The aim of this paper is to investigate the interplay between knowledge shared by a group of agents and its coalition ability. We investigate this relation in the standard context of imperfect information concurrent game. We assume that whenever a set of agents form a coalition to achieve a goal, they share their knowledge before acting. Based on this assumption, we propose a new semantics for alternating-time temporal logic with imperfect information and perfect recall. It turns out that this semantics is sufficient to preserve all the desirable properties of coalition ability in traditional coalitional logics. Meanwhile, we investigate how knowledge sharing within a group of agents contributes to its coalitional ability through the interplay of epistemic and coalition modalities. This work provides a partial answer to the question: which kind of group knowledge is required for a group to achieve their goals in the context of imperfect information.
Finally, it is also worth mentioning that @cite_4 adopts a similar meaning of coalition so as to capture the notion of knowing how to play''. Besides the different motivations, that work is based on STIT framework and just considers one-step uniform strategies without investigating the interplay of epistemic and coalitional operators.
@cite_4
2127813674 2170620672 1576108793 2126233665
Coalitional games allow subsets (coalitions) of players to cooperate to receive a collective payoff. This payoff is then distributed “fairly” among the members of that coalition according to some division scheme. Various solution concepts have been proposed as reasonable schemes for generating fair allocations. The Shapley value is one classic solution concept: player i’s share is precisely equal to i’s expected marginal contribution if the players join the coalition one at a time, in a uniformly random order. In this paper, we consider the class of supermodular games (sometimes called convex games), and give a fully polynomial-time randomized approximation scheme (FPRAS) to compute the Shapley value to within a (1 ±e) factor in monotone supermodular games. We show that this result is tight in several senses: no deterministic algorithm can approximate Shapley value as well, no randomized algorithm can do better, and both monotonicity and supermodularity are required for the existence of an efficient (1 ±e)-approximation algorithm. We also argue that, relative to supermodularity, monotonicity is a mild assumption, and we discuss how to transform supermodular games to be monotonic. Coalition formation is the process of bringing together two or more agents so as to achieve goals that individuals on their own cannot, or to achieve them more efficiently. Typically, in such situations, the agents have conflicting preferences over the set of possible joint goals. Thus, before the agents realize the benefits of cooperation, they must find a way of resolving these conflicts and reaching a consensus. In this context, cooperative game theory offers the voting game as a mechanism for agents to reach a consensus. It also offers the Shapley value as a way of measuring the influence or power a player has in determining the outcome of a voting game. Given this, the designer of a voting game wants to construct a game such that a player's Shapley value is equal to some desired value. This is called the inverse Shapley value problem. Solving this problem is necessary, for instance, to ensure fairness in the players' voting powers. However, from a computational perspective, finding a player's Shapley value for a given game is #P-complete. Consequently, the problem of verifying that a voting game does indeed yield the required powers to the agents is also #P-complete. Therefore, in order to overcome this problem we present a computationally efficient approximation algorithm for solving the inverse problem. This method is based on the technique of 'successive approximations'; it starts with some initial approximate solution and iteratively updates it such that after each iteration, the approximate gets closer to the required solution. This is an anytime algorithm and has time complexity polynomial in the number of players. We also analyze the performance of this method in terms of its approximation error and the rate of convergence of an initial solution to the required one. Specifically, we show that the former decreases after each iteration, and that the latter increases with the number of players and also with the initial approximation error. Coalition formation is an important capability for automated negotiation among self-interested agents. In order for coalitions to be stable, a key question that must be answered is how the gains from cooperation are to be distributed. Coalitional game theory provides a number of solution concepts for this. However, recent research has revealed that these traditional solution concepts are vulnerable to various manipulations in open anonymous environments such as the Internet. To address this, previous work has developed a solution concept called the anonymity-proof core, which is robust against such manipulations. That work also developed a method for compactly representing the anonymity-proof core. However, the required computational and representational costs are still huge. In this paper, we develop a new solution concept which we call the anonymity-proof Shapley value. We show that the anonymity-proof Shapley value is characterized by certain simple axiomatic conditions, always exists, and is uniquely determined. The computational and representational costs of the anonymity-proof Shapley value are drastically smaller than those of existing anonymity-proof solution concepts. Coalition formation is a key aspect of automated negotiation among self-interested agents. In order for coalitions to be stable, a key question that must be answered is how the gains from cooperation are to be distributed. Various solution concepts (such as the Shapley value, core, least core, and nucleolus) have been proposed. In this paper, we demonstrate how these concepts are vulnerable to various kinds of manipulations in open anonymous environments such as the Internet. These manipulations include submitting false names (one acting as many), collusion (many acting as one), and the hiding of skills. To address these threats, we introduce a new solution concept called the anonymity-proof core, which is robust to these manipulations. We show that the anonymity-proof core is characterized by certain simple axiomatic conditions. Furthermore, we show that by relaxing these conditions, we obtain a concept called the least anonymity-proof core, which is guaranteed to be non-empty. We also show that computational hardness of manipulation may provide an alternative barrier to manipulation.