Hello.

I have a question how does it solve?

Consider a jury voting model, where a defendant is guilty (G) with probability >1/2 and innocent (I) with probability 1. Each juror has a payoff of 1 when the correct outcome is realised, (acquitting an innocent defendant and convicting a guilty defendant) while acquitting a guilty defendant or convicting an innocent defendant leads to a utility of 0. The defendant is convicted if and only if all jurors vote for conviction. There are two juries. Each one gets a private signal about the defendant {g, n}, which corresponds to a guilty or not guilty signal. The signal is accurate with probabilityp >1/2. (Meaning,P(=g|G) =P(=n|I) =pandP(=n|G) =P(=g|I) = 1p.

a. First, show that it is not a Bayesian Nash Equilibrium for both players to convict upon guilty signal and acquit upon innocent signal.

b. Now, show the condition under which it is a Bayesian Nash Equilibrium for both players to always convict regardless of the signal?