Essays in uncertainty and incomplete information
This dissertation consists of investigating the role of incomplete information and uncertainty in certain specific contexts of static models of game theory. The work may be divided into two parts. The first part, comprising the first two chapters, consists of a theoretical continuation of recent work by Stephen Morris and coauthors. In chapter 1, I suggest a reinterpretation of the 'uniqueness due to contagion' literature in games of incomplete information. A deductive algorithm is provided that each player in an n player game might use to deduce his way to playing what we call the strong-risk dominant equilibrium when a game is common knowledge. The strong-risk dominant equilibrium coincides in 2 x 2 games with the risk-dominant equilibrium of Harsanyi and Selten. In chapter 2, we formalize a metric of robustness of equilibria of normal form games implicitly used by Morris and Kajii (Econometrica 1997), and make the case for a weaker metric. We show that every strict equilibria of a normal form game is robust in our metric. The second part of the dissertation investigates the extent of horizontal merging in markets when there is uncertainty about the profit functions of firms. This is the third and last chapter. Using the most inhospitable environment for mergers, we show that symmetric uncertainty (no private information) allows a firm to fully monopolize the industry when there are three firms whereas in the absence of uncertainty the only equilibrium would have been the status quo. Further, the resulting merger is always privately profitable and yet socially undesirable, in contrast to the observations that have appeared in the literature, where equilibria in a market with potential for horizontal merging have generally been Pareto-optimal. Since the addition of such plausible uncertainty is able to significantly change the nature of the equilibrium by bringing about monopolization in the canonical example of the 'no horizontal merging' model (linear demands and costs), we suggest that incentives for mergers and monopolization may also be appreciably enhanced in less restrictive models.
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