1-convex extensions of incomplete cooperative games and the average value

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10468920" target="_blank" >RIV/00216208:11320/23:10468920 - isvavai.cz</a>

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=5mbnLLeirx" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=5mbnLLeirx</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11238-023-09946-8" target="_blank" >10.1007/s11238-023-09946-8</a>

Result language

angličtina

Original language name

1-convex extensions of incomplete cooperative games and the average value

Original language description

The model of incomplete cooperative games incorporates uncer7tainty into the classical model of cooperative games by considering a partial8 characteristic function. Thus the values for some of the coalitions are not9 known. The main focus of this paper is 1-convexity under this framework.10 We are interested in two heavily intertwined questions. First, given an11 incomplete game, how can we ll in the missing values to obtain a complete12 1-convex game? Second, how to determine in a rational, fair, and ecient way13 the payos of players based only on the known values of coalitions?14 We illustrate the analysis with two classes of incomplete games - minimal15 incomplete games and incomplete games with dened upper vector. To answer16 the rst question, for both classes, we provide a description of the set of 1-17 convex extensions in terms of its extreme points and extreme rays. Based on18 the description of the set of 1-convex extensions, we introduce generalisations19 of three solution concepts for complete games, namely the -value, the Shapley20 value and the nucleolus. For minimal incomplete games, we show that all21 of the generalised values coincide. We call it the average value and provide22 dierent axiomatisations. For incomplete games with dened upper vector, we23 show that the generalised values do not coincide in general. This highlights24 the importance and also the diculty of considering more general classes of25 incomplete games.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

50201 - Economic Theory

Project

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Continuities

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Theory and Decision

ISSN

0040-5833

e-ISSN

1573-7187

Volume of the periodical

Neudeven

Issue of the periodical within the volume

2023

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

29

Pages from-to

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UT code for WoS article

001026595300001

EID of the result in the Scopus database

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