Makoto Shimoji

Conditional Dominance, Rationalizability, and Game Forms

We propose a notion of conditional dominance for games whose representations designate information sets. We prove that iterated conditional dominance is equivalent to extensive form rationalizability. We also conduct a general analysis of these concepts, yielding new insights on rationalizability and on the equivalence of solutions when applied to different representations of a game.

On the equivalence of weak dominance and sequential best response

In this paper, we identify the conditions under which a strategy is weakly dominated if and only if it is not sequential best response. In addition, we explore the implication for extensive form rationalizability.

A Comment on “Can Relaxation of Beliefs Rationalize the Winner's Curse?: An Experimental Study”

Ivanov, Levin, and Niederle (2010) use a common‐value second‐price auction experiment to reject beliefs‐based explanations for the winners curse. ILNs conclusion, however, stems from the misuse of theoretical arguments. Beliefs‐based models are even compatible with some observations from ILNs experiment.

Outcome-equivalence of self-confirming equilibrium and Nash equilibrium

We introduce a condition, Nash-equivalent self-confirming equilibrium. If beliefs are assumed to be independent and unitary, Nash-equivalent self-confirming equilibrium and Nash equilibrium are outcome-equivalent. We show that the set of Nash-equivalent self-confirming equilibria and the set of self-confirming equilibria which are outcome-equivalent to Nash equilibria coincide. Our condition identifies the collection of information sets and requires the existence of beliefs shared by (certain sets of) players regarding these information sets. If the information sets are off the equilibrium path, the beliefs regarding them do not have to be correct. Our condition is weaker than that of strongly consistent self-confirming equilibrium by Kamada (2010).