Question
A man is stabbed in broad daylight by a criminal. This crime takes place in front of spectators. Each spectator gets a benefit of 16
A man is stabbed in broad daylight by a criminal.
This crime takes place in front of spectators. Each spectator gets a benefit of 16 if the crime is reported, which means that the perpetrator will be caught and justice will be served. However, it costs 8 for any spectator if he/she reports the crime because all witnesses who report a crime must appear in court and spend time during the trial. Suppose two spectators, Sandy and Jason, witness the crime from a safe distance. A) Is the diagram the correct normal form representation of the game?
B) If the table is correct, are the pure strategy Nash equilibria denoted by the payoffs {16,8} and {8,16}? C) If there is a pure strategy Nash equilibria, why would a player be incentivized to randomize in equilibrium? D) In computing for a mixed strategy Nash equilibrium, is it correct to say that the probability that the crime will be unreported is 25%? E) Compared to (D), is it safe to say that the probability that a crime will be unreported under pure strategy Nash equilibria is lower? F) In computing for a mixed strategy Nash equilibrium, is it correct to say that the sum of both player's payoffs is 16? G) Compared to (F), why is the total payoff for both players lower under a mixed strategy Nash equilibrium compared to each of the pure strategy Nash equilibria?
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