The selectope for cooperative games

Derks, Jean; Haller, Hans; Peters, Hans

doi:10.1007/s001820050003

Cited by 74 publications

(69 citation statements)

References 15 publications

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“…We call this set the Harsanyi set; it is considered first in Hammer et al (1997) (as the Selectope) and, independently, in Vasil'ev (1978, in Russian, and. These articles show that the Harsanyi set encloses the core of the game, and Vasil'ev furthermore proved that this set has a core-type structure, a result that is shown independently in Derks et al (2000).…”

Section: Introductionmentioning

confidence: 85%

On the Harsanyi payoff vectors and Harsanyi imputations

2008

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This article discusses the set of Harsanyi payoff vectors of a cooperative TU-game, also known as the Selectope. We reconsider some results on Harsanyi payoff vectors within a more general framework. First, an intuitive approach is used, showing that the set of Harsanyi payoff vectors is the core of an associated convex game. Next, the set of individual rational Harsanyi payoff vectors, the Harsanyi imputations in short, is considered. Existence conditions are provided, and if non-empty, we provide a description as the core of a well-defined convex game, and show that it is an externally stable set.

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Section: Introductionmentioning

confidence: 85%

On the Harsanyi payoff vectors and Harsanyi imputations

2008

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“…It should be noticed that the Harsanyi set of a game is equal to its selectope, introduced by Hammer et al (1977), see also Derks et al (2000). First, a selector chooses for every nonempty coalition a particular player in the coalition to whom to assign the dividend of that coalition, i.e., a selector is a function α:…”

Section: Preliminariesmentioning

confidence: 99%

“…In a game with ordered players, consisting of a game and a digraph, the payoff assigned to a player may depend on both the worths of the coalitions as well as the position of the player in the graph. In the spirit of the Harsanyi set (Vasil'ev (1978(Vasil'ev ( , 1981; Vasil'ev and van der Laan (2002)) or selectope (Hammer et al (1977); Derks et al (2000)), we consider solutions that are based on distributing the Harsanyi dividends (see Harsanyi, 1959) of a game. The Harsanyi set of a game is the set of those payoff vectors that are obtained by distributing the dividend of every coalition in any possible way among its members.…”

Section: Introductionmentioning

confidence: 99%

Constrained core solutions for totally positive games with ordered players

2013

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In many applications of cooperative game theory to economic allocation problems, such as river games, polluted river games and sequencing games, the game is totally positive (i.e., all dividends are nonnegative), and there is some ordering on the set of the players. A totally positive game has a nonempty core. In this paper we introduce constrained core solutions for totally positive games with ordered players which assign to every such a game a subset of the core. These solutions are based on the distribution of dividends taking into account the hierarchical ordering of the players. The Harsanyi constrained core of a totally positive game with ordered players is a subset of the core of the game and contains the Shapley value. For special orderings it coincides with the core or the Shapley value. The selectope constrained core is defined for acyclic orderings and yields a subset of the Harsanyi constrained core. We provide a characterization for both solutions.

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“…In fact, the position value even may give a payoff vector outside the Harsanyi set of the corresponding restricted game. The Harsanyi set or Selectope of a game v, independently introduced by Vasil'ev (1978), and Hammer et al (1977), respectively (see also van der Laan 2002 andDerks et al 2000), is the set…”

Section: Proposition 33 For a Symmetric Positive Power Measurementioning

confidence: 99%

“…These Harsanyi solutions are proposed as solutions for TU-games in Vasil'ev (1982Vasil'ev ( , 2003) (see also Derks et al 2000, where a Harsanyi solution is called a sharing value). The idea behind a Harsanyi solution is that it distributes the Harsanyi dividends (see Harsanyi 1959) over the players in the corresponding coalitions according to a chosen sharing system which assigns to every coalition S a sharing vector specifying for every player in S its share in the dividend of S. The payoff to each player i is thus equal to the sum of its shares in the dividends of all coalitions of which he is a member.…”

Section: Introductionmentioning

confidence: 99%

Harsanyi power solutions for graph-restricted games

2010

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We consider cooperative transferable utility games, or simply TU-games, with limited communication structure in which players can cooperate if and only if they are connected in the communication graph. Solutions for such graph games can be obtained by applying standard solutions to a modified or restricted game that takes account of the cooperation restrictions. We discuss Harsanyi solutions which distribute dividends such that the dividend shares of players in a coalition are based on power measures for nodes in corresponding communication graphs. We provide axiomatic characterizations of the Harsanyi power solutions on the class of cycle-free graph games and on the class of all graph games. Special attention is given to the Harsanyi degree solution which equals the Shapley value on the class of complete graph games and equals the position value on the class of cycle-free graph games. The Myerson value is the Harsanyi power solution that is based on the equal power measure. Finally, various applications are discussed.

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The selectope for cooperative games

Cited by 74 publications

References 15 publications

On the Harsanyi payoff vectors and Harsanyi imputations

On the Harsanyi payoff vectors and Harsanyi imputations

Constrained core solutions for totally positive games with ordered players

Harsanyi power solutions for graph-restricted games

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