark the distributed mechanism, we design a centralised protocol for this scenario.
A Mechanism Employing
Simultaneous Auctions
In this chapter, we address requirement 1 of this thesis (as detailed in chapter 1), by studying a distributed allocation mechanism. We do so by analysing a market in which the goods are auctioned concurrently by a number of sellers, rather than by a single centralised auctioneer. Thus, the allocation of the goods is not computed by a centre, but rather is determined by the behaviour of the buyers in each of the parallel auctions. This therefore results in a distributed allocation mechanism whose properties we study in this chapter. Furthermore, we choose these simultaneous auctions, since they provide us with a baseline performance for distributed allo- cation mechanisms in which the agents are selfish. This is because neither the sellers nor the buyers can coordinate in order to set the price of an item (unlike in the CDA where this occurs indirectly via a billboard).
In order to study the distributed allocation mechanism, we first need to design and analyse the optimal strategy for a bidder (assumed to be rational) in such a market. We can then investigate an important global property of this distributed market, namely its efficiency, contingent upon this strategy. Now, the optimal strategy for a bidder is dependent on the type of competing bidders it faces and the amount of knowledge it has about the market (as we shall see later on in this chapter). Furthermore, the efficiency of the market depends on the type of bidders that participate in these markets.
The remainder of this chapter is structured as follows. Section 3.1 places this research in the global context of MASs and details the advances we make to the state of the art in this area. In Section 3.2, we describe the MSN scenario in which such distributed auctions occur. We then discuss the related work in the field of simultaneous auction in Section 3.3. In Section 3.4 we describe the bidders and the auctions in more detail. In Section 3.5 we investigate the case with a single global bidder and characterise the optimal bidding behaviour for it. Section 3.6 considers the case with multiple global bidders and in Section 3.7 we address the market efficiency and the impact of a global bidder. Section 3.8 concludes and discusses future work.
3.1
Introduction
In recent years, there has been a surge in the application of auctions, both online and within multi-agent systems [Airiau and Sen, 2003; Clearwater, 1996; Gerding et al., 2006b; Dash et al., 2005; Rosenthal and Wang, 1996; Roth and Ockenfels, 2002]. As a result, there are an increasing number of auctions offering very similar or even identical goods and services. In eBay alone, for example, there are often hundreds or sometimes even thousands of concurrent auctions running worldwide selling such substitutable items1. Against this background, it is important to develop bidding strategies that agents can use to operate effectively across a wide number of auctions. To this end, in this chapter we devise and analyse optimal bidding strategies for a bidder that participates in multiple simultaneous auctions for goods that are perfect substitutes.
To date, much of the existing literature on simultaneous auctions focuses either on complemen- tarities, where the value of items together is greater than the sum of the individual items, or on heuristic strategies for simultaneous auctions (see Section 3.3 for more details). In contrast, here we consider bidding strategies analytically and for the case of perfect substitutes. In par- ticular, our focus is on simultaneous Vickrey or second-price sealed bid auctions. We choose these because they are communication efficient (since they are direct mechanisms as defined in Chapter 2) and well known for their capacity to induce truthful bidding [Krishna, 2002], which makes them suitable for many multi-agent system settings. Within this setting, we are able to characterise, for the first time, a bidder’s utility-maximising strategy for bidding in any number of such auctions and for any type of bidder valuation distribution.
In more detail, we first consider a market where a single bidder, called the global bidder, can bid in any number of auctions, whereas the other bidders, called the local bidders, are assumed to bid only in a single auction. For this case, we find the following results:
• Whereas in the case of a single second-price auction a bidder’s best strategy is to bid its true value, this is generally not the case for a global bidder. As we shall show, its best strategy is in fact to bid below its true value.
• We are able to prove that, even if a global bidder requires only one item, the expected utility is maximised by participating in all the auctions that are selling the desired item.
• Finding the optimal bid for each auction can be an arduous task when considering all possible combinations. However, for most common bidder valuation distributions, we are able to significantly reduce this search space.
• Empirically, we find that a bidder’s expected utility is maximised by bidding at a relatively high value in one of the auctions, and equal or lower in all other auctions.
We then go on to consider markets with more than one global bidder. Due to the complexity of the problem, we combine analytical results with a discrete simulation in order to numerically
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derive the optimal bidding strategy. By so doing, we find that, in a market with only global bidders, the optimal strategy does not converge. In fact it fluctuates between two states. If the market consists of both local and global bidders, however, the global bidders’ strategy quickly reaches a stable solution and we approximate a symmetric Nash equilibrium outcome.
Finally, we consider the issue of market efficiency when there are such simultaneous auctions. Efficiency is an important system-wide consideration within multi-agent systems since it char- acterises how well the allocations in the system maximise the overall utility (see section 2.3). Now, efficiency is maximised when the goods are allocated to those who value them the most. However, a certain amount of inefficiency is inherent to a distributed market where the auctions are held separately. In this chapter, we measure the inefficiency of markets with local bidders only and consider the impact of global bidders on this inefficiency. In so doing, we first prove that the efficiency of distributed markets with only local bidders has a lower bound given by
1−1/e. Furthermore, we find that the presence of a global bidder has a slight, but positive, impact on the efficiency when the number of local bidders is known, but is, in general, negative when there exists uncertainty about the exact number of bidders. Therefore, information about the market plays an important role in the social welfare of the system.
In the next section, we discuss how a market consisting of multiple simultaneous auctions arises within the MSN scenario we introduced in section 1.2.