"Cournot (1838), Bertrand (1883), and Stackelberg (1934)'s models of strategic interaction between competing firms have become the primary workhorses for the analysis of imperfect competition, being employed in a variety of fields, notably industrial organization and international trade. Among others, Anderson and Engers (1992) have argued that the simultaneous-move Cournot model is applicable to characterize an industry where lags in the observation of output decisions are long, whereas the sequential-move Stackelberg model applies when the reverse holds. While many industries fit the Cournot framework better, Shinkai (2000) has argued that the DRAM market (i.e., the market for the main memory component of most computers and many electronic systems) is better described by the Stackelberg model because firms make sequential capacity choices in an irreversible manner. It is important to understand how the implications of the these models differ with respect to total output, welfare and producer surplus for at least two reasons. First, such an understanding provides insights into the mechanics of these important theoretical models. Relatedly, it also helps us in deciding which framework (if either) is more appropriate for studying a given industry given the observed price and output levels. Second, once it has been decided which model better captures the characteristics of a given industry, a policy maker can better assess whether mergers or other industry developments may help or hurt consumers. The answer may very well depend on which model one thinks is more appropriate to describe an industry. In Chapter 1 of my thesis, I compare an n-firm Cournot game with a Stackelberg model, where n firms choose outputs sequentially, in a stochastic demand environment with private information. The Stackelberg perfect revealing equilibrium expected price is higher, therefore expected output and total surplus are lower; total expected profits are higher than in Cournot equilibrium irrespective of how noisy both the demand shocks and private demand signals of firms are. These rankings are the opposite to the rankings of prices, total- output, surplus, and profits between Cournot and Stackelberg models under perfect information. In the second part of Chapter 1, I also extend the analyses of Gal-Or (1987) and Shinkai (2000) on last-mover advantage to the above n-firm Stackelberg oligopoly set-up. I show that at the perfect revealing equilibrium, the first n - 1 firms' expected profits form a decreasing sequence from the first to the (n - 1)st. If, in addition, there are no more than four firms, then the last mover earns the highest expected profit. We explain these results by discussing strategic substitutability and complementarity relationships among the quantity decisions of firms. We use the fact that there is a discontinuity between the Stackelberg equilibrium of the perfect information game and the limit of Stackelberg perfect revealing equilibria of the incomplete information games as the noise of the demand information vanishes to zero. It is in Chapter 2 that I study the applications of Cournot and Bertrand models to mergers. I investigate the welfare effects of mergers on merging firms (insiders), non-merging firms (outsiders), and consumers in a differentiated product market. I extend many results in this literature by both considering imperfect substitution (and complementarity) among goods and varying the number of firms merged. If mergers do not generate any cost efficiencies, then any size of horizontal mergers among firms producing substitutable goods decreases both consumer and total welfare under both quantity and price setting games. Moreover, horizontal mergers with full cost efficiency gains are still mostly welfare reducing especially when the cost-demand ratio is sufficiently low. However, any size of conglomerate merger among suppliers of complementary products are both consumer and welfare enhancing under both game settings. I also introduce a price approach for calculating total welfare to identify the effects causing these results. In both Chapters 1 and 2, the common assumption was that all firms actively produce. However, in several markets some firms are not able to actively participate, and many decide to shut down. A cost reducing innovation by competitors, the inability to adapt changing market conditions, a cost-efficient merger among rival firms, or an increase in fixed costs may increase the incentives of a firm to exit from the market. In line with these concerns, we relax the assumption of positive production by all firms and allow firms to not produce. It is well known that the theorems that state the existence and uniqueness of Cournot equilibrium would straightforwardly extend to environments where firms prefer to be not active. However, in Chapter 3, we argue that when firms are allowed to charge their marginal costs, Bertrand models lead to very unexpected results. We show that differentiated linear Bertrand oligopolies with constant unit costs and continuous best replies do not need to satisfy supermodularity (Topkis (1979)) or the single crossing property (Milgrom and Shannon (1994)). In particular, Bertrand best replies might be negatively sloped and there are (infinite) multiple undominated Bertrand-Nash equilibria on a wide range of parameter values when the number of firms is more than two. These results are very different from the existing literature on Bertrand models, where uniqueness, supermodularity, and single crossing usually hold under a linear market demand assumption and best reply functions slope upwards. We further provide an iteration algorithm to find the set of players that are active in any equilibrium. This set is uniquely defined. We also characterize the whole set of undominated equilibria"--Pages v-viii.

We analyze wage inequality, extending the Burdett and Mortensen (International Economic Review 39 (1998), 257-73) model by incorporating worker heterogeneity through skill requirements. We provide sufficient conditions for existence of an equilibrium where more productive firms offer higher wages. The unique such equilibrium is characterized in a closed form solution. Both within- and between-group inequality are explicitly calculated. We then calibrate the model to explain the joint movement of both within- and between-group inequality in the late 1980s and 1990s, an explanation that has been elusive in the literature so far.

Patents are a useful but imperfect reward for innovation. In sectors like pharmaceuticals, where monopoly distortions seem particularly severe, there is growing international political pressure to identify alternatives to patents that could lower prices. Innovation prizes and other non-patent rewards are becoming more prevalent in government's innovation policy, and are also widely implemented by private philanthropists. In this paper we develop a model in which a patent buyout is effective, using information from market outcomes as a guide to the payment amount. We allow for the fact that sales may be manipulable by the innovator in search of the buyout payment, and show that in a wide variety of cases the optimal policy in our model still involves some form of patent buyout. The buyout uses two key pieces of information: market outcomes observed during the patent's life, and the competitive outcome after the patent is bought out. We show that such dynamic market information can be effective at determining both marginal and total willingness to pay of consumers in many important cases, and therefore can generate the right innovation incentives in our model.

We consider a model of directed search where the sellers are allowed to post general mechanisms. Regardless of the number of buyers and sellers, the sellers are able extract all the surplus of the buyers by introducing entry fees and making their price schedule positively sloped in the number of buyers arriving to their shops. Therefore, shopping card membership fees - similar to our entry fee component - may act as a collusion device between sellers. If there is a lower bound on the prices or there is an upper bound on the entry fees that can be charged, then the equilibrium with full rent extraction may not exist any more. However, the seller optimal equilibrium still features positive entry fees and increasing price schedules. When the constraint is on the entry fees in the seller optimal equilibrium all sellers offer auctions. This implies that if the firms can coordinate on an equilibrium they would not choose a fixed price one (studied by Burdett, Shi and Wright (2001)) or one without entry fees (as in Coles and Eeckhout (2003)). When the market becomes infinitely large, and the sellers face constraints on the prices or entry fees they can choose, then any equilibrium yields the same profits and the sellers cannot sustain collusion in equilibrium.

Burdett, Shi and Wright (2001) offer a directed search model where the buyers decide which seller to visit after observing the price each seller posts, and showed that there exists a unique symmetric equilibrium. Coles and Eeckhout (2003) showed that there is a continuum of symmetric equilibria, if the sellers are allowed to post general mechanisms and not only fixed prices. I show that many of the equilibria that Coles and Eeckhout identify, including the fixed price equilibria suggested by Burdett, Shi and Wright (2001), are not robust to introducing heterogeneous buyers with two possible types. In this case only ex-post efficient equilibria exist, i.e. a buyer with a lower valuation can never win against a buyer with a higher valuation if they visit the same seller. This suggests that mechanisms like auctions that utilize buyer competition in an efficient manner may endogenously arise when sellers post competing mechanisms. When the type space is continuous instead of having two possible types, the ex-post efficiency result is not maintained. If the sellers' strategy space is unrestricted, then any allocation respecting sequential rationality of the buyers, can be implemented in equilibrium. However, posting simple fixed price mechanisms never constitute an equilibrium, while posting (second-price or first-price) auctions does if the distribution function is convex.