Bayesian Games

12.10 Purification: Consider the perturbed Matching Pennies game described in Section 12.5 and show that the Bayesian Nash equilibrium identified is the unique Bayesian Nash equilibrium. (Hint: Some insights can be gained by looking at the solution to the study group example in Section 12.2.2.) 12.5 Mixed Strategies Revisited: Harsanyi's Interpretation In particular imagine that the payoffs are given by this "perturbed" Matching Pennies game: Player 2 H T H 1+ 81, -1+ 82 -1+81, 1 Player 1 T -1, 1 + 82 1, - 1 and imagine that both &, and &2 are independent and uniformly distributed on the interval [-8, 8] for some small & > 0. This means that if &; > 0 is realized then player i has a strict preference for choosing H over T when he believes his opponent is choosing H with probability 5, and similarly, if &;