slides-SIT3-article - F. Koessler / November 22, 2007...

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Unformatted text preview: F. Koessler / November 22, 2007 Strategic Information Transmission: Persuasion Games 1/ Strategic Information Transmission: Persuasion Games Outline (November 22, 2007) • The revelation principle revisited • Hard evidence and information certification in games • Geometric Characterization of Nash Equilibrium Outcomes • Sceptical strategies and worst case inferences in monotonic relationships • Persuasion with type-dependent biases (Seidmann and Winter, 1997) • Long persuasion games 2/ Verifiable Information and Certification Some private information like – individual preferences – tastes – ideas – intentions – the quality of a project – the cost of effort are usually non-certifiable / non-provable, and cannot be objectively measured by a third party On the other hand, – the health or income of an individual – the debt of a firm – the history of a car maintenance – a doctor’s degree may be directly certified, or authenticated by a third party F. Koessler / November 22, 2007 Strategic Information Transmission: Persuasion Games 3/ How does one person make another believe something ? The answer depends importantly on the factual question, “Is it true ?” It is easier to prove the truth of something that is true than of something false. To prove the truth about our health we can call on a reputable doctor ; to prove the truth about our costs or income we may let the person look at books that have been audited by a reputable firm or the Bureau of Internal Revenue. But to persuade him of something false we may have no such convincing evidence. Schelling, 1960, p. 23. 4/ F. Koessler / November 22, 2007 Strategic Information Transmission: Persuasion Games 5/ The information that can be revealed by a player may depend on his actual state of knowledge ⇒ M i ( k ) : set of messages of player i when his type is k ☞ Physical proofs (“hard information”) • Documents • Observable characteristics of a product • Endowments, costs • Income tax return • Claims about health conditions ☞ Legal constraints • Revelation of accounting data • Advertisement, labels, guarantee of quality, . . . ☞ Psychological constraints • Honesty / Observable emotions (blushing, stress . . . ) 6/ The Revelation Principle Revisited Set of possible announcements for an agent of type θ : M ( θ ) ⊆ Θ , with θ ∈ M ( θ ) How an optimal mechanism and the revelation principle is affected by this new feature? ➥ Green and Laffont (1986) Utility of the agent when his type is θ and the decision is x ∈ X : u ( x,θ ) Direct mechanism : x : Θ → X (More generally, a mechanism is x : M → X , where M is any set of messages) F. Koessler / November 22, 2007 Strategic Information Transmission: Persuasion Games 7/ An allocation , or social choice function y : Θ → X is directly M-implementable if there exists a direct mechanism x : Θ → X such that x ( m ∗ ( θ )) = y ( θ ) where m ∗ is the optimal reporting strategy of the agent, i.e.,is the optimal reporting strategy of the agent, i....
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slides-SIT3-article - F. Koessler / November 22, 2007...

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