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Recent applications of game theory to the oligopoly have characterized the nature of the competition in an industry by examining payoff matrices and the strategies chosen by the players. In this study, a game-theoretic model of an oligopoly is developed, wherein the marketing-mix decisions made by the participating firms are represented as alternate strategic options. Econometric methods are employed to estimate the payoffs in the game matrices. Issues in model operationalization are discussed; then the model is applied to two real situations. In each case, the game matrix derived is used to describe the competitive nature of the industry (by examining the strategic decisions made over time), to evaluate the strategies chosen, given the intentions of the firms, and to recommend desirable strategies for the future. / La théorie des jeux, appliquée à l’étude des oligopoles, permet de caractériser la nature de la concurrence industrielle grâce à l’examen des sommes à gagner et des stratégies suivies par les joueurs. Cette étude développe un modèle d’oligopole basé sur la théorie des jeux et dans lequel les décisions de marketing prises par les participants sont représentées par des choix stratégiques. Lps sommes à gagner sont estimées par des methodes économètriques. Le modèle est operationnel et appliqué à deux situations réelles. Dans chaque cas, on parvient à décrire la nature de la concurrence dans l’industrie; à evaluer les stratégies passées; et à recommander de meilleures stratégies pour l’avenir.

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This thesis develops a framework to investigate and design novel optimization methods for two important problems: computational advertising (particularly, sponsored search) and wind farm turbine-layout planning. Whereas very different in specifics, both problems share some common abstractions. The existing solution in sponsored search is based on a greedy pay-per-click auction and is suitable only for advertisers seeking a direct response. It does not apply to advertisers who target certain numbers of clicks in a predefined time period. To address this new challenge, we introduce a unified optimization framework combining pay-per-click auctions and guaranteed delivery in sponsored search. Our new method maximizes the revenue of the search engine, targets a guaranteed number of ad clicks per campaign for advertisers willing to pay a premium, and enables keyword auctions for all others. Results combining revenue to the search engine and click rates for the advertisers show superior performance over strong baselines. The proposed framework is based on linear programming with delayed column generation for computational tractability at scale. We design a game theoretic approach to optimize the strategy for individual advertisers, i.e. to optimize their choices between auctions and guaranteed delivery, and analyze the behavior of the new market formed by our framework. Specifically, we introduce a new method for computing the approximate Nash equilibrium where an exact computation would prove computationally intractable. We rely on approximations of complex utility functions, a combination of simulated annealing and integer linear programming as our principled approach. Wind farm layout optimization is the selection of optimal locations for placement of large wind turbines taking into account factors such as topographical features, prevalent but non-constant wind direction and turbine-wake interference. Existing approaches are deficient in their inability to consider long distance turbine interference, changing wind speed and direction and multiple types of wind turbines in optimization. The dissertation develops an optimization framework based on a scalable divided-and-conquer strategy that enables scalability to real-world wind farm scales taking into account the aforementioned complexities in the optimization process. Essentially the process optimizes in a hierarchical manner at different levels of granularity. This hierarchical decomposition approach to optimization is common to both search-advertisement and wind-farm layout challenges.

This paper modifies the two-player Rubinstein bargaining game to include a third player. Analyzing the game through a dynamic model provides parametric changes that cause a longer negotiation period and fewer concessions from each player’s initial demand upon an agreement. The introduction of a free rider problem and limited computational abilities cause these consequences with the addition of a third player. The free rider problem discourages players from conceding their demands and since players have limited strategic abilities, the additional player requires more effort for players to understand the game and thus more time to understand the environment enough to reach an agreement.

The major objective of this thesis is to study optimization problems in finance. Most of the effort is directed towards studying the impact of transaction costs in those problems. In addition, we study dynamic meanvariance asset allocation problems. Stochastic HJB equations, Pontryagin Maximum Principle and perturbation analysis are the major mathematical techniques used. In Chapter 1, we introduce the background literature. Following that, we use the Pontryagin Maximum Principle to tackle the problem of dynamic mean-variance asset allocation and rediscover the doubling strategy. In Chapter 2, we present one of the major results of this thesis. In this chapter, we study a financial optimization problem based on a market model without transaction costs first. Then we study the equivalent problem based on a market model with transaction costs. We find that there is a relationship between these two solutions. Using this relationship, we can obtain the solution of one when we have the solution of another. In Chapter 3, we generalize the results of chapter 2. In Chapter 4, we use Pontryagin Maximum Principle to study the problem limit of the no-transaction region when transaction costs tend to 0. We find that the limit is the no-transaction cost solution.

Multi-asset credit derivatives trade in huge volumes, yet no models exist that are capable of properly accounting for the spread behaviour of dependent companies. In this thesis we consider new ways of incorporating a richer and more realistic dependence structure into multi-firm models. We focus on the structural framework in which firm value is modelled as a geometric Brownian motion, with default as the first hitting time of an exponential default threshold. Specification of a dependence structure consisting of a common driving influence and firm-specific inter-company ties allows for both default causality and default asymmetry and we incorporate default contagion in the first passage framework for the first time. Building on the work by Zhou (2001a), we propose an analytical model for corporate bond yields in the presence of default contagion and two-firm credit default swap baskets. We derive closed-form solutions for credit spreads, and results clearly highlight the importance of dependence assumptions. Extending this framework numerically, we calculate CDS spreads for baskets of three firms with a wide variety of credit dependence specifications. We examine the impact of firm value correlation and credit contagion for symmetric and asymmetric baskets, and incorporate contagion that has a declining impact over time.

How should we model learning behaviour in economic agents? This thesis addresses this question in two distinct ways. In the first set of chapters the assumption is that agents learn through the observation of others. They use Bayesian updating which together with specific informational assumptions can generate the problem known as herding with the potential for significant welfare losses. In the final set of chapters the agent is instead modelled as learning by example. Here the agent cannot learn by observing others, but has a pool of experience to fall back on. This allows us to examine how an economic agent will perform if he sees a particular economic situation (or game) for the first time, but has experience of playing related games. The tool used to capture the notion of learning through example is a neural network. Throughout the thesis the central theme is that economic agents will naturally use as much information as they can to help them make decisions. In many cases this should mean they take into consideration others' actions or their own experiences in similar but non-identical situations. Learning throughout the thesis will be rational or bounded-rational in the sense that either the best possible way to learn will be utilized (so players achieve full rational play, for example, through Bayesian updating), or a suitable local error-minimizing algorithm will be developed (for example, a rule of thumb which optimizes play in a subclass of games, but not in the overall set of possible games). Several themes permeate the whole thesis, including the scope for firms or planners to manipulate the information that is used by agents for their own ends, the role of rules of thumb, and the realism of current theories of learning in economics.

Pricing single asset American options is a hard problem in mathematical finance. There are no closed form solutions available (apart from in the case of the perpetual option), so many approximations and numerical techniques have been developed. Pricing multi–asset (high dimensional) American options is still more difficult. We extend the method proposed theoretically by Glasserman and Yu (2004) by employing regression basis functions that are martingales under geometric Brownian motion. This results in more accurate Monte Carlo simulations, and computationally cheap lower and upper bounds to the American option price. We have implemented these models in QuantLib, the open–source derivatives pricing library. The code for many of the models discussed in this thesis can be downloaded from quantlib.org as part of a practical pricing and risk management library. We propose a new type of multi–asset option, the “Radial Barrier Option” for which we find analytic solutions. This is a barrier style option that pays out when a barrier, which is a function of the assets and their correlations, is hit. This is a useful benchmark test case for Monte Carlo simulations and may be of use in approximating multi–asset American options. We use Laplace transforms in this analysis which can be applied to give analytic results for the hitting times of Bessel processes. We investigate the asymptotic solution of the single asset Black–Scholes–Merton equation in the case of low volatility. This analysis explains the success of some American option approximations, and has the potential to be extended to basket options.

This thesis is divided into three parts; an intensity based network model of firm default, an agent based network model of firm default, and an agent based model of feedback effects from dynamic hedging. The common theme among all three parts is the application of ideas from both physics and mathematics to the solution of problems motivated by the financial markets. Less broadly, in the first two parts, the common themes are credit markets, networks, and dependent defaults. Part one tackles the problem of default dependence from a probabilistic perspective, modeling the default of companies as generalised Poisson processes, with the default dependence structure given by a network. We present a mathematical framework to solve a generalised version of the Jarrow Yu model of looping defaults [27] and study the relationship between network structure and the resilience of a network of firms to default events. Using this model we then show how to price simple multi-name credit products such as kth to default baskets. Part two again considers dependent defaults, but here the network is dynamic and firms are modelled as simple agents, defined by strategies, whose interactions determine a network of trading links. Using our agent based network model of firm default we study network structure and their degree distributions, firm lifetimes, and look for evidence of agent learning and default clustering. We then study the effect of default on a network of firms and the response of remaining firms to that default event. Part three considers a relatively more established agent based framework, called the Minority Game. We first describe in detail the Minority Game and discuss its suitability as a market model. We then show how it may be applied to modelling the actions of traders delta hedging a short option position. We show that for a variety of option positions, in a sufficiently illiquid market feedback effects arise from the actions of the traders as their trades impact upon the underlying market.