Trembles in the Bayesian foundations of solution concepts of games

Article Abstract:

A revision of the probability theory proposed by Armbruster and Boge was provided in an effort to extend the use of the Bayesian approach to the concept of games. By considering trembles as a series of events with non-standard probabilistic tendencies, rational players were made to assume that other players, likewise, experience trembles. The framework further provides a proof for hierarchical Bayesian rationality, which states that players tend to impose a specified hierarchical order over trembles by others.

Game theory

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A note on stochastic independence without Savage-null events

Article Abstract:

Two approaches for conditional probability systems (CPS) combined with the concept of stochastic independence result in a condition favorable to the handling of 0-prior probability events called Savage-null events. This condition is extremely intuitive and plays an important role in Battigali. One approach is dependent upon the theory of lexicographic expected utility while the other depends on the theory of conditional expected utility maximization.

Stochastic systems

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Strategic independence and perfect Bayesian equilibria

Article Abstract:

Restrictions on assessments applied with the Bayer rule produces refinements of subgame perfection called 'perfect Bayesian equilibria' when combined with sequential rationality. These restrictions all provide the same answer to the question on conditional probability. They are also related to the principle of strategic independence; thus, the strategic preferences of various players are deemed stochastically independent events.

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