It is demonstrated that for certain markets where traders have constant elasticity of substitution utility (CES) functions, the existence of a price equilibrium can be determined in polynomial time. It is also shown that for a certain range of elasticity of substitution where the CES market does not satisfy gross subsitutability that price equilibira can be computed in polynomial time. It is also shown that for markets satisfying gross substitutability, equilibria can be computed in polynomial time even if the excess demand is a correspondence. On the experimental side, equilibrium computation algorithms from computer science without running time guarantees are shown to be competitive with software packages used in applied microeconomics.Simulations also lend support to the Nash equilibrium solution concept by showing that agents employing heuristics in a restricted form of Texas Holdem converge to an approximate equilibrium. Monte Carlo simulations also indicate the long run preponderance of skill over chance in Holdem tournaments. Abstract Approved: Thesis Supervisor To my wife Jennifer, my mother Patricia, my father Daniel, and my sister Julie for their many years of love and support ii I am especially grateful to my advisor, Dr. Kasturi Varadajan. Having come to Iowa without having taken a course in computer science, it was Kasturi who first introduced me to the study of algorithms through his excellent course and sparked my first real interest in theoretical computer science. Kasturi was always generous with both time and ideas. This was critical as time after time, many days of confusion would be cleared upon his blackboard. This work would not have been possible iv without his kind advice, erudition, encouragement and, not least, his patience. And for that, I will remain grateful. v ABSTRACT It is demonstrated that for certain markets where traders have constant elasticity of substitution utility (CES) functions, the existence of a price equilibrium can be determined in polynomial time. It is also shown that for a certain range of elasticity of substitution where the CES market does not satisfy gross subsitutability that price equilibira can be computed in polynomial time. It is also shown that for markets satisfying gross substitutability, equilibria can be computed in polynomial time even if the excess demand is a correspondence. On the experimental side, equilibrium computation algorithms from computer science without running time guarantees areshown to be competitive with software packages used in applied microeconomics.Simulations also lend support to the Nash equilibrium solution concept by showing that agents employing heuristics in a restricted form of Texas Holdem converge to an approximate equilibrium. Monte Carlo simulations also indicate the long run preponderance of skill over chance in Holdem tournaments.vi Proof: Both σ and σ 0 are in B, so it must be the case that for each j, |σ j − σ 0j | < 1.Therefore, we only need to bound each component of ▽g(σ 0 ) −ᾱ by ǫ ′ 4n . One can see the formula...
