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**1 - 2**of**2**### Algorithmic Bayesian Persuasion

, 2015

"... We consider the Bayesian Persuasion problem, as formalized by Kamenica and Gentzkow [27], from an algorithmic perspective in the presence of high dimensional and combinatorial uncer-tainty. Specifically, one player (the receiver) must take one of a number of actions with a-priori unknown payoff; ano ..."

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We consider the Bayesian Persuasion problem, as formalized by Kamenica and Gentzkow [27], from an algorithmic perspective in the presence of high dimensional and combinatorial uncer-tainty. Specifically, one player (the receiver) must take one of a number of actions with a-priori unknown payoff; another player (the sender) is privy to additional information regarding the payoffs of the various actions for both players. The sender can commit to revealing a noisy signal regarding the realization of the payoffs of various actions, and would like to do so as to maximize her own payoff in expectation assuming that the receiver rationally acts to maximize his own payoff. This models a number of natural strategic interactions, in domains as diverse as e-commerce, advertising, politics, law, security, finance, and others. When the payoffs of various actions follow a joint distribution (the common prior), the sender’s problem is nontrivial, and its complexity depends on the representation of the prior. Assuming a Bayesian receiver, we study the sender’s problem with an algorithmic and ap-proximation lens. We show two results for the case in which the payoffs of different actions are i.i.d and given explicitly: a polynomial-time (exact) algorithmic solution, and a “simple”

### Approved: S. Viswanathan, Supervisor

, 2015

"... In my first chapter, I present a model in which sellers can signal the quality of an asset both by retaining a fraction of the asset and by choosing the liquidity of the market in which they search for buyers. Although these signals may seem interchangeable, I present two settings which show they ar ..."

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In my first chapter, I present a model in which sellers can signal the quality of an asset both by retaining a fraction of the asset and by choosing the liquidity of the market in which they search for buyers. Although these signals may seem interchangeable, I present two settings which show they are not. In the first setting, sellers have private information regarding only asset quality, and I show that liquidity dominates retention as a signal in equilibrium. In the second setting, both asset quality and seller impatience are privately known, and I show that both retention and liquidity operate simultaneously to fully separate the two dimensions of private information. Contrary to received theory, the fully separating equilibrium of the second setting may contain regions where market liquidity is increasing in asset quality. Finally, I show that if sellers design an asset-backed security before receiving private information regarding its quality, then the optimality of standard debt is robust to the paper’s various settings. In my second chapter, I explore the question of how informative bank stress