Lecture_5b_(Communications)(1).pdf - HE3002 Game Theory Lecture 5b Dynamic Games of Incomplete Information(Application of PBE Communication and Cheap

Lecture_5b_(Communications)(1).pdf - HE3002 Game Theory...

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HE3002: Game Theory Lecture 5b: Dynamic Games of Incomplete Information (Application of PBE: Communication and Cheap Talk Games) (Semester 1, AY 2019/20) 1 / 40
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Talk is cheap When you know a salesman is trying to sell you a product, how much do you believe in his words that the product is good? When you know your broker earns a commission each time you buy a stock, how much do you believe in his words that the stock is worth buying? When you know your doctor earns each time you come in for a consultation, how much do you believe in his words that it is in your best interest to come back for check-up every week? 2 / 40
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Talk is cheap Consider the following scenario: An employer faces a worker of unknown ability θ , which can be θ = H or θ = L , where H > L > 0. The ability is known to the worker though. Think of θ as the profit that the worker can generate for the employer. Naturally, employers are willing to pay H workers higher than L workers. Suppose you are the worker: I When the employer asks you what your θ is, how would you reply? I Do you think he will believe your reply? We solve this problem in the next lecture. For now... 3 / 40
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Can Cheap-talk Have Any Impact? However, the message-senders often “know the world better than you”, so it might be advisable to listen afterall. I The salesman probably knows how good the product is better than you. I Your broker probably has superior information about the stock market than you. I Your doctor probably knows your health condition better than you. I You know your own θ . The question is: How much value do you place on their words? 4 / 40
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Communication Game We model communication between two people: A Sender (he) and a Receiver (she). I Sender has private information about the state of the world that both players are interested in. I Sender can costlessly send a message to the Receiver (hence, cheap talk). I Receiver, upon receiving the message, decides “how much to believe” the Sender. I Receiver then takes an action that affects the payoff of both players. Note that the only way Sender can influence his own payoff is via the message he sends to the Receiver to “persuade” her to take some particular action. This is a dynamic Bayesian game. 5 / 40
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Communication Game A communication game can be formally modeled as follows: There are two players: A Sender (S, he) and a Receiver (R, she). At t = 0, Nature decides a true state of the world θ Θ and privately informs S. I R does not know θ . At t = 1, S sends a message m M to R: I m need not be a “message”. It could be an action such as raising the right hand or left hand. I The crucial part is it must be costless for S to do so. At t = 2, R, upon observing m , takes an action a A . I The choice of a affects the payoff of both players, and it can be dependent on the true state θ .
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