منابع مشابه
Computing solutions for matching games
A matching game is a cooperative game (N, v) defined on a graph G = (N,E) with an edge weighting w : E → R+. The player set is N and the value of a coalition S ⊆ N is defined as the maximum weight of a matching in the subgraph induced by S. First we present an O(nm+n logn) algorithm that tests if the core of a matching game defined on a weighted graph with n vertices and m edges is nonempty and...
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In this paper we survey some applications of Scarf’s Lemma. First, we introduce the notion of fractional core for NTU-games, which is always nonempty by the Lemma. Stable allocation is a general solution concept for games where both the players and their possible cooperations can have capacities. We show that the problem of finding a stable allocation, given a finitely generated NTU-game with c...
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I introduce cooperative product games (CPGs), a cooperative game where every player has a weight, and the value of a coalition is the product of the weights of the players in the coalition. I only look at games where the weights are at least 2. I show that no player in such a game can be a dummy. I show that the game is convex, and therefore always has a non-empty core. I provide a simple metho...
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We present a new algorithm for solving Simple Stochastic Games (SSGs), which is fixed parameter tractable when parametrized with the number of random vertices. This algorithm is based on an exhaustive search of a special kind of positional optimal strategies, the f-strategies. The running time is O( |VR|! · (log(|V |)|E| + |p|) ), where |V |, |VR|, |E| and |p| are respectively the number of ver...
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We define the class of simple recursive games. A simple recursive game is defined as a simple stochastic game (a notion due to Anne Condon), except that we allow arbitrary real payoffs but disallow moves of chance. We study the complexity of solving simple recursive games and obtain an almost-linear time comparison-based algorithm for computing an equilibrium of such a game. The existence of a ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1969
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1969-0378868-x