We investigate the manipulation of power indices in TU-cooperative games by stimulating (subject to a budget constraint) changes in the propensity of other players to participate to the game. We display several algorithms that show that the problem is often tractable for so-called network centrality games and influence attribution games, as well as an example when optimal manipulation is intractable, even though computing power indices is feasible.
A lot of work has been devoted recently to measuring and characterizing in multi-agent settings @cite_29 @cite_22 @cite_19 . Synergies between players in cooperative games are obviously relevant to the theme of this paper: synergic agents' participation to coalitions increases the Shapley value of the given agent. The nature of some of our results (Theorems , and ), that target nodes in a fixed order, provide a concrete way for ranking synergies between these nodes and the attacked one.
@cite_19 @cite_29 @cite_22
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Previous approaches to select agents to form a team rely on single-agent capabilities, and team performance is treated as a sum of such known capabilities. Motivated by complex team formation situations, we address the problem where both single-agent capabilities may not be known upfront, e.g., as in ad hoc teams, and where team performance goes beyond single-agent capabilities and depends on the specific synergy among agents. We formally introduce a novel weighted synergy graph model to capture new interactions among agents. Agents are represented as vertices in the graph, and their capabilities are represented as Normally-distributed variables. The edges of the weighted graph represent how well the agents work together, i.e., their synergy in a team. We contribute a learning algorithm that learns the weighted synergy graph using observations of performance of teams of only two and three agents. Further, we contribute two team formation algorithms, one that finds the optimal team in exponential time, and one that approximates the optimal team in polynomial time. We extensively evaluate our learning algorithm, and demonstrate the expressiveness of the weighted synergy graph in a variety of problems. We show our approach in a rich ad hoc team formation problem capturing a rescue domain, namely the RoboCup Rescue domain, where simulated robots rescue civilians and put out fires in a simulated urban disaster. We show that the weighted synergy graph outperforms a competing algorithm, thus illustrating the efficacy of our model and algorithms. 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., antagonistic) 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 theoretical result is that any graph specifying synergistic and antagonistic pairs can arise even from a restricted class of cooperative games. We also study the computational complexity of determining whether a given pair of agents is synergistic. Finally, 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. The performance of a team at a task depends critically on the composition of its members. There is a notion of synergy in human teams that represents how well teams work together, and we are interested in modeling synergy in multi-agent teams. We focus on the problem of team formation, i.e., selecting a subset of a group of agents in order to perform a task, where each agent has its own capabilities, and the performance of a team of agents depends on the individual agent capabilities as well as the synergistic effects among the agents. We formally define synergy and how it can be computed using a synergy graph, where the distance between two agents in the graph correlates with how well they work together. We contribute a learning algorithm that learns a synergy graph from observations of the performance of subsets of the agents, and show that our learning algorithm is capable of learning good synergy graphs without prior knowledge of the interactions of the agents or their capabilities. We also contribute an algorithm to solve the team formation problem using the learned synergy graph, and experimentally show that the team formed by our algorithm outperforms a competing algorithm.