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The following payoff matrix describes a variation of the repeated Golden Ball game introduced in...

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Finance

The following payoff matrix describes a variation of the repeated Golden Ball game introduced in class. The payoff matrix is given as follows

Nick (Player B)

Split

Steal

Ibrahim

(Player A)

Split

(20, 20)

(3, 29)

Steal

(29, 3)

(4, 4)

(a) (5 points) Suppose the game is played only once. Find the Nash equilibrium (NE) (No justification required)

(b) (15 points) The two players compete repeatedly forever, and each has a per-period discount factor (0 < < 1). Suppose both players follow the grim trigger strategy: I will play Split in the first round, and then play Split as long as my opponent has been playing Split. If my opponent plays Steal once, I will play Steal forever, starting from the next round. Find , the minimal , such that (Split, Split) every period is the equilibrium path as long as > .

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