I propose the following game: I flip a coin, and while it is in the air, you call either heads or tails. If you call the coin correctly, you get to keep the coin. Suppose that you know that the coin always comes up heads. What is the best strategy for you to pursue? _____________
(a) Suppose that the coin is unbalanced and comes up heads 80% of the time and tails 20% of the time. Now what is your best strategy?
(b) What if the coin comes up heads 50% of the time and tails 50% of the time? What is your best strategy?
(c) Now, suppose that I am able to choose the type of coin that I will toss (where a coin’s type is the probability that it comes up heads), and that you will know my choice. What type of coin should I choose to minimize my losses?
(d) What is the Nash mixed strategy equilibrium for this game?