Three Essays in Theory of Vertical Contracting and Extensive Form Games

Jakub Kaluzny

doi:https://doi.org/10.21985/N2KX7R

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Three Essays in Theory of Vertical Contracting and Extensive Form Games

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In the first chapter we analyze profits and efficiency implications of a relation between an upstream duopoly and downstream monopoly in Hotelling linear city model. While exclusive contracts maximize the monopolist's profit, at the same time socially they are inefficient. Linear prices, while more efficient, usually also do not achieve maximum efficiency. The efficient outcome can be achieved by using general, non-linear contracts, but they can also lead to inefficient equilibria. Restricting the set of available contracts to two part tariffs yields the same efficient outcome as general non-linear contracts, and at the same time rules out other inefficient equilibria, so from efficiency standpoint seems most desirable. In the second chapter we analyze effects of licensing a cost-reducing innovation in a similar Hotelling spatial model. We construct a formal model that illustrates in a unified framework a number of results from earlier literature. The most important one of them states that in a symmetric Cournot model fixed fees always generate higher revenue than linear royalties. The model is extended to arrive at a different conclusion by introducing modifications such as asymmetric firms, differentiated products, asymmetric information and insider patentee. In the second part of the essay, we show that in a spatial competition linear royalties always generate higher revenue than fixed fees for both the outsider and an insider patent holder. In the third chapter we consider an abstract issue related to backward induction in extensive form games with many stages. While each extensive form game of complete information can be solved by backward induction, the solution can be computationally intensive. We show that in a class of these games, even though the solution is difficult to compute exactly, it can be described precisely in terms of probability distributions. Contrary to results in the earlier literature, we show, that the outcome of each individual game need not be efficient. Moreover, the probability that the solution is efficient is bounded away form 0. But as the game gets larger, the magnitude of the inefficiency decreases to 0. We conclude that a solution of such games need not be efficient, but is asymptotically efficient.

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