Partition function form games with probabilistic beliefs
Paraskevas V. Lekeas, Giorgos Stamatopoulos
TLDR
This paper introduces probabilistic beliefs into partition function games to analyze core non-emptiness under various externalities.
Key contributions
- Reimagines partition function games with probabilistic beliefs about outsiders.
- Models coalition worth based on non-consistent probabilistic beliefs.
- Applies framework to symmetric games with positive or negative externalities.
- Identifies conditions on beliefs ensuring the non-emptiness of the game's core.
Why it matters
This research extends the understanding of cooperative game theory by integrating uncertainty into coalition formation. By identifying conditions for core stability, it offers insights into designing robust cooperative agreements in complex systems where players have incomplete information about others' actions.
Original Abstract
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. These beliefs are not necessarily consistent with respect to the actual choices of the outsiders. We apply this framework to symmetric partition function form games characterized by either positive or negative externalities and we derive conditions on coalitional beliefs that guarantee the non-emptiness of the core of the induced games.
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