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**1 - 5**of**5**### A Hybrid Exact Algorithm for Complete Set Partitioning

"... In the Complete Set Partitioning problem we are given a finite set of elements where every subset is associated with a problem captures the Coalition Structure Generation problem in cooperative games in characteristic function form, where each subset, or coalition, of agents can make a profit when w ..."

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In the Complete Set Partitioning problem we are given a finite set of elements where every subset is associated with a problem captures the Coalition Structure Generation problem in cooperative games in characteristic function form, where each subset, or coalition, of agents can make a profit when working together, and the goal is to partition the set of agents into coalitions to maximise the total profit. It also captures the special case of the Winner Determination problem in combinatorial auctions, where bidders place bids on every possible bundle of goods, and the goal is to find an allocation of goods to bidders that maximises the profit of the auctioneer. The main contribution of this article is an extensive theoretical analysis of the search space of the Complete Set Partitioning problem, which reveals that two fundamentally different exact algorithms can be significantly improved upon in terms of actual runtime. These are (1) a dynamic programming algorithm called “DP ” [48, 36] and (2) a tree-search algorithm called “IP ” [32]. We start by drawing a link between DP and a certain graph describing the structure of the search space. This link reveals that many of DP’s operations are in fact redundant. Consequently, we develop ODP— an optimal version of DP that avoids all of its redundant operations. Since ODP and IP are based on different design paradigms, each has its own strengths and weaknesses compared to the other. Thus, one has to trade off the advantages of

### People are Processors: Coalitional Auctions for Complex Projects

"... To successfully complete a complex project, be it a construction of an airport or of a backbone IT system or crowd-sourced projects, agents (companies or individuals) must form a team (a coalition) having required competences and resources. A team can be formed either by the project issuer based on ..."

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To successfully complete a complex project, be it a construction of an airport or of a backbone IT system or crowd-sourced projects, agents (companies or individuals) must form a team (a coalition) having required competences and resources. A team can be formed either by the project issuer based on individual agents ’ offers (cen-tralized formation); or by the agents themselves (decentralized for-mation) bidding for a project as a consortium—in that case many feasible teams compete for the employment contract. In these mod-els, we investigate rational strategies of the agents (what salary should they ask? with whom should they team up?) under different organizations of the market. We propose various concepts allowing to characterize the stability of the winning teams. We show that there may be no (rigorously) strongly winning coalition, but the weakly winning and the auction-winning coalitions are guaranteed to exist. In a general setting, with an oracle that decides whether a coalition is feasible, we show how to find winning coalitions with a polynomial number of calls to the oracle. We also determine the complexity of the problem in a special case in which a project is a set of independent tasks. Each task must be processed by a single agent, but processing speeds differ between agents and tasks.

### On the Structure of Synergies in Cooperative Games

"... We investigate synergy, or lack thereof, between agents in co-operative games, building on the popular notion of Shapley value. We think of a pair of agents as synergistic (resp., an-tagonistic) if the Shapley value of one agent when the other agent participates in a joint effort is higher (resp. lo ..."

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We investigate synergy, or lack thereof, between agents in co-operative games, building on the popular notion of Shapley value. We think of a pair of agents as synergistic (resp., an-tagonistic) if the Shapley value of one agent when the other agent participates in a joint effort is higher (resp. lower) than when the other agent does not participate. Our main theoret-ical result is that any graph specifying synergistic and antag-onistic pairs can arise even from a restricted class of cooper-ative games. We also study the computational complexity of determining whether a given pair of agents is synergistic. Fi-nally, we use the concepts developed in the paper to uncover the structure of synergies in two real-world organizations, the European Union and the International Monetary Fund. 1

### Cooperation through social influenceI

"... We consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents. We model this scenario by an influence game, a cooperative simple game in which ..."

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We consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents. We model this scenario by an influence game, a cooperative simple game in which a team (or coalition) of players succeeds if it is able to convince enough agents to participate in the task (to vote in favor of a decision). We take the linear threshold model as the influence model. We show first the expressiveness of influence games showing that they capture the class of simple games. Then we characterize the computational complexity of various problems on influence games, including measures (length and width), values (Shapley-Shubik and Banzhaf) and properties (of teams and players). Finally, we analyze those problems for some particular extremal cases, with respect to the propagation of influence, showing tighter complexity characterizations.