Title: Sequential games under positional uncertainty
Description: This dissertation focuses on sequential games of imperfect information. I study settings in which not only do agents face imperfect information in the traditional sense of not possessing all payoff-relevant information, but they also face uncertainty about their position of movement in the sequence. I have utilized this framework to study financial investment decisions by individuals, production decisions by firms, and implications on information aggregation in observational learning. In order to study production decisions by firms I utilize a Stackelberg oligopoly model with a stochastic consumer demand. In this setting firms do not know their position of movement, and as a result of the stochastic demand they cannot infer from the prevailing price if another firm has yet entered the market. I find that as a result of uncertainty firms produce a higher quantity than they otherwise would have, resulting in a more competitive outcome. In fact, as the number of firms in the market increases, with positional uncertainty the equilibrium quantity actually exceeds the perfectly competitive quantity.

I then investigate the impact of positional uncertainty when agents must choose levels of investment in a financial asset. Investors receive a signal about the value of the asset but are not necessarily aware of their position in the sequence of investors. As a result, they are unsure to what extent the signal they receive represents profit-relevant information, or if the signal is “stale” in the sense that the information has been incorporated into the price by other investors. This results in more cautious levels of investment, and an asset price that does not represent the true underlying value. To study the behavioral aspects of financial investment, I introduce in this model a notion of confidence. While much work in the area of behavioral finance has studied the role of confidence over the accuracy of information, my interest is in confidence over the timing of information. I define an agent as overconfident if they believe they are more likely to have received the signal earlier than other agents, and are thus more likely to be early investors.

The effect of overconfidence can overwhelm the cautious nature of positionally uncertain investors, even potentially leading to an overreaction to information. This effect can explain overvaluation of assets and volatility of prices in response to information. In a model of observational learning, limited information about the history of actions slows the integration of information. However, I show that in the limit, even in the presence of limited histories complete learning occurs. In the environment of limited access to historical information I introduce uncertainty over position of action. This uncertainty even further dampens the process of learning from a welfare standpoint, but as the number of agents grows large complete learning still obtains in the limit for all levels of uncertainty. The common finding in all these settings is that uncertainty about the order of action causes agents to be cautious about exploiting profitable opportunities. In the case of oligopoly this leads to more competitive outcomes, whereas in the cases of investment and social learning uncertainty leads to less effective information aggregation.