Question

Consider the normal form game G.

	L	C	R
T	(0,0)	(4,0)	(-3,0)
M	(0,4)	(2,2)	(-2,0)
B	(0,-3)	(0,-2)	(-4,-4)

Let G∞(δ) denote the game in which the game G is played by the same players at times 0, 1, 2, 3, ... and payoff streams are evaluated using the com- mon discount factor δ ∈ (0, 1).

a. Find the minimal value of δ for which playing (M,C) is sustained as a SPNE via Grim-Trigger (Nash reversion).

b. For δ = 1/3 design a simple penal code (as defined in class) that would sustain the payoff vector (2, 2) as a stage game SPNE payoff. Show that the simple penal code that you have constructed is enforcing itself (you don’t need to show other requirements for being SPNE).

c. Is it possible to sustain (−4,−4) as a stage game SPNE payoff?

Answer 1

So as Vc> Vd, this stategy could sustain Payoff (2,2) as stage game SPNE Payoff

C) as -4 is the least payoff , a player could earn , so (-4,-4) could not be sustained as SPNE