We study a message passing network where nodes keep a numeric attitude toward a subject. Messages are created by a message factory and each is sent to a random seed-node, which then gets eventually propagated in the network. Each message has some information about the subject, which is interpreted by the receiving node based on its features. Hence, the same message could be interpreted quite differently by two different nodes. Once a message is interpreted, the attitude of the node toward the subject is updated. In this setting, the thesis is that an external agent can influence (in a desired way) the average attitude of the network, by sending the messages to specific nodes (rather than sending them randomly) based on the message content. We call this agent a leader which its goal is to minimize (maximize) the average attitude of the network, and its actions are choosing one of the seed-nodes for a given message. The leader does not have any information about the nodes in advance, instead, it eventually learns the interests of the seed-nodes through sending messages and receiving the feedback of the network. We formulate this as a contextual bandit problem and study the effectiveness of a leader in different network configurations. Moreover, we study the case that there are two adversarial leaders, and present different policies and evaluate their effectiveness. Finally, we study the leader's performance when there are dynamic changes in the nodes features and network's topology.

This dissertation studies the competitive dynamics between two non-identical providers competing for customers seeking low-cost and quick service. Providers have generic delay functions where, asdemand received by each provider grows, so does delay in processing customers' requests. Given a pricing or capacity decision by each provider, customers determine the proportion of demand to send to each provider by minimizing generalized cost (monetary cost plus delaycost). This problem is formulated as a bilevel optimization, with providers competing at the upper level subject to the customers' decisions at the lower level. Occurrence of Nash equilibria between the providers is studied.First studied is the providers' problem of making decisions on capacities, while competing for a single customer. Conditions are derived for one provider to claim the entire market share, and for the occurrence of an equilibrium where both providers receive positivedemand. A numerical example in which no equilibrium exists is presented. Both the inelastic and elastic demand cases are studied for this scenario. In a second model, providers make pricing decisions with capacity fixed. Under some assumptions, it is shownthat a Nash equilibrium between providers always exists and a numerical example is presented. These models are then combined, in which providers make capacity decisions where prices equilibrate based on the results from the second model.Two competing customers with demand for a homogeneous product are then introduced, where providers choose prices as they compete for customers. This model is extended to an application along a highway corridor with a high-occupancy/toll (HOT) lane in parallel with a free road and transit line. A government agency chooses the transit service frequency while a private toll operator competes by choosing a toll to charge single-occupancy vehicles who wish to use the HOT lane.This scenario is also modeled as a bilevel program. For the lower level, a new dynamic equilibration process where homogeneous users make mode choice decisions based on previous generalized costs ofusing a particular mode is developed. Two numerical examples are presented showing a unique Nash equilibrium between the providers and an example in which multiple equilibria exist.