Chapter one focuses on optimal pricing in markets of consumption chains. These are markets in which one good is necessary for access to further consumption goods. I analyse optimal pricing for different market structures, focusing on the case of an integrated monopolist and the case of separate firms being in competition across markets, but not within markets. I then compare the outcomes of different market structures using basic welfare measures. I show that, compared to the first best allocation, the allocation implemented under the integrated monopolist tends to have significantly lower consumer surplus and larger producer surplus. Aggregate welfare is surprisingly not much smaller under the integrated firm when compared to a welfare maximising allocation. In some settings the integrated monopolist even implements a welfare maximising allocation. The paper explains and highlights how these results depend largely on which assumptions are made about the information available to consumers. The second chapter contributes towards the existing literatures on lobbying and on media bias by combining and extending features of both. It aims to analyse optimal slanting policies of interest or media groups and their effect on the distribution of public opinion and its evolution over time by introducing an intertemporal model of grassroots lobbying or media bias. I also allow for more general results than existing models by making fewer distributive assumptions and by allowing for further incentives of agents. In the chapter I combine demand and supply side models for bias. A main focus lies on how optimal slanting, the distribution of public opinion and its evolution over time depend on competition. The chapter aims to examine in which circumstances competition in the media market or the existence of multiple rival lobby groups can be detrimental. It shows how this can be the case because competition can create an incentive to split the public up and cater only to the own market. This can lead to a loss of the middle ground and increased dispersion of public opinion. The third chapter aims to extend the existing literature on the (in)efficiencies of voluntary contribution mechanisms for public goods. The existing body of research tries to analyse how group size affects the outcomes of such mechanisms asymptotically, while I also focus on results for given group sizes and the effect of the level of group heterogeneity in combination with group size. Agents are ex post heterogeneous in the existing literature; I also allow for them to be heterogeneous ex ante. This means that agents do not only have different valuations for the public good ex post, but different agents are also perceived differently by other agents ex ante. I show that a form of price discrimination can be used when agents are ex ante heterogeneous. Not using such price discrimination is shown to be costly in terms of efficiency in small groups. Small heterogeneous groups are outperformed by their homogeneous counterparts when price discrimination is not applied. However, this inefficiency in small groups can be eliminated by using price discrimination. The use of price discrimination becomes irrelevant in large groups and heterogeneous groups always outperform their homogeneous counterparts, whether price discrimination is used or not.

We develop and analyze a class of CAC algorithms for resource management in wireless networks with the goal not only to satisfy QoS constraints, but also to maximize a value or reward objective function specified by the system. We demonstrate through analytical modeling and simulation validation that the CAC algorithms developed in this research for resource management can greatly improve the system reward obtainable with QoS guarantees, when compared with existing CAC algorithms designed for QoS satisfaction only. We design hybrid partitioning-threshold, spillover and elastic CAC algorithms based on the design techniques of partitioning, setting thresholds and probabilistic call acceptance to use channel resources for servicing distinct QoS classes. For each CAC algorithm developed, we identify optimal resource management policies in terms of partitioning or threshold settings to use channel resources. By comparing these CAC algorithms head-to-head under identical conditions, we determine the best algorithm to be used at runtime to maximize system reward with QoS guarantees for servicing multiple service classes in wireless networks. We study solution correctness, solution optimality and solution efficiency of the class of CAC algorithms developed. We ensure solution optimality by comparing optimal solutions achieved with those obtained by ideal CAC algorithms via exhaustive search. We study solution efficiency properties by performing complexity analyses and ensure solution correctness by simulation validation based on real human mobility data. Further, we analyze the tradeoff between solution optimality vs. solution efficiency and suggest the best CAC algorithm used to best tradeoff solution optimality for solution efficiency, or vice versa, to satisfy the system's solution requirements. Moreover, we develop design principles that remain applicable despite rapidly evolving wireless network technologies since they can be generalized to deal with management of 'resources' (e.g., wireless channel bandwidth), 'cells' (e.g., cellular networks), "connections" (e.g., service calls with QoS constraints), and "reward optimization" (e.g., revenue optimization in optimal pricing determination) for future wireless service networks. To apply the CAC algorithms developed, we propose an application framework consisting of three stages: workload characterization, call admission control, and application deployment. We demonstrate the applicability with the optimal pricing determination application and the intelligent switch routing application. / Ph. D.

In this thesis, we consider stochastic systems which arise in different real-world application contexts. The first problem we consider is based on product adoption and pricing. A monopolist selling a product has to appropriately price the product over time in order to maximize the aggregated profit. The demand for a product is uncertain and is influenced by a number of factors, some of which are price, advertising, and product technology. We study the influence of price on the demand of a product and also how demand affects future prices. Our approach involves mathematically modelling the variation in demand as a function of price and current sales. We present a simulation-based algorithm for computing the optimal price path of a product for a given period of time. The algorithm we propose uses a smoothed-functional based performance gradient descent method to find a price sequence which maximizes the total profit over a planning horizon. The second system we consider is in the domain of sensor networks. A sensor network is a collection of autonomous nodes, each of which senses the environment. Sensor nodes use energy for sensing and communication related tasks. We consider the problem of finding optimal energy sharing policies that maximize the network performance of a system comprising of multiple sensor nodes and a single energy harvesting(EH) source. Nodes periodically sense a random field and generate data, which is stored in their respective data queues. The EH source harnesses energy from ambient energy sources and the generated energy is stored in a buffer. The nodes require energy for transmission of data and and they receive the energy for this purpose from the EH source. There is a need for efficiently sharing the stored energy in the EH source among the nodes in the system, in order to minimize average delay of data transmission over the long run. We formulate this problem in the framework of average cost infinite-horizon Markov Decision Processes[3],[7]and provide algorithms for the same.

This thesis analyzes the optimal strategies of rational agents in incomplete financial markets. The incompleteness may arise from the stochastic volatility of stock prices, in which case we study the optimal pricing and hedging strategies of an option trader. We introduce a new concept that we call the relative indifference price, which is the price at which a trader is indifferent to trade in an additional option, given that he is currently holding and dynamically hedging a portfolio of options. We find that the appropriate volatility risk premium depends on the trader's risk aversion coeffcient and his portfolio position before selling or buying the additional option. More generally, the incompleteness of the market may arise from both the drift and volatility of the stock being driven by a correlated factor. In this setting, we study the optimal consumption and investment policies of CARA, conservative CRRA and aggressive CRRA agents. In particular, we provide interpretations of the non-myopic investment in terms of martingale measures and the risk monitoring strategy of a path-dependent option. / text

This dissertation consists of three chapters on the topic of differential games and resource economics. The first chapter extends the envelope theorem to the class of discounted infinite horizon differential games that posses locally differentiable Nash equilibria. The theorems cover both the open-loop and feedback information structures, and are applied to a simple analytically solvable linear-quadratic game. The results show that the conventional interpretation of the costate variable as the shadow value of the state variable along the equilibrium path is only valid for feedback Nash equilibria, but not for open-loop Nash equilibria. The specific linear-quadratic structure provides some extra insights on the theorem. For example, the costate variable is shown to uniformly overestimate the shadow value of the state variable in the open-loop case, but the growth rate of the costate variable are the same as the shadow value under open-loop and feedback information structures. Chapter two investigates the qualitative properties of symmetric open-loop Nash equilibria for a ubiquitous class of discounted infinite horizon differential games. The results show that the specific functional forms and the value of parameters used in the game are crucial in determining the local asymptotic stability of steady state, the steady state comparative statics, and the local comparative dynamics. Several sufficient conditions are provided to identify a local saddle point type of steady state. An important steady state policy implication from the model is that functional forms and parameter values are not only quantitatively important to differentiate policy tools, but they are also qualitatively important. Chapter three shifts the interests to the lottery mechanism for rationing public resources. It characterizes the optimal pricing strategies of lotteries for a welfare-maximization agency. The optimal prices are shown to be positive for a wide range of individual private value distributions, suggesting that the sub-optimal pricing may result in a significant efficiency loss and that the earlier studies under zero-pricing may need to be re-examined. In addition, I identify the revenue and welfare equivalency propositions across lottery institutions. Finally, the numerical simulations strongly support the findings.