Player 2 is informed as to whether Player 1’s prediction was right or wrong (but she is not informed of the prediction or the coin that was used), and then must guess whether coin A or coin B was used. If Player 2 guesses correctly she wins 1 dollar from Player 1. If Player 2 guesses incorrectly and Player 1’s prediction was right, Player 1 wins 2 dollars from Player 2. If both are wrong there is no payoff.
I have trouble drawing the game tree for this question. Can anyone help?
When you draw the game tree, you will need to identify the events. In our case the events are as follows:
Player1 chooses head or tail.
The coin is tossed
Player2 guesses what Player1's choice was
The winner is determined
So, you have four levels. The root of the tree is Player1 chooses head or tail. On the second level you have two nodes denoting the same event, which is the coin toss, but the vertices going into the two nodes would show what Player1 has chosen. On the third level, you have a head and a tail as children for both nodes from the second level, four items on the fourth level in total. At this point we already know whether Player1 can win the game. At the fourth level you have two nodes as children for all the four nodes from level 3. Each node from level 3 would have a child "Player 2 guesses head" and another for tail. You can describe the situation besides the vertices or inside the nodes, with the exception of the last level, where the results can be displayed.
I do not have a proper application now to draw the tree, but I hope the description was clear. You wonder whether it should be a graph. Yes, it should. Every tree is a graph. However, it should not hold cycles, because the events might be similar, but they are different. For example, if the second player guesses head, then the situation is very different if Player 1 said head or tail, not to mention the result of the toss.