Question

2. In 1812 Napoleon attempted an adventure that finally 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. Each general can either charge, flank, or retreat. Napoleon is on the left and Kutuzov on top, and their payoffs are on the left/right, respectively. Which of Napolean's strategies is dominated? Which of Kutuzov's strategies is dominated? Find the Nash equilibrium. You must show and explain your work to get full points. Charge Flank Retreat Charge Flank 4/2 2 /1 3/4 3/-1 -5/5 -1/1 Retreat 3/ -6 2/0 -3/3

Answer 1

Nash equilibrium is the strategy where each player earns highest payoff given other player's strategy. It means any one player can't earn a higher payoff by deviating from the Nash equilibrium given the other player doesn't change his strategy.

At [charge, charge], each player earns his best payoff given other player's strategy.

When Napoleon charges, it is best for Kutuzov to charge and when Kutuzov charges, it is best for Napoleon to charge as well.

Therefore, [charge, charge] is a Nash equilibrium.

At Nash equilibrium, Napoleon earns 4 and Kutuzov earns 2.

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