The Ducks and Beavers football teams are involved in a recruiting battle to add new talent to their programs. Both can simultaneously choose whether to spend their recruiting efforts on trying to attract in-state or out-of-state recruits. Because of their recent history of success, the Ducks hold an advantage and can attract better recruits than the Beavers:1) if they both recruit from the same pool (in or out of state). 2) If they both recruit in-state the Ducks will have a 10-2 season and the Beavers 5-5, 3) if they both recruit out-of-state Ducks will have a 11-1 season and the Beavers 4-6. 4) if the Beavers recruit in-state and the Ducks out-of-state the Ducks will have an 8-4 season and the Beavers 7-5.5) if the Beavers recruit out-of-state and the Ducks in-state then the Beavers will have a 6-6 season and the Ducks 9-3. The objective of both teams is to maximize wins.
(a) Construct a payoff matrix to illustrate this game
(b) From your payoff matrix compute each teams optimal recruitment strategy
(c) Give an intuitive explanation of the equilibrium that arrises in this game
(d) Compute the expected number of games the Ducks and Beavers wil win.