The concept of the core is reformulated to handle externality problems where the total payoff for a coalition depends upon the actions of the players outside the coalition. A deviating coalition has rational expectations of the outsiders’ individual attempts to stop the deviation and their coalitional response if the deviaiton cannot be stopped, with the coalitional response itself a core solut...

We provide the first anytime algorithm for finding the -core in a nontransferable utility coalitional game. For a given set of possible joint actions, our algorithm calculates , the maximum utility any agent could gain by deviating from this set of actions. If is too high, our algorithm searches for a subset of the joint actions which leads to a smaller . Simulations show our algorithm is more ...

We discuss the carpool problem, where one has to assign drivers to subsets of participants who commute regularly. Fagin and Williams defined a notion of fair share for participants (the FW share). We provide an axiomatic characterization of the fair share and show that the FW share is the unique one satisfying these requirements. We define a coalitional game where the Shapley value is the FW sh...

In this note we use the Shapley value to define a valuation function. A valuation function associates with every non-empty coalition of players in a strategic game a vector of payoffs for the members of the coalition that provides these players’ valuations of cooperating in the coalition. The Shapley valuation function is defined using the lowervalue based method to associate coalitional games ...

This paper studies the core of combined games, obtained by summing different coalitional games when bargaining over multiple independent issues. It is shown that the set of balanced transferable utility games can be partitioned into equivalence classes of component games to determine whether the core of the combined game coincides with the sum of the cores of its components. © 2009 Elsevier Inc...

In coalitional game theory, the issue of stability in presence of externalities has been given very little attention. Moreover, there is no solution concept in the literature which guarantees non-emptiness of the set of stable outcomes under this environment. Using the partition function form representation, we propose a new solution concept which is unique and always non-empty. It is also prov...

The effective classification of urban domestic waste is the key to achieve a “waste-free city” and provides an essential guarantee for resource utilization. This article takes coalitional game perspective study dilemmas in separation from cooperative interaction residents, government, enterprises. finds that China currently facing many problems, focusing on: 1) insufficient consensus among 2) s...

We study 3-person noncooperative games of coalition formation where the underlying situation is represented by a game in coalitional form without side payments. We look at coalition-proof Nash equilibria and we show that if the underlying game is balanced (in the sense of Scarf), then, except for indifferences, the grand coalition forms, and the payoff is in the core. If the underlying game has...

A coalitional (or cooperative) game is a model of interacting decision-makers that focuses on the behavior of groups of players. N denotes the set of players. A coalition is a group of players S ⊂ N . We refer to N as the grand coalition. Every coalition S has a set of available actions AS. An outcome consists of a partition of N (coalition structure) and one action associated with each coaliti...