Coalition formation is a key topic in multiagent systems. One would prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. But then, can the coalition structure found via a partial search be guaranteed to be within a bound from optimum? We show that none of the previous coalition structure generation algorithms can establish any bound because they search fewer nodes than a threshold that we show necessary for establishing a bound. We present an algorithm that establishes a tight bound within this minimal amount of search, and show that any other algorithm would have to search strictly more. The fraction of nodes needed to be searched approaches zero as the number of agents grows. If additional time remains, our anytime algorithm searches further, and establishes a progressively lower tight bound. Surprisingly, just searching one more node drops the bound in half. As desired, our algorithm lowers the bound rapidly early on, and exhibits diminishing returns to computation. It also drastically outperforms its obvious contenders. Finally, we show how to distribute the desired search across selfinterested manipulative agents. Solving the optimization problem of each coalition.This means pooling the tasks and resources of the agents in the coalition, and solving this joint problem. The coalition's objective is to maximize monetary value: money received from outside the system for accomplishing tasks minus the cost of using resources.3. Dividing the value of the generated solution among agents.

rtificial-intelligence assistants and recommendation algorithms interact with billions of people every day, influencing lives in myriad ways, yet they still have little understanding of humans. Self-driving vehicles controlled by artificial intelligence (AI) are gaining mastery of their interactions with the natural world, but they are still novices when it comes to coordinating with other cars and pedestrians or collaborating with their human operators.The state of AI applications reflects that of the research field. It has long been steeped in a kind of methodological individualism. As is evident from introductory textbooks, the canonical AI problem is that of a solitary machine confronting a non-social environment. Historically, this was a sensible starting point. An AI agent -much like an infant -must first master a basic understanding of

No abstract

Problems of cooperation-in which agents seek ways to jointly improve their welfare-are ubiquitous and important. They can be found at scales ranging from our daily routines-such as driving on highways, scheduling meetings, and working collaboratively-to our global challenges-such as peace, commerce, and pandemic preparedness. Arguably, the success of the human species is rooted in our ability to cooperate. Since machines powered by artificial intelligence are playing an ever greater role in our lives, it will be important to equip them with the capabilities necessary to cooperate and to foster cooperation.We see an opportunity for the field of artificial intelligence to explicitly focus effort on this class of problems, which we term Cooperative AI. The objective of this research would be to study the many aspects of the problems of cooperation and to innovate in AI to contribute to solving these problems. Central goals include building machine agents with the capabilities needed for cooperation, building tools to foster cooperation in populations of (machine and/or human) agents, and otherwise conducting AI research for insight relevant to problems of cooperation. This research integrates ongoing work on multi-agent systems, game theory and social choice, human-machine interaction and alignment, natural-language processing, and the construction of social tools and platforms. However, Cooperative AI is not the union of these existing areas, but rather an independent bet about the productivity of specific kinds of conversations that involve these and other areas. We see opportunity to more explicitly focus on the problem of cooperation, to construct unified theory and vocabulary, and to build bridges with adjacent communities working on cooperation, including in the natural, social, and behavioural sciences.Conversations on Cooperative AI can be organized in part in terms of the dimensions of cooperative opportunities. These include the strategic context, the extent of common versus conflicting interest, the kinds of entities who are cooperating, and whether researchers take the perspective of an individual or of a social planner. Conversations can also be focused on key capabilities necessary for cooperation, such as understanding, communication, cooperative commitments, and cooperative institutions. Finally, research should study the potential downsides of cooperative capabilities-such as exclusion and coercion-and how to channel cooperative capabilities to best improve human welfare. This research would connect AI research to the broader scientific enterprise studying the problem of cooperation, and to the broader social effort to solve cooperation problems. This conversation will continue at: www.cooperativeAI.com

In this paper, we propose a novel incentive mechanism for promoting honesty in electronic marketplaces that is based on trust modeling. In our mechanism, buyers model other buyers and select the most trustworthy ones as their neighbors to form a social network which can be used to ask advice about sellers. In addition, however, sellers model the reputation of buyers based on the social network. Reputable buyers provide truthful ratings for sellers, and are likely to be neighbors of many other buyers. Sellers will provide more attractive products to reputable buyer to build their own reputation. We theoretically prove that a marketplace operating with our mechanism leads to greater profit both for honest buyers and honest sellers. We emphasize the value of our approach through a series of illustrative examples and in direct contrast to other frameworks for addressing agent trustworthiness. In all, we offer an effective approach for the design of e-marketplaces that is attractive to users, through its promotion of honesty.