96-072
INDEPENDENCE ON RELATIVE PROBABILITY SPACES AND CONSISTENT
ASSESSMENTS IN GAME TREES
Elon Kohlberg and Philip J. Reny
Relative probabilities compare the likelihoods of any pair of events, even those
with probability zero. Definitions of weak and strong independence of random variables
on finite relative probability spaces are introduced. The former is defined directly, while
the latter is defined in terms of approximations by ordinary probabilities. Our main result
is a characterization of strong independence in terms of weak independence and
exchangeability. The result is applied to game theory to obtain a natural interpretation of
consistent assessment, an essential yet controversial ingredient in the definition of
sequential equilibrium. Keywords: relative probabilities, conditional probability
systems, strong independence, weak independence, exchangeability, consistent
assessments, sequential equilibrium.
C&S
43 pages
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