Dissertation, Oxford University (
2014)
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Abstract
Standard models in epistemic game theory make strong assumptions
about agents’ knowledge of their own beliefs. Agents are typically assumed to be
introspectively omniscient: if an agent believes an event with probability p, she is
certain that she believes it with probability p. This paper investigates the extent to
which this assumption can be relaxed while preserving some standard epistemic results.
Geanakoplos (1989) claims to provide an Agreement Theorem using the “truth”
axiom, together with the property of balancedness, a significant relaxation of introspective
omniscience. I provide an example which shows that Geanakoplos’s statement
is incorrect. I then introduce a new property, local balancedness, which allows
us both to correct Geanakoplos’s result, and to extend it to cases where the truth
axiom may fail. I exploit this general Agreement Theorem to provide novel epistemic
conditions for correlated and Nash equilibrium, both of which relax the assumption of
introspective omniscience. In all three cases, the results are also extended to infinite
state spaces. (This is Chapter 5 of my 2014 Oxford DPhil (PhD) thesis.)