Models of Persuasion

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I study several aspects of a game-theoretic model of persuasion. A speaker attempts to persuade a listener to take an action which is highly ranked by the speaker. The listener knows the speaker's preference but is uncertain about what the speaker can say. The listener can commit to a persuasion rule, which is a response to the speaker's messages. Chapter 1 provides an introduction. Chapter 2 studies conditions under which optimal persuasion rules are deterministic and credible, extending results of Glazer and Rubinstein (2006) from two to many actions. Chapter 3 studies the lattice theoretic structure underlying the persuasion problem. I study implementable outcome functions (i.e., mappings from types to actions induced by some persuasion rule). Families of implementable outcome functions which can arise in some persuasion problem correspond to interior systems on the set of types, a notion from lattice theory. This leads to a characterization of messages as being essential or redundant. Chapter 4 studies the additional structure which imposed by the assumption that the speaker does not face time, attention, or other similar communication constraints. The absence of such constraints is captured by the notion of normality of Bull and Watson (2006), and related to the nested range condition of Green and Laffont (1986). Under normality, the representation in terms of interior systems reduces to one in terms of quasi-orders. The main result of Chapter 5 is that in the finite case, the listener's utility function is guaranteed to be a modular function of the set of implementable outcome functions exactly when normality holds; oherwise, the listener's utility function may not be quasisupermodular. It follows that under normality, all messages become more persuasive as the interests of the speaker and listener become more aligned, and when normality fails, one can always find a counter-example. Likewise, under normality, there always exists a symmetric optimal rule, whereas when it fails, examples in which all optimal rules are asymmetric are found. Chapter 6 studies an integer programming formulation of the problem

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  • 05/30/2018
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