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tainty was addressed in [21]. In this approach, the payoffs are assumed
to be stochastic variables, and agent's preferences over those stochastic
variables are used to determine the stability of a coalition.
In 2004, Chalkiadakis and Boutilier [22] handled the second type of
uncertainty by proposing the Bayesian-core concept, where the agents
are assumed to belong to various types, which are unknown to other
agents. The agents need to estimate the value of potential coalitions
by maintaining a Bayesian belief system regarding the possible types
of their potential partners, and update their private beliefs in a rein-
forcement learning-based approach in repeated game scenario. A ran-
domized mechanism for reaching the Bayesian core was also proposed.
While uncertainty in TU games has recently been addressed, still
little work has been done on the counter-part for NTU games. In the
remaining chapters, we will fill in this gap by proposing NTU game
stability criteria under both uncertainty and private beliefs. Corre-
sponding mechanisms will be developed and analysed, and example
applications will be discussed.
References
[1]
Aumann R J, Peleg B. Von neumann-morgenstern solutions to cooperative
games without side payments. In Bulletin of the American Mathematical
Society, 66: 173-179, 1960.
[2]
Osborne M J, Rubinstein A. A Course in Game Theory. Cambridge: MIT
Press, 1994.
[3]
Pareto V. Manuale dieconomia politico. In Piccola Biblioteca Scientifica.
Milan: Societa Editrice, 1906.
[4]
Aumann R J. The core of a cooperative game without side payments. In
Transactions of the American Mathematical Society, 98: 539-552, 1961.
[5]
von Neumann J, Morgenstern O. Theory of Games and Economic Behavior.
Princeton: Princeton University Press, 1944.
[6]
Edgeworth F Y. Mathematical psychics: An essay on the application of
mathematics to the moral sciences, 1881.
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