Problem 1 (10 points) In a football game played between Navy and Army, the Navy\

Question

Problem 1 (10 points) In a football game played between Navy and Army, the Navy's offense has 3 strategies: run, long pass and short pass, the Army's defense has 3 strategies: 4-3, 5-2, and cover- 2. The payoff's are listed in the following table (the higher the numbers, the better payoffs). Use game theory approach, to find Equilibrium strategy (strategies), if there exists one. Army Defense 5-2 formation 4-3 formation Cover-2 formation 5,3 5,3 6,6 Navy Offense Run 0,4 Long Pass 4,0 Short Pass 3,5 4,0 0,4 3,5

Explanation / Answer

In the above question it is given that the Army Defense has 3 strategies which are as follows:-

5-2 formation which is STRATEGY 1

4-3 formation which is STRATEGY 2

Cover-2 formation which is STRATEGY 3

While the Navy Offense has also three strategies which are:-

Run- Strategy 1

Long Pass- Strategy 2

Short Pass-Strategy 3

In nash equilibrium we see the best strategic response of strategies which helps in better desicion making.

Here, Navy Offense's best strategis response to Army Defence's strategy 1 is long pass that is 4. Likewise for stragety 2 & 3 of Army defense the best stragety of Navy offense is run(4) and Short pass(6) respectively.

Similarly, the Army defence's best strategic response to Navy offense's strategy 1 is 5-2 formation(4). Likewise for strategy 2 & 3 it is 4-3 formation (4) & cover 2 formation(6) respectively.

Thus, here the only equilibrium strategy would be (6,6).

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