The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions

This work consists of a theoretical part and an experimental one. The first part provides a simple treatment of the celebrated von Neumann minimax theorem as formulated by Nikaid6 and Sion. It also discusses its relationships with fundamental theorems of convex analysis. The second part is about externality in sponsored search auctions. It shows that in these auctions, advertisers have externality effects on each other which influence their bidding behavior. It proposes Hal R.Varian model and shows how adding externality to this model will affect its properties. In order to have a better understanding of the interaction among advertisers in on-line auctions, it studies the structure of the Google advertisements networ.k and shows that it is a small-world scale-free network.

Scales, networks and uncertainty : an examination of environmental policy-making in Ontario

Through a case-study analysis of Ontario's ethanol policy, this thesis addresses a number of themes that are consequential to policy and policy-making: spatiality, democracy and uncertainty. First, I address the 'spatial debate' in Geography pertaining to the relevance and affordances of a 'scalar' versus a 'flat' ontoepistemology. I argue that policy is guided by prior arrangements, but is by no means inevitable or predetermined. As such, scale and network are pragmatic geographical concepts that can effectively address the issue of the spatiality of policy and policy-making. Second, I discuss the democratic nature of policy-making in Ontario through an examination of the spaces of engagement that facilitate deliberative democracy. I analyze to what extent these spaces fit into Ontario's environmental policy-making process, and to what extent they were used by various stakeholders. Last, I take seriously the fact that uncertainty and unavoidable injustice are central to policy, and examine the ways in which this uncertainty shaped the specifics of Ontario's ethanol policy. Ultimately, this thesis is an exercise in understanding sub-national environmental policy-making in Canada, with an emphasis on how policy-makers tackle the issues they are faced with in the context of environmental change, political-economic integration, local priorities, individual goals, and irreducible uncertainty.

A game-theoretic network formation model

We study the dynamics of a game-theoretic network formation model that yields large-scale small-world networks. So far, mostly stochastic frameworks have been utilized to explain the emergence of these networks. On the other hand, it is natural to seek for game-theoretic network formation models in which links are formed due to strategic behaviors of individuals, rather than based on probabilities. Inspired by Even-Dar and Kearns (2007), we consider a more realistic model in which the cost of establishing each link is dynamically determined during the course of the game. Moreover, players are allowed to put transfer payments on the formation of links. Also, they must pay a maintenance cost to sustain their direct links during the game. We show that there is a small diameter of at most 4 in the general set of equilibrium networks in our model. Unlike earlier model, not only the existence of equilibrium networks is guaranteed in our model, but also these networks coincide with the outcomes of pairwise Nash equilibrium in network formation. Furthermore, we provide a network formation simulation that generates small-world networks. We also analyze the impact of locating players in a hierarchical structure by constructing a strategic model, where a complete b-ary tree is the seed network.

Dynamics in large scale networks

In this thesis we study the properties of two large dynamic networks, the competition network of advertisers on the Google and Bing search engines and the dynamic network of friend relationships among avatars in the massively multiplayer online game (MMOG) Planetside 2. We are particularly interested in removal patterns in these networks. Our main finding is that in both of these networks the nodes which are most commonly removed are minor near isolated nodes. We also investigate the process of merging of two large networks using data captured during the merger of servers of Planetside 2. We found that the original network structures do not really merge but rather they get gradually replaced by newcomers not associated with the original structures. In the final part of the thesis we investigate the concept of motifs in the Barabási-Albert random graph. We establish some bounds on the number of motifs in this graph.