Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures

Brink, René van den; Gilles, Robert P.

doi:10.1006/game.1996.0008

Cited by 114 publications

(53 citation statements)

References 4 publications

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“…Since a large body of literature deals with axiomatizations of the Shapley value, one possible purpose is to develop new axiomatizations of the ϕ E value and to compare them. In addition, the effects of excluding coalitions could be analyzed in the framework of other structures of cooperative game theory like partitions [16,17], levels [18,19], networks [3,20] or hierarchies [21][22][23]. Another theoretical development could be a modified version of the ϕ E value that is based on other value-like solution concepts of cooperative game theory [24].…”

Section: Discussionmentioning

confidence: 99%

The Effects of Excluding Coalitions

Hiller

2018

Games

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Abstract:One problem in cooperative game theory is to model situations when two players refuse to cooperate (or the problem of quarreling members in coalitions). One example of such exclusions is the coalition statements of parliamentary parties. Other situations in which incompatible players affect the outcome are teams in firms and markets, for example. To model these exclusions in cooperative game theory, the excluded coalitions value (ϕ E value) was introduced. This value is based on the Shapley value and takes into account that players exclude coalitions with other players. In this article, we deduce some properties of this new value. After some general results, we analyze the apex game that could be interpreted as a team situation and the glove game that models markets where sellers and buyers deal. For team situations, we show that all employees have a common interest for cooperation. On asymmetric markets, excluding coalitions affect the market players of the scarce side to a higher extent.

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Section: Discussionmentioning

confidence: 99%

The Effects of Excluding Coalitions

Hiller

2018

Games

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“…The relation between asset ownership and relational contracts is studied in Baker et al (2002). In van den Brink and Gilles (2003) also hierarchical organizations are considered but they look at 'what game is played' within a hierarchy where superiors have the power to veto their subordinates.…”

Section: Discussionmentioning

confidence: 99%

“…The permission value for games with a permission structure is studied by Gilles et al (1992), van den Brink and Gilles (1996) and van den Brink (1997) as an adaptation of the well-known and often applied Shapley value (Shapley 1953) for cooperative games. A full characterization of the permission pay-system can be found in van den Brink (2007).…”

Section: The Pay-systemmentioning

confidence: 99%

Technology driven organizational structure of the firm

Brink

Ruys

2007

Ann Finance

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We model a corporate firm with a variable internal organizational structure that adapts to various degrees of technological cooperation. The entrepreneur determines the organizational structure that maximizes profits under participation constraints. Wages are determined by an internal cooperative pay-system, constrained by external reservation wages. We show that closer cooperation between productionworkers results in a shorter organization with enhanced positional wages relative to the external benchmarks. The corporate firm is embedded in a competitive market economy that determines reservation wages and market prices. We also allow for more general technologies and provide conditions guaranteeing a finite optimal size of the firm.

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“…Alternatively, in the conjunctive approach as developed in Gilles et al (1992), van den Brink and Gilles (1996) and van den Brink (1999), it is assumed that each player needs permission from all its predecessors before it is allowed to cooperate. This means that a coalition E is feasible if and only if for every player in the coalition it holds that all its predecessors belong to the coalition.…”

Section: Preliminaries: Games With a Permission Structurementioning

confidence: 99%

“…In the disjunctive approach as considered in Gilles and Owen (1999) and van den Brink (1997) it is assumed that every player needs permission from at least one of its predecessors before it is allowed to cooperate with other players. Alternatively, in the conjunctive approach as developed in Gilles et al (1992) and van den Brink and Gilles (1996), it is assumed that every player needs permission from all its predecessors before it is allowed to cooperate.…”

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confidence: 99%

Axiomatizations of Banzhaf permission values for games with a permission structure

Brink

2010

Int J Game Theory

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In games with a permission structure it is assumed that players in a cooperative transferable utility game are hierarchically ordered in the sense that there are players that need permission from other players before they are allowed to cooperate. We provide axiomatic characterizations of Banzhaf permission values being solutions that are obtained by applying the Banzhaf value to modified TU-games. In these characterizations we use power-and player split neutrality properties. These properties state that splitting a player's authority and/or contribution over two players does not change the sum of their payoffs.

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Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures

Cited by 114 publications

References 4 publications

The Effects of Excluding Coalitions

The Effects of Excluding Coalitions

Technology driven organizational structure of the firm

Axiomatizations of Banzhaf permission values for games with a permission structure

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