1 The beginning of the end (5 points) In 1812 Napoleon attempted an adventure th

Question

1 The beginning of the end (5 points) In 1812 Napoleon attempted an adventure that finally cost him his crown: he invaded Russia. He victory, as the Russians were able to defeat the French in the aftermath. Each general can either charge, flank, or retreat. Find the Nash equilibrium in pure strategies for the game depicted in the following payoff matrix (where Napoleon is on the left and Kutuzov on top, and their payoffs are on the left right): Kutuzov Charge Flank Retreat Charge 4/22/13/-6 Flank | 3/-413/-11 2/o Retreat-55 -1/1-3/3 Uni here it's historical facts (or made up. whatever can count as such in history). The game itself is of course completely

Explanation / Answer

First we shall make the possible outcomes for both

charge=c flank=f retreat=r

napoleon is depicted by N

Kutuzov is depicted by K

we will assume that eash player will try to maximise the gain and minimise the loss

lets start with napoleons possible playoffs

Nc = max benefit of 4 at Kc , min benefit of 2 at Kf

Nf = max benefit of 3 at Kc/Kf, min benefit of 2 at Kr

Nr = max loss of -5 at Kc, min loss of -1 at Kf

now we can see, that napolean maximises the gain if he charges, flank policy is close enough but not the best outcome

now lets see playoffs for kutuzov

Kc = max benefit of 5 at Nr , max loss of -4 at Kf

Kf = max profit of 1 at Nc/Nr, min loss of -1 atNf

Kr = max profit of 3 at Nr , max loss of -6 at Nc

we can see that kutuzov is getting the minimum possible loss if it flanks. if he decides to charge or retreat he can increase the potential loss. therefore kurutov will select to flank

Now, if we come back to napoleons policy, we can see that given kurutov is going to flank, napoleon has a better payoff (3) if he choses to flank as well, instead of charging (2) as we initiall thought

therefore both napoleon and kurutov will flank and outcome will be 3/-1

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