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We consider the problem of sharing water from a river among the group of countries located along it. The benefit of each country depends on the amount of water it consumes. An allocation of the water is efficient when it maximizes the total benefits of the countries. The problem of finding a...
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We show that the core of any n-player TU-game with a non-empty core can be accessed with at most n−1 blocks. It turns out that this bound is optimal in the sense there are TU-games for which the number of blocks required to access the core is exactly n−1.
Persistent link: https://www.econbiz.de/10011049836
We provide a new and concise characterization of the Banzhaf value on the (linear) space of all TU-games on a fixed player set by means of two transparent axioms. The first one is the well-known Dummy player axiom. The second axiom, called Strong transfer invariance, indicates that a player's...
Persistent link: https://www.econbiz.de/10010945581
In this article, we study cooperative games with limited cooperation possibilities, represented by a tree on the set of agents. Agents in the game can cooperate if they are connected in the tree. We first derive direct-sum decompositions of the space of TU-games on a fixed tree, and two new...
Persistent link: https://www.econbiz.de/10010945582
In this article, we provide a new basis for the kernel of the Shapley value (Shapley, 1953), which is used to construct a new axiom of invariance, and to provide a new axiomatic characterization of the Shapley value. This characterization only invokes marginalistic principles, and does not rely...
Persistent link: https://www.econbiz.de/10010945583
The axiom of Balanced collective contributions is introduced as a collective variant of the axiom of Balanced contributions proposed by Myerson (1980). It requires that the identical average impact of the withdrawal of any agent from a game on the remaining population. It turns out that Balanced...
Persistent link: https://www.econbiz.de/10010945584
We study the set of allocation rules generated by component efficiency and weighted component fairness, a generalization of component fairness introduced by Herings et al. (2008). Firstly, if the underlying TU-game is superadditive, this set coincides with the core of a graph-restricted game...
Persistent link: https://www.econbiz.de/10011065197
This paper presents results on stochastic stability in evolutionary game theory. We will see that imitation processes with bounded memory and sampling (Josephson, Matros, 2004) select Pareto outcomes whereas Fictitious Play processes with bounded memory select risk-dominant outcomes in the sense...
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