Question 1

Verify that all of the interior Nash equilibria in Exercise Sheet 6 Q2-Q5 can be determined using partial derivatives.

Question 2

Consider the Stop-Go game. Two drivers meet at an intersection at the same time. They have the options of stopping and waiting for the other driver to continue, or going. Suppose the game is given by

Strategy 1 Strategy 2
Strategy 1 \((1,1)\) \((1-\epsilon,2)\)
Strategy 2 \((2,1-\epsilon)\) \((0,0)\)

Assume that \(0<\epsilon<1\), and find all Nash equilibria.

Question 3

Find the unique mixed Nash equilibrium for the game given by

Strategy 1 Strategy 2 Strategy 3
Strategy 1 \((0,0)\) \((5,4)\) \((4,5)\)
Strategy 2 \((4,5)\) \((0,0)\) \((5,4)\)
Strategy 3 \((5,4)\) \((4,5)\) \((0,0)\)