21 research outputs found
The Harsanyi paradox and the 'right to talk' in bargaining among coalitions
We introduce a non-cooperative model of bargaining when players are divided into coalitions. The model is a modification of the mechanism in Vidal-Puga (Economic Theory, 2005) so that all the players have the same chances to make proposals. This means that players maintain their own 'right to talk' when joining a coalition. We apply this model to an intriguing example presented by Krasa, Tamimi and Yannelis (Journal of Mathematical Economics, 2003) and show that the Harsanyi paradox (forming a coalition may be disadvantageous) disappears.cooperative games bargaining coalition structure Harsanyi paradox
Assignment problems in wildfire suppression: a case study on control of flight resources
The phenomenon of wildfires has become one of the biggest problems
our forests are suffering due to the high frequency and intensity
that has acquired in recent decades. As the budget and fire resources
are limited, it is essential to control these catastrophic fires by making
efficient decisions. In this paper, we make use of operations research
techniques that allow the optimal assignments of aircrafts to extinguishing
wheels and to refueling points, which are two important tasks
to be performed by the controller of aerial resources in a forest fire.The authors wish to thank the interesting proposals, comments, and computing support made by W. González-Manteiga, B. Pateiro-López, A. Riera-Álvarez, two referees, and an anonymous associate editor. This research received financial support from the Ministerio de Economía y Competitividad of Spain through grant MTM2014-53395-C3-2-P, MTM2016-76969-P, MTM2017-87197-C3-3-P, and from ITMATI, Technological Institute of Industrial Mathematics, Santiago de Compostela, Spain, through the Enjambre project, which are gratefully acknowledgeS
A Focal-Point Solution for Bargaining Problems with Coalition Structure
In this paper we study the restriction, to the class of bargaining problems with coalition structure, of several values which have been proposed on the class of non-transferable utility games with coalition structure. We prove that all of them coincide with the solution independently studied in Chae and Heidhues (2004) and Vidal-Puga (2005a). Several axiomatic characterizations and two noncooperative mechanisms are proposed.coalition structure bargaining values
Weighted Shapley hierarchy levels values
In this paper we present a new class of values for cooperative games with level structure.
We use a multi-step proceeding, suggested first in Owen (1977), applied to the weighted
Shapley values. Our first axiomatization is an generalisation of the axiomatization given
in Gómez-Rúa and Vidal-Puga (2011), itselves an extension of a special case of an axiomatization given in Myerson (1980) and Hart and Mas-Colell (1989) respectively by
efficiency and weighted balanced contributions. The second axiomatization is completely
new and extends the axiomatization of the weighted Shapley values introduced in Hart
and Mas-Colell (1989) by weighted standardness for two player games and consistency.
As a corollary we obtain a new axiomatization of the Shapley levels value
Weighted Shapley hierarchy levels values
In this paper we present a new class of values for cooperative games with level structure.
We use a multi-step proceeding, suggested first in Owen (1977), applied to the weighted
Shapley values. Our first axiomatization is an generalisation of the axiomatization given
in Gómez-Rúa and Vidal-Puga (2011), itselves an extension of a special case of an axiomatization given in Myerson (1980) and Hart and Mas-Colell (1989) respectively by
efficiency and weighted balanced contributions. The second axiomatization is completely
new and extends the axiomatization of the weighted Shapley values introduced in Hart
and Mas-Colell (1989) by weighted standardness for two player games and consistency.
As a corollary we obtain a new axiomatization of the Shapley levels value
The axiomatic approach to three values in games with coalition structure
We study three values for transferable utility games with coalition structure, including the Owen coalitional value and two weighted versions with weights given by the size of the coalitions. We provide three axiomatic characterizations using the properties of Efficiency, Linearity, Independence of Null Coalitions, and Coordination, with two versions of Balanced Contributions inside a Coalition and Weighted Sharing in Unanimity Games, respectively.coalition structure; coalitional value
Weighted Shapley hierarchy levels values
In this paper we present a new class of values for cooperative games with level structure.
We use a multi-step proceeding, suggested first in Owen (1977), applied to the weighted
Shapley values. Our first axiomatization is an generalisation of the axiomatization given
in Gómez-Rúa and Vidal-Puga (2011), itselves an extension of a special case of an axiomatization given in Myerson (1980) and Hart and Mas-Colell (1989) respectively by
efficiency and weighted balanced contributions. The second axiomatization is completely
new and extends the axiomatization of the weighted Shapley values introduced in Hart
and Mas-Colell (1989) by weighted standardness for two player games and consistency.
As a corollary we obtain a new axiomatization of the Shapley levels value
The weighted Shapley support levels values
This paper presents a new class of weighted values for level structures. The new values, called weighted Shapley support levels values, extend the weighted Shapley values to level
structures and contain the Shapley levels value (Winter, 1989) as a special case. Since a level structure with only two levels coincides with a coalition structure we obtain, as a
side effect, also new axiomatizations of weighted coalition structure values, presented in
Levy and McLean (1989)
Two classes of weighted values for coalition structures with extensions to level structures
In this paper we introduce two new classes of weighted values for coalition structures with related extensions to level structures. The values of both classes coincide on given player sets with Harsanyi payoffs and match therefore adapted standard axioms for TU-values which are satisfied by these values.
Characterizing elements of the values from the new classes are a new weighted proportionality within components property and a null player out property, but on different
reduced games for each class. The values from the first class, we call them weighted Shapley alliance coalition structure values (weighted Shapley alliance levels values), satisfy the null player out property on usual reduced games. By contrast, the values from the second class, named as weighted Shapley collaboration coalition structure values (weighted
Shapley collaboration levels values) have this property on new reduced games where a component decomposes in the components of the next lower level if one player of this
component is removed from the game. The first class contains as a special case the Owen value (Shapley levels value) and the second class includes a new extension of the Shapley
value to coalition structures (level structures) as a special case