The San Francisco 49ers and the New York Jets are in the Super Bowl. It is fourt

Question

The San Francisco 49ers and the New York Jets are in the Super Bowl. It is fourth down with 10 seconds left in the game. The score it New York 10, San Francisco 7, and San Francisco has possession of the ball 8 yards from the goal line. Neither team has any time-outs left, so this will be the last play of the game. San Francisco has two options: (1) kick a field goal and the the game; or (2) go for the touchdown and either win or lose the game. Should San Francisco go for the touchdown, they will end up playing a static "Touchdown Game" with New York. The objective of each team is to maximize the probability of winning the game. The resulting payoff matrix is given in the table that follows. Notice that New York wants to match its defense against San Francisco's offense, while San Francisco wants to avoid such a match. Determine whether this game has Nash equilibrium in pure strategies, if not, find the Mixed strategy Nash Equilibrium. Show your work.

Explanation / Answer

In this case we compare our payoffs. SF compares colum 1 vetically and NY compares colums 2 horizontally.
In this game, SF compares 50 and 90 and chooses 90. TYhey then compare 60 and 20 and choose 60. Likewise NY compares 50 and 40 and chooses 50. They then compare 10 and 80 and choose 80.

In this case, there is no Nash Equilibrium in this game and there is not a mixed strategy equilibrium
50,50     60,40

90.10     20,80

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