This paper analyzes coalitions among self-interested agents that need to solve combinatorial optimization problems to operate e ciently in the world. By colluding (coordinating their actions by solving a joint optimization prob-lem) the agents can sometimes save costs compared to operating individually. A model of bounded rationality is adopted where computation resources are costly. It is not worthwhile solving the problems optimally: solution quality is decision-theoretically traded o against computation cost. A normative, application- and protocol-independent theory of coalitions among bounded-rational agents is devised. The optimal coalition structure and its stability are signi cantly a ected by the agents ' algorithms ' performance pro les and the cost of computation. This relationship is rst analyzed theoretically. Then a domain classi cation including rational and bounded-rational agents is in-troduced. Experimental results are presented in vehicle routing with real data from ve dispatch centers. This problem is NP-complete and the instances are so large that|with current technology|any agent's rationality is bounded by computational complexity. 1

A Dissertation Presented by TUOMAS W. SANDHOLM

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This paper analyzes coalition formation among self-interested agents that need to solve combinatorial optimization problems to operate efficiently in the world. By colluding (coordinating their actions by solving a joint optimization problem), the agents can sometimes save costs compared to operating individually. A model of bounded rationality is adopted, where computation resources are costly. It is not worth solving the problems optimally: solution quality is decision-theoretically traded off against computation cost. A normative theory of coalitions among bounded rational (BR) agents is devised. The optimal coalition structure and its stability are significantly affected by the agents ' algorithms ' performance profiles (PPs) and the cost of computation. This relationship is first analyzed theoretically. A domain classification including rational and BR agents is introduced. Experimental results are presented in the distributed vehicle routing domain using real data from 5 dispatch centers; the optimal coalition structure for BR agents differs significantly from the one for rational agents. These problems are NP-complete and the instances are so large that, with current technology, any agent's rationality is bounded by computational complexity. 1

This paper analyzes individually-rational ex post equilibrium in the VC (Vickrey-Clarke) combinatorial auctions. If \Sigma is a family of bundles of goods, the organizer may restrict the participants by requiring them to submit their bids only for bundles in \Sigma. The \Sigma-VC combinatorial auctions (multi-good auctions) obtained in this way are known to be individually-rational truthtelling mechanisms. In contrast, this paper deals with non-restricted VC auctions, in which the buyers restrict themselves to bids on bundles in \Sigma, because it is rational for them to do so. That is, it may be that when the buyers report their valuation of the bundles in \Sigma, they are in an equilibrium. We fully characterize those \Sigma that induce individually rational equilibrium in every VC auction, and we refer to the associated equilibrium as a bundling equilibrium. The number of bundles in \Sigma represents the communication complexity of the equilibrium. A special case of bundling equilibrium is partition-based equilibrium, in which \Sigma is a field, that is, it is generated by a partition. We analyze the tradeoff between communication complexity and economic efficiency of bundling equilibrium, focusing in particular on partition-based equilibrium.

Coalition formation is a key problem in automated negotiation among self-interested agents, and other multiagent applications. A coalition of agents can sometimes accomplish things that the individual agents cannot, or can do things more efficiently. However,

The allocation problem stems from the diversification e#ect observed in risk measurements of financial portfolios: the sum of the risk measures of many portfolios is typically larger than the risk of all portfolios taken together. The allocation problem is to apportion this "diversification advantage" to the portfolios in a fair manner, to obtain new, firm-internal risk evaluations of the portfolios. Our approach is axiomatic, in the sense that we first establish arguably necessary properties of an allocation scheme, and then study schemes that fulfill the properties. Important results from the area of game theory find a direct application, and are used here. Keywords: allocation of risk; coherent risk measure; game theory; Shapley value; Aumann-Shapley prices; RORAC; risk-adjusted performance measure. 1 Introduction The underlying theme of this paper is the sharing of costs within the di#erent constituents of a firm. We call this sharing "allocation", as it is assumed that a higher au...

The language of game theory—coalitions, payo¤s, markets, votes— suggests that it is not a branch of abstract mathematics; that it is motivated by and related to the world around us; and that it should be able to

Coalition formation is a key problem in automated negotiation among selfinterested agents, and other multiagent applications. A coalition of agents can sometimes accomplish things that the individual agents cannot, or can accomplish them more efficiently. Motivating the agents to abide by a solution requires careful analysis: only some of the solutions are stable in the sense that no group of agents is motivated to break off and form a new coalition. This constraint has been studied extensively in cooperative game theory: the set of solutions that satisfy it is known as the core. The computational questions around the core have received less attention. When it comes to coalition formation among software agents (that represent real-world parties), these questions become increasingly explicit. In this

A general ordertheoretic linear programming model for the study of matroid-type greedy algorithms is introduced. The primal restrictions are given by so-called weakly increasing submodular functions on antichains. The LP-dual is solved by a Monge-type greedy algorithm. The model offers a direct combinatorial explanation for many integrality results in discrete optimization. In particular, the submodular intersection theorem of Edmonds and Giles is seen to extend to the case with a rooted forest as underlying structure. The core of associated polyhedra is introduced and applications to the existence of the core in cooperative game theory are discussed.