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Cooperative games with uncertainty: a survey

Michel Grabisch, Silvia Lorenzini

Abstract

The main stream of the literature in cooperative game theory considers games as being deterministic. In this survey, we review the main models incorporating uncertainty in cooperative games, starting from the seminal paper of Charnes and Granot (1976) and finishing with our own contribution, called Bel coalitional games. The different models are explained and compared, making a focus on the notion of allocation and core, since all the described models propose a notion of core.

Cooperative games with uncertainty: a survey

Abstract

The main stream of the literature in cooperative game theory considers games as being deterministic. In this survey, we review the main models incorporating uncertainty in cooperative games, starting from the seminal paper of Charnes and Granot (1976) and finishing with our own contribution, called Bel coalitional games. The different models are explained and compared, making a focus on the notion of allocation and core, since all the described models propose a notion of core.
Paper Structure (9 sections, 13 theorems, 39 equations)

This paper contains 9 sections, 13 theorems, 39 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Cooperative games in stochastic characteristic form
  4. Cooperative games with stochastic payoffs
  5. Uncertain cooperative games
  6. Bayesian coalitional games
  7. Transferable utility games with uncertainty
  8. Bel coalitional games
  9. Concluding remarks

Key Result

theorem 1

(Bondareva bon63, Shapley sha67) A game $(N,v)$ has a nonempty core if and only if it is balanced.

Theorems & Definitions (17)

  • definition 1
  • theorem 1
  • definition 2
  • definition 3
  • theorem 2
  • theorem 3
  • theorem 4
  • theorem 5
  • theorem 6
  • theorem 7
  • ...and 7 more