Janet decides to play a game with her children, Jay and Jill (who are fraternal twins) and Mo. Each child is in their own room and cannot communicate with each other. Suppose Jill and Jay share everything, while Mo, the older sister, never shares. Janet proposes to give each child an envelope with $9 in it, and they are given the option of keeping the money and giving back an empty envelope or leaving the money in the envelope when they return the envelope to Janet.
Janet will invite everyone to join her at the kitchen table, and will add $6 to the funds when she empties the envelopes, if there is still $9 in it. The children then get to split the funds and keep it.
a. How many strategy combinations are there? Let K stand for keep the $9, and let P stand for leaving the $9 in the envelope. Write out a table listing the strategy combinations in the first column, Jay's payoff in the second column, Jill's payoff in column three, Mo's payoff in column four and the total payoff in column 5.
b. Is there a dominant strategy combination? If so, what is it?