Abstract
This paper analyzes the probabilistic Harsanyi power solutions (PHPSs) for probabilistic graph games (PGGs), which distribute the Harsanyi dividends proportional to weights determined by a probabilistic power measure for probabilistic graph structure. The probabilistic power measure considers the role of players in all possible deterministic graphs, which can reflect the powers of players more effectively. Three axiomatic systems of the PHPSs on PGGs and cycle-free probabilistic graph games (CFPGGs) are provided to show the rationality of the PHPSs, and their independence is analyzed.
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