On robustness and dynamics in (un)balanced coalitional games

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Abstract

We build upon control theoretic concepts like robustness and dynamics to better accommodate all the situations where the coalitions’ values are uncertain and subject to changes over time. The proposed robust dynamic framework provides an alternative perspective on the study of sequences of coalitional games or interval valued games. For a sequence of coalitional games, either balanced or unbalanced, we analyze the key roles of instantaneous and average games. Instantaneous games are obtained by freezing the coalitions’ values at a given time and come into play when coalitions’ values are known. On the other hand, average games are derived from averaging the coalitions’ values up to a given time and are key part of our analysis when coalitions’ values are unknown. The main theoretical contribution of our paper is a design method of allocation rules that return solutions in the core and/or $\epsilon$-core of the instantaneous and average games. Theoretical results are then specialized to a simulated example to shed light on the impact of the design method and on the performance of the resulting allocation rules.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages18
Publication statusPublished - Feb 2010

Publication series

NameMemorandum
PublisherUniversity of Twente, Department of Applied Mathematics
No.1916
ISSN (Print)1874-4850
ISSN (Electronic)1874-4850

Keywords

  • Unbalancedness
  • IR-69962
  • EWI-17405
  • METIS-270728
  • Cooperative games
  • Dynamic games

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