Problem #4: Construct Game Matrix (12 pts) 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 if they both recruit from the same pool (in or out of state). If they both recruit in-state, the Ducks will have a 10-2 season and the Beavers 5-5; if they both recruit out-of-state Ducks will have an 11-1 season and the Beavers 4-6. 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. If the Beavers recruit out-of-state and the Ducks in-state, the Beavers will have a 6-6 season and the Ducks 9-3. The objective of both teams is to maximize wins. (Dr. Christopher Ellis, University of Oregon) Notice that the season outcomes denote (Wins, Losses). Teams don't care about losses and should not be included in your matrix. a. Explicitly state players and strategies for both players b. Construct a payoff matrix to illustrate this game c. Find pure strategy Nash equilibrium using best responses.

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