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Partition Function Form Games

Partition Function Form Games
Author: László Á. Kóczy
Publisher: Springer
Total Pages: 320
Release: 2018-04-13
Genre: Mathematics
ISBN: 3319698419

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This book presents a systematic overview on partition function form games: a game form in cooperative game theory to integrate externalities for various applications. Cooperative game theory has been immensely useful to study a wide range of issues, but the standard approaches ignore the side effects of cooperation. Recently interest shifted to problems where externalities play the main roles such as models of cooperation in market competition or the shared use of public resources. Such problems require richer models that can explicitly evaluate the side-effects of cooperation. In partition function form games the value of cooperation depends on the outsiders' actions. A recent surge of interest driven by applications has made results very fragmented. This book offers an accessible, yet comprehensive and systematic study of properties, solutions and applications of partition function games surveying both theoretical results and their applications. It assembles a survey of existing research and smaller original results as well as original interpretations and comparisons. The book is self-contained and accessible for readers with little or no knowledge of cooperative game theory.


Partition Function Form Games With Probabilistic Beliefs

Partition Function Form Games With Probabilistic Beliefs
Author: Giorgos Stamatopoulos
Publisher:
Total Pages: 12
Release: 2019
Genre:
ISBN:

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We revisit games in partition function form, i.e. cooperative games where the payoff of a coalition depends on the partition of the entire set of players. We assume that each coalition computes its worth having probabilistic beliefs over the coalitional behavior of the outsiders, i.e., it assigns various probability distributions over the set of partitions that the outsiders can form. We apply this framework to symmetric games with either positive or negative externalities and we derive conditions on coalitional beliefs that guarantee the non-emptiness of the core.