In 1812 Napoleon attempted an adventure that nally cost him his crown: he invade
ID: 1107226 • Letter: I
Question
In 1812 Napoleon attempted an adventure that nally cost him his crown: he invaded Russia. He
met the army of Russian general Kutuzov at Borodino. Napoleon won, but it proved to be a Pyrrhic victory, as the Russians were able to defeat the French in the aftermath.1 Each general can either
charge, ank, or retreat. Find the Nash equilibrium in pure strategies for the game depicted in the
following payo matrix (where Napoleon is on the left and Kutuzov on top, and their payos are
on the left / right):
Kutuzov
Charge Flank Retreat
Napoleon
Charge 4 / 2 2 / 1 3 / -6
Flank 3 / -4 3 / -1 2 / 0
Retreat -5 / 5 -1 / 1 -3 / 3
Explanation / Answer
To find the Nash equilibrium, I will begin by evaluating Kutuzov’s best response given Napoleon’s strategy and use a single underline to represent this response. Next, I will find Napoleon’s best response given Kutuzov’s strategy and use a double underline to mark that response. The Nash equilibrium will be the cell where two payoffs have been underlined. Napoleon plays Change, the best response or Kutuzov is to play Change since it has the highest payoffs. Napoleon plays Flank, the best strategy or Kutuzov is to play Retreat since 0 is bigger than -1 and -4. Napoleon plays retreat, Kutuzov should play change. Kutuzov plays change, the best response or Napoleon is to play change because the payoffs are highest. Kutuzov plays Flank, Napoleon should also Flank to get a payoff of 3. Kutuzov retreats, Napoleon should change to get a payoff of 3. (Change, change) is the pure Nash equilibrium because at this point, neither Kutuzov nor Napoleon is willing to choose a different strategy given the choice of the opponent.
Napolean Kutuzov Charge Flank Retreat Charge 4 2 2 1 3 -6 Flank 3 -4 3 -1 2 0 Retreat -5 5 -1 1 -3 3