Reference no: EM133260107

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  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. Before flipping the coin, player one gets to choose its "weighting". This means that player one gets to choose the probability that it will land heads up (and hence the probability that it will land tails up). Player two does not observe the "weighting" of the coin that is selected by player one. Assume that both players are risk neutral (which means that each player's objective is to maximize his expected monetary payoff in the game). Let p denote the probability that the coin chosen by player one will land "heads up", and q denote the probability that player two calls out "heads".

1. What is player one's best response function (or correspondence) in this game? Express it in the form p (q). Illustrate it in a diagram with q on the horizontal axis and p on the vertical axis.

2. What is player two's best response function (or correspondence) in this game? Express it in the form q (p). Illustrate it in a diagram with p on the horizontal axis and q on the vertical axis.

3. Illustrate both player one's best response function (or correspondence) in this game and player two's best response function (or correspondence) in this game in a diagram with q on the horizontal axis and p on the vertical axis.

4. Find all of the Nash equilibria for this game, and illustrate them in a new version of the diagram that you provided as your answer to the previous part of this question.