This thesis consists of five essays on non-Walrasian economics. There are two essays on rational conjectural equilibrium, RCE, two on repeated games and one on general equilibrium with price-making firms and increasing returns to scale. The first two essays consider rational conjectural equilibrium from a game theoretic perspective. It is shown that (i) in general there is a continuum of RCE. (ii) Some interesting price behaviour, such as kinked demand behaviour and mark-up pricing can be supported as a RCE in a partial equilibrium model. (iii) Conjectural models can be regarded as a static representation of either a repeated game story with adjustment cost, or an instantaneous response repeated game, and that the rationality condition (in the 'correctness' sense) on conjectures amounts to sub-game perfectness in the super-game. In the third essay the solutions to repeated games with bounded memory are considered. It is shown that the Folk Theorem of repeated games (multiplicity of equilibria) can be extended to repeated games with one-period memory either if the action space of each player at each stage of the repeated game contains 'many elements' or if there is uncertainty. In the fourth essay the solutions to anonymous repeated game with a large but finite number of players are considered. In the fifth essay a General Equilibrium model with oligopolistic firms is developed (the model is based on my results in earlier chapters). Each oligopolistic firm is assumed to perceive (correctly) a kinked demand curve. I shall prove the existence of an equilibrium for such an economy without excluding increasing returns to scale or assuming concave revenue functions for the oligopolists.

The mathematical modelling of a market, and the proof of existence of equilibria have been of central importance in mathematical economics. Since the existence proof is non-constructive in general, a natural question is if computation of equilibria can be done efficiently. Moreover, the emergence of Internet and e-commerce has given rise to new markets that have completely changed the traditional notions. Add to this the pervasiveness of computing resources, and an algorithmic theory of market equilibrium becomes highly desirable. The goal of this thesis is to provide polynomial time algorithms for various market models. Two basic market models are the Fisher model: one in which there is a demarcation between buyers and sellers, buyers are interested in the goods that the sellers possess, and sellers are only interested in the money that the buyers have; and the Arrow-Debreu model: everyone has an endowment of goods, and wants to exchange them for other goods. We give the first polynomial time algorithm for exactly computing an equilibrium in the Fisher model with linear utilities. We also show that the basic ideas in this algorithm can be extended to give a strongly polynomial time approximation scheme in the Arrow-Debreu model. We also give several existential, algorithmic and structural results for new market models: - the *spending constraint* utilities (defined by Vazirani) that captures the "diminishing returns" property while generalizing the algorithm for the linear case. - the capacity allocation market (defined by Kelly), motivated by the study of fairness and stability of the Transmission Control Protocol (TCP) for the Internet, and more generally the class of Eisenberg-Gale (EG) markets (defined by Jain and Vazirani). In addition, we consider the adwords market on search engines and show that some of these models are a natural fit in this setting. Finally, this line of research has given insights into the fundamental techniques in algorithm design. The primal-dual schema has been a great success in combinatorial optimization and approximation algorithms. Our algorithms use this paradigm in the enhanced setting of Karush-Kuhn-Tucker (KKT) conditions and convex programs.

We present in this thesis three distinct models in Financial Economics. In the first chapter we present a pure exchange economy model with collateral constraints in the spirit of Kiyotaki and Moore (1997). As a first result in this chapter we prove the existence of an equilibrium for this type of economies. We show that in this type of models bubbles can exist and provide a bubble example in which the asset containing the bubble pays positive dividends. We also show for the case of high interest rates the equivalence between this type of models and the Arrow-Debreu market structure. In the second chapter we present a model with limited commitment and one-side exclusion from financial markets in case of default. For this type of models we prove a no-trade theorem in the spirit of Bulow and Rogoff (1989). This is done for an economy with and without bounded investment in a productive activity. The third chapter presents a 2 period economy with complete markets, and 250 states of the world and assets. For this economies we generate a sequence of observed returns, and we show that a market proxy containing only 80% of the assets in the economy provides similar results as the true market portfolio when estimating the CAPM. We also show that for the examples we present a vast amount of observations is required in order to reject the CAPM. This raises the question what the driving force behind the bad empirical performance of the CAPM is.

The aim of this study is to compare the performance of the four interest rate models (Vasicek Model, Cox Ingersoll Ross Model, Ho Lee Model and Black Der- man Toy Model) that are commonly used in pricing zero coupon bond options. In this study, 1{5 years US Treasury Bond daily data between the dates June 1, 1976 and December 31, 2007 are used. By using the four interest rate models, estimated option prices are compared with the real observed prices for the begin- ing work days of each months of the years 2004 and 2005. The models are then evaluated according to the sum of squared errors. Option prices are found by constructing interest rate trees for the binomial models based on Ho Lee Model and Black Derman Toy Model and by estimating the parameters for the Vasicek and the Cox Ingersoll Ross Models.