Consider the following game. Player one flips a coin, and while it is in the air, player two calls out either heads or tails. If the side of the coin that player two called out lands facing upwards, then player one gives him one dollar. If the side of the coin that player two did not call out lands facing upwards, then player two gives one dollar to player one. Assume that player two is risk-neutral (which means that his objective is to maximize his expected monetary payoff in the game).

1. Suppose that player two knows that the coin always comes up heads. What is the best strategy for him to pursue?

2. Suppose that player two believes that a "fair coin" is being flflipped, so that the probability that it will land "heads up" is 1/2 and the probability that it will land "tails up" is 1/2. What is the best strategy for him to pursue?

3. Suppose that player two believes that the coin that is being flipped is "unbalanced" in such a way that the probability that it will land "heads up" is 4/5 and the probability that it will land "tails up" is 1/5. What is the best strategy for him to pursue?

4. Suppose that player two believes that the coin that is being flipped has a probability of landing "heads up" equal to p [0, 1] and a probability of landing "tails up" equal to (1 p). What is the best strategy for him to pursue?