ECN 416 - Game Theory and Economic Behavior Assignment

Assignment Help Game Theory

Reference no: EM132411583

ECN 416 - Game Theory and Economic Behavior Assignment, Department of Economics - Arizona State University, USA

Problem Set -

1. There is a murder committed in a house and the detective (player 1) suspects the butler (player 2) of the house and engages in evidence collection. However, evidence collection is a random process, and concrete evidence will be available to the detective only with probability 1/2. The butler knows the evidence generating process, but does not know whether the detective received evidence or not. The game proceeds as follows: The detective realizes if he has evidence or not, and then can choose his action, whether to Accuse the butler (A), or Bounce the case (B) and forget it. Once accused, the butler has two options: he can either Confess (C) or Deny (D). Payoffs are realized as follows: If the detective bounces the case then both players get 0 utils. If the detective accuses the butler, and the butler confesses, the detective gains 2 utils and the butler loses 2 utils. If the detective accuses the butler and the butler denies, then payoffs depend on the evidence: If the detective has no evidence then he loses face which is losing 4 utils, while the butler gains glory which gives him 4 utils. If, however, the detective has evidence then he is triumphant and gains 4 utils, while the butler is put in jail and loses 4 utils. Draw the extensive form game, and find the set of SPNE, pure or mixed.

2. For each of the game in attached file, find the set of Perfect Bayesian Equilibria (PBE), in pure strategies only.

Attachment:- Game Theory and Economic Behavior Assignment File.rar

Reference no: EM132411583

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