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1.
The 'dollar game' represents a kind of diffusion process on a graph. Under the rules of the game some cofigurations are both stable and recurrent, and these are known as critical cofigurations. The set of critical configurations can be given the structure of an abelian group, and it turns out that the order of the group is the tree-number of the graph. Each critical configuration can be assigned a positive weight, and the generating function that enumerates critical configurations according to weight is a partial evaluation of the Tutte polynomial of the graph. It is shown that the weight enumerator can also be interpreted as a growth function, which leads to the conclusion that the (partial) Tutte polynomial itself is a growth function.  相似文献   

2.
On the core of information graph games   总被引:1,自引:0,他引:1  
This paper considers a subclass of minimum cost spanning tree games, called information graph games. It is proved that the core of these games can be described by a set of at most 2n — 1 linear constraints, wheren is the number of players. Furthermore, it is proved that each information graph game has an associated concave information graph game, which has the same core as the original game. Consequently, the set of extreme core allocations of an information graph game is characterized as the set of marginal allocation vectors of its associated concave game. Finally, it is proved that all extreme core allocations of an information graph game are marginal allocation vectors of the game itself, though not all marginal allocation vectors need to be core allocations.  相似文献   

3.
Ethno-religious conflict in multi-cultural societies has been one of the major causes of loss of life and property in recent history. In this paper, we present and analyze a multi-agent game theoretic model for computational study of ethno-religious conflicts in multi-cultural societies. Empirical fact-based research in sociology and conflict resolution literature have identified (a) ethno-religious identity of the population, (b) spatial structure (distribution) of the population, (c) existing history of animosity, and (d) influence of leaders as some of the salient factors causing ethno-religious violence. It has also been experimentally shown by Lumsden that multi-cultural conflict can be viewed as a Prisoner’s Dilemma (PD) game. Using the above observations, we model the multi-cultural conflict problem as a variant of the repeated PD game in graphs. The graph consists of labeled nodes corresponding to the different ethno-religious types and the topology of the graph encodes the spatial distribution and interaction of the population. We assume the structure of the graph to have the statistical properties of a social network with the high degree nodes representing the leaders of the society. The agents play the game with neighbors of their opponent type and they update their strategies based on neighbors of their same type. This strategy update dynamics, where the update neighborhood is different from the game playing neighborhood, distinguishes our model from conventional models of PD games in graphs. We present simulation results showing the effect of various parameters of our model to the propensity of conflict in a population consisting of two ethno-religious groups. We also compare our simulation results to real data of occurrence of ethno-religious violence in Yugoslavia.  相似文献   

4.
We consider the problem of cost allocation among users of a minimum cost spanning tree network. It is formulated as a cooperative game in characteristic function form, referred to as a minimum cost spanning tree (m.c.s.t.) game. We show that the core of a m.c.s.t. game is never empty. In fact, a point in the core can be read directly from any minimum cost spanning tree graph associated with the problem. For m.c.s.t. games with efficient coalition structures we define and construct m.c.s.t. games on the components of the structure. We show that the core and the nucleolus of the original game are the cartesian products of the cores and the nucleoli, respectively, of the induced games on the components of the efficient coalition structure.This paper is a revision of [4].  相似文献   

5.
李理  单而芳 《运筹学学报》2018,22(4):99-107
1977年,Myerson建立了以图作为合作结构的可转移效用博弈模型(也称图博弈),并提出了一个分配规则,也即"Myerson值",它推广了著名的Shapley值.该模型假定每个连通集合(通过边直接或间接内部相连的参与者集合)才能形成可行的合作联盟而取得相应的收益,而不考虑连通集合的具体结构.引入图的局部边密度来度量每个连通集合中各成员之间联系的紧密程度,即以该连通集合的导出子图的边密度来作为他们的收益系数,并由此定义了具有边密度的Myerson值,证明了具有边密度的Myerson值可以由"边密度分支有效性"和"公平性"来唯一确定.  相似文献   

6.
A directed graph game consists of a cooperative game with transferable utility and a digraph which describes limited cooperation and the dominance relation among the players. Under the assumption that only coalitions of strongly connected players are able to fully cooperate, we introduce the digraph-restricted game in which a non-strongly connected coalition can only realize the sum of the worths of its strong components. The Myerson value for directed graph games is defined as the Shapley value of the digraph-restricted game. We establish axiomatic characterizations of the Myerson value for directed graph games by strong component efficiency and either fairness or bi-fairness.  相似文献   

7.
The paper presents an O(mn2n log Z) deterministic algorithm for solving the mean payoff game problem, m and n being the numbers of arcs and vertices, respectively, in the game graph, and Z being the maximum weight (the weights are assumed to be integers). The theoretical basis for the algorithm is the potential theory for mean payoff games. This theory allows one to restate the problem in terms of solving systems of algebraic equations with minima and maxima. Also, in order to solve the mean payoff game problem, the arc reweighting technique is used. To this end, simple modifications, which do not change the set of winning strategies, are applied to the game graph; in the end, a trivial instance of the problem is obtained. It is shown that any game graph can be simplified by n reweightings. Bibliography: 16 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 340, 2006, pp. 61–75.  相似文献   

8.
This paper studies a class of delivery problems associated with the Chinese postman problem and a corresponding class of delivery games. A delivery problem in this class is determined by a connected graph, a cost function defined on its edges and a special chosen vertex in that graph which will be referred to as the post office. It is assumed that the edges in the graph are owned by different individuals and the delivery game is concerned with the allocation of the traveling costs incurred by the server, who starts at the post office and is expected to traverse all edges in the graph before returning to the post office. A graph G is called Chinese postman-submodular, or, for short, CP-submodular (CP-totally balanced, CP-balanced, respectively) if for each delivery problem in which G is the underlying graph the associated delivery game is submodular (totally balanced, balanced, respectively). For undirected graphs we prove that CP-submodular graphs and CP-totally balanced graphs are weakly cyclic graphs and conversely. An undirected graph is shown to be CP-balanced if and only if it is a weakly Euler graph. For directed graphs, CP-submodular graphs can be characterized by directed weakly cyclic graphs. Further, it is proven that any strongly connected directed graph is CP-balanced. For mixed graphs it is shown that a graph is CP-submodular if and only if it is a mixed weakly cyclic graph. Finally, we note that undirected, directed and mixed weakly cyclic graphs can be recognized in linear time. Received May 20, 1997 / Revised version received August 18, 1998?Published online June 11, 1999  相似文献   

9.
We introduce directed acyclic graph (DAG) games, a generalization of standard tree games, to study cost sharing on networks. This structure has not been previously analyzed from a cooperative game theoretic perspective. Every monotonic and subadditive cost game—including monotonic minimum cost spanning tree games—can be modeled as a DAG-game. We provide an efficiently verifiable condition satisfied by a large class of directed acyclic graphs that is sufficient for the balancedness of the associated DAG-game. We introduce a network canonization process and prove various structural results for the core of canonized DAG-games. In particular, we characterize classes of coalitions that have a constant payoff in the core. In addition, we identify a subset of the coalitions that is sufficient to determine the core. This result also guarantees that the nucleolus can be found in polynomial time for a large class of DAG-games.  相似文献   

10.
We consider a game that can be viewed as a random graph process. The game has two players and begins with the empty graph on vertex set . During each turn a pair of random edges is generated and one of the players chooses one of these edges to be an edge in the graph. Thus the players guide the evolution of the graph as the game is played. One player controls the even rounds with the goal of creating a so-called giant component as quickly as possible. The other player controls the odd rounds and has the goal of keeping the giant from forming for as long as possible. We show that the product rule is an asymptotically optimal strategy for both players.

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