Essays on Two-player Games with Asymmetric Information<br />

This thesis contributes to the economic theory literature in three aspects: price dynamics in financial

markets with asymmetric information, belief updating and equilibrium refinements in signalling

games, and introducing ambiguity in limit pricing theory.<br />

In chapter 2, we formulate a zero-sum trading game between a better informed sector and a less

informed sector to endogenously determine the underlying price dynamics. In this model, player 1

is informed of the state (L) but is uncertain about player 2's belief about the state, because player 2

is informed through some message (M) related to the state. If L and M are independent, then the

price process will be a Continuous Martingale of Maximal Variation (CMMV), and player 1 can

benefit from his informational advantage. However, if L and M are not independent, player 1 will

not reveal his information during the trading process, therefore, he does not benefit from his

informational advantage.<br />

In chapter 3, I propose a definition of Hypothesis Testing Equilibrium (HTE) for general signalling

games with non-Bayesian players nested by an updating rule according to the Hypothesis Testing

model characterized by Ortoleva (2012). An HTE may differ from a sequential Nash equilibrium

because of dynamic inconsistency. However, in the case in which player 2 only treats a zeroprobability

message as an unexpected news, an HTE is a refinement of sequential Nash equilibrium

and survives the Intuitive Criterion in general signalling games but not vice versa. We provide an

existence theorem covering a broad class of signalling games often studied in economics.<br />

In chapter 4, I introduce ambiguity in a standard industry organization model, in which the

established firm is either informed of the true state of aggregate demand or is under classical

measurable uncertainty about the state, while the potential entrant is under Knightian uncertainty

(ambiguity) about the state. I characterize the conditions under which limit pricing emerges in

equilibria, and thus ambiguity decreases the probability of entry. Welfare analysis shows that limit

pricing is more harmful in a market with higher expected demand than in a market with lower

expected demand.