Asked by Yasmin Neves on Jul 12, 2024
Verified
The old Michigan football coach had only two strategies, Run the Ball to the Left Side of the line, and Run the Ball to the Right Side.The defense can concentrate either on the left side or the right side of Michigan's line.If the opponent concentrates on the wrong side, Michigan is sure to gain at least 5 yards.If the defense defended the left side and Michigan ran left, Michigan would be stopped for no gain.But if the opponent defended the right side when Michigan ran right, Michigan would still gain at least 5 yards with probability .70.It is the last play of the game and Michigan needs to gain 5 yards to win.Both sides choose Nash equilibrium strategies.In Nash equilibrium, Michigan would
A) run to the right side with probability .77.
B) be sure to run to the right side.
C) run to the right side with probability .87.
D) run to the two sides with equal probability.
E) run to the right side with probability .70.
Nash Equilibrium
A concept in game theory where each player's strategy is optimal, given the strategies of all other players, leading to a situation where no player has an incentive to unilaterally change their strategy.
Michigan Football
Refers to the college football program representing the University of Michigan, known for its long history and success in the sport.
Probability .70
A statistical measure indicating that an event has a 70% chance of occurring.
- Gain an understanding of the Nash equilibrium concept across diverse strategic scenarios.
- Utilize mixed strategy equilibria in the realm of game theory contexts.
- Acknowledge the significance of probability-based decisions within strategic game contexts.
Verified Answer
HR
Hannah RussellJul 13, 2024
Final Answer :
A
Explanation :
In Nash equilibrium, Michigan's strategy should maximize their expected gain, given the opponent's strategy. If the opponent defends the left side with probability p and the right side with probability 1-p, Michigan's expected gain from running to the right side is .70(1-p) and from running to the left side is 0p = 0. Thus, Michigan should run to the right side with probability 1 if .70(1-p) ≥ 5 and with probability 0 if .70(1-p) < 5. Solving for p, we get p ≤ .77. Therefore, the best strategy for Michigan is to run to the right side with probability .77.
Learning Objectives
- Gain an understanding of the Nash equilibrium concept across diverse strategic scenarios.
- Utilize mixed strategy equilibria in the realm of game theory contexts.
- Acknowledge the significance of probability-based decisions within strategic game contexts.