The allocation of marginal surplus for cooperative games with transferable utility

2021 ◽  
Author(s):  
Wenzhong Li ◽  
Genjiu Xu ◽  
Rong Zou ◽  
Dongshuang Hou
Keyword(s):  
Cooperative Games ◽  
Transferable Utility

AN AXIOM SYSTEM FOR A VALUE FOR GAMES IN PARTITION FUNCTION FORM

2005 ◽  
Vol 07 (01) ◽  
pp. 63-72 ◽  
Author(s):  
M. J. ALBIZURI ◽  
J. ARIN ◽  
J. RUBIO
Keyword(s):  
Partition Function ◽  
Shapley Value ◽  
Cooperative Games ◽  
Axiom System ◽  
Axiomatic Characterization ◽  
Transferable Utility ◽  
Function Form ◽  
A Value ◽  
The Shapley Value ◽  
Partition Function Form

Lucas and Trall (1963) defined the games in partition function form as a generalization of the cooperative games with transferable utility. In our work we propose by means of an axiomatic characterization a solution for such games in partition function form. This solution will be a generalization of the Shapley value (1953).

scholarly journals A NOTE ON NTU CONVEXITY AND POPULATION MONOTONIC ALLOCATION SCHEMES

2003 ◽  
Vol 05 (04) ◽  
pp. 385-390
Author(s):  
RUUD HENDRICKX
Keyword(s):  
Cooperative Games ◽  
Transferable Utility ◽  
Allocation Scheme ◽  
Population Monotonic Allocation Scheme ◽  
Monotonic Allocation Scheme ◽  
Population Monotonic Allocation Schemes

For cooperative games with transferable utility, convexity has turned out to be an important and widely applicable concept, mainly because it implies some very nice and handy properties. One of these is that every extended marginal vector constitutes a population monotonic allocation scheme. In this note, this well-known result is generalised to games with nontransferable utility.

scholarly journals Hart–Mas-Colell consistency and the core in convex games

2021 ◽  
Author(s):  
Bas Dietzenbacher ◽  
Peter Sudhölter
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Individual Rationality ◽  
Transferable Utility ◽  
Convex Games ◽  
The Core ◽  
The Shapley Value ◽  
Scale Covariance

AbstractThis paper formally introduces Hart–Mas-Colell consistency for general (possibly multi-valued) solutions for cooperative games with transferable utility. This notion is used to axiomatically characterize the core on the domain of convex games. Moreover, we characterize all nonempty solutions satisfying individual rationality, anonymity, scale covariance, superadditivity, weak Hart–Mas-Colell consistency, and converse Hart–Mas-Colell consistency. This family consists of (a) the Shapley value, (b) all homothetic images of the core with the Shapley value as center of homothety and with positive ratios of homothety not larger than one, and (c) their relative interiors.

The Need for Permission, the Power to Enforce, and Duality in Cooperative Games with a Hierarchy

2016 ◽  
Vol 18 (04) ◽  
pp. 1650015 ◽  
Author(s):  
Frank Huettner ◽  
Harald Wiese
Keyword(s):  
Cooperative Game ◽  
Cooperative Games ◽  
Transferable Utility ◽  
Tu Game ◽  
Tu Games ◽  
Permission Value

A cooperative game with transferable utility (TU game) captures a situation in which players can achieve certain payoffs by cooperating. We assume that the players are part of a hierarchy. In the literature, this invokes the assumption that subordinates cannot cooperate without the permission of their superiors. Instead, we assume that superiors can force their subordinates to cooperate. We show how both notions correspond to each other by means of dual TU games. This way, we capture the idea that a superiors’ ability to enforce cooperation can be seen as the ability to neutralize her subordinate’s threat to abstain from cooperation. Moreover, we introduce the coercion value for games with a hierarchy and provide characterizations thereof that reveal the similarity to the permission value.

Uncoupled Aspiration Adaptation Dynamics Into the Core

2019 ◽  
Vol 20 (2) ◽  
pp. 243-256 ◽  
Author(s):  
Heinrich H. Nax
Keyword(s):  
Finite Time ◽  
Cooperative Games ◽  
Transferable Utility ◽  
The Core ◽  
Best Response ◽  
Dynamic Blocking ◽  
Evolutionary Interpretation ◽  
Require Information ◽  
Empty Core

Abstract Dynamics for play of transferable-utility cooperative games are proposed that require information regarding own payoff experiences and other players’ past actions, but not regarding other players’ payoffs. The proposed dynamics provide an evolutionary interpretation of the proto-dynamic ‘blocking argument’ (Edgeworth, 1881) based on the behavioral principles of ‘aspiration adaptation’ (Sauermann and Selten, 1962) instead of best response. If the game has a non-empty core, the dynamics are absorbed into the core in finite time with probability one. If the core is empty, the dynamics cycle infinitely through all coalitions.

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