Browsing by Subject "Robust"

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    Robustness and Games with Linear Best Replies: Theory and Applications
    (2019-08) Marku, Keler
    This thesis consists of three chapters on games with linear best replies. In the first chapter we show how in the context of a common agency game, when principals seek robustness, then linearity in total output emerges as an equilibrium outcome. More specifically we consider a game between several principals and a common agent, where principals design contracts that are robust to misspecification of the agent's technology. The principals know a subset of the actions available to the agent, but other unknown actions could exist. Principals demand robustness and evaluate contracts on the worst-case performance over all possible actions of the agent. Despite the complexity of the game, we show that a pure strategy equilibrium always exists, by constructing a pseudo-potential for the game. Equilibrium contracts are linear in total output and imply that all players (the principals and the agent) receive a share of total output. The higher the share of total output accruing to the agent, the more efficient the outcome of the game. The crisp characterization of the equilibrium allows us to revisit the classical question of the efficiency of competitive outcomes relative to collusion among principals. We also consider a game where principals collude and offer a joint contract. The efficiency of the competitive outcome depends crucially on the ability of principals to offer side-payments to one another through the agent. In the second chapter we consider several applications of the framework introduced in the first chapter. Linearity allows for sharp predictions of the model in several contexts. The main application of the model in the first chapter is in analyzing the taxation of multinational firms where we study the effects of tax competition among countries. We show that a flat tax on domestic and foreign profits with a full deduction of foreign taxes provides the best worst-case guarantee for each country's revenues. Furthermore we consider a procurement auction setup, as well as an application of the model to private provision of public goods. In the third chapter we depart from the robustness framework and focus on the network structure of games with linear best replies. Games played on fixed networks capture a variety of economic settings including public goods, peer effects, and technology adaption. Bramoulle et al. (2014) analyze a large class of one dimensional linear best reply games and provides general results on how the network affect social and economic outcomes. In this paper we first provide an isomorphism between games with linear best replies and the threshold-linear recurrent networks used in neuroscience to study the encoding of memory patterns in the brain, connecting two seemingly unrelated literatures. Inspired by the isomorphism we extend games of linear best replies in understanding Lindahl equilibria and to games with multidimensional actions. In particular we show how Cournot competition among several firms leads to specialization in production. We show how the network structure of competition in demand for consumers shape the decision of firms in which goods to specialize.