Complexity of coalition structure generation

We revisit the coalition structure generation problem in which the goal is to partition the players into exhaustive and disjoint coalitions so as to maximize the social welfare. One of our key results is a general polynomial-time algorithm to solve the problem for all coalitional games provided that player types are known and the number of player types is bounded by a constant. As a corollary, we obtain a polynomial-time algorithm to compute an optimal partition for weighted voting games with a constant number of weight values and for coalitional skill games with a constant number of skills. We also consider well-studied and well-motivated coalitional games defined compactly on combinatorial domains. For these games, we characterize the complexity of computing an optimal coalition structure by presenting polynomial-time algorithms, approximation algorithms, or NP-hardness and inapproximability lower bounds.Comment: 17 page

A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work

Human-agent collectives

We live in a world where a host of computer systems, distributed throughout our physical and information environments, are increasingly implicated in our everyday actions. Computer technologies impact all aspects of our lives and our relationship with the digital has fundamentally altered as computers have moved out of the workplace and away from the desktop. Networked computers, tablets, phones and personal devices are now commonplace, as are an increasingly diverse set of digital devices built into the world around us. Data and information is generated at unprecedented speeds and volumes from an increasingly diverse range of sources. It is then combined in unforeseen ways, limited only by human imagination. People’s activities and collaborations are becoming ever more dependent upon and intertwined with this ubiquitous information substrate. As these trends continue apace, it is becoming apparent that many endeavours involve the symbiotic interleaving of humans and computers. Moreover, the emergence of these close-knit partnerships is inducing profound change. Rather than issuing instructions to passive machines that wait until they are asked before doing anything, we will work in tandem with highly inter-connected computational components that act autonomously and intelligently (aka agents). As a consequence, greater attention needs to be given to the balance of control between people and machines. In many situations, humans will be in charge and agents will predominantly act in a supporting role. In other cases, however, the agents will be in control and humans will play the supporting role. We term this emerging class of systems human-agent collectives (HACs) to reflect the close partnership and the flexible social interactions between the humans and the computers. As well as exhibiting increased autonomy, such systems will be inherently open and social. This means the participants will need to continually and flexibly establish and manage a range of social relationships. Thus, depending on the task at hand, different constellations of people, resources, and information will need to come together, operate in a coordinated fashion, and then disband. The openness and presence of many distinct stakeholders means participation will be motivated by a broad range of incentives rather than diktat. This article outlines the key research challenges involved in developing a comprehensive understanding of HACs. To illuminate this agenda, a nascent application in the domain of disaster response is presented

An Approximate "Law of One Price" in Random Assignment Games

Assignment games represent a tractable yet versatile model of two-sided markets with transfers. We study the likely properties of the core of randomly generated assignment games. If the joint productivities of every firm and worker are i.i.d bounded random variables, then with high probability all workers are paid roughly equal wages, and all firms make similar profits. This implies that core allocations vary significantly in balanced markets, but that there is core convergence in even slightly unbalanced markets. For the benchmark case of uniform distribution, we provide a tight bound for the workers' share of the surplus under the firm-optimal core allocation. We present simulation results suggesting that the phenomena analyzed appear even in medium-sized markets. Finally, we briefly discuss the effects of unbounded distributions and the ways in which they may affect wage dispersion

Complexity of Coalition Structure Generation

We revisit the coalition structure generation problem in which the goal is to partition the players into exhaustive and disjoint coalitions so as to maximize the social welfare. One of our key results is a general polynomial-time algorithm to solve the problem for all coalitional games provided that player types are known and the number of player types is bounded by a constant. As a corollary, we obtain a polynomial-time algorithm to compute an optimal partition for weighted voting games with a constant number of weight values and for coalitional skill games with a constant number of skills. We also consider well-studied and well-motivated coalitional games defined compactly on combinatorial domains. For these games, we characterize the complexity of computing an optimal coalition structure by presenting polynomial-time algorithms, approximation algorithms, or NP-hardness and inapproximability lower bounds