CIA - two types each prob 1/2 - informed - uninformed Type remains throughout th

ID: 1129948 • Letter: C

Question

CIA - two types each prob 1/2

- informed

- uninformed

Type remains throughout the game, and no discounting

To intervene, must be informed type.

If informed type, does not have to intervene

If CIA doesn't intervene, the current period mission succeeds 1/2 time and fails 1/2 time

Period 1

KKK succeeds gets a payoff of 1, and CIA gets a payoff or 0.

KKK fails gets a payoff of 0, and CIA gets a payoff of 1.

Probability of success depends on the CIA's period 1 intervention decision.

If mission fails KKK doesn't know if that is because CIA intervened or happened due to something else.

Period 2

If KKK quits each gets payoff of 3/7

If KKK initiates, KKK succeeds gets 2 and CIA gets 0, KKK Fails gets 0 and CIA gets 2

Payoff is sum of his payoff in period one and two.

Conditions

i) the informed type of CIA sometimes intervenes in period 1, v,

ii) the KKK initiates a second period mission following a first period failure with prob f.

iii) the KKK always initiates a second period mission following a first period success.

QUESTION

WHat is the informed CIA's payoff of intervening in period 1.

What is the CIA's payoff of not intevening in period 1.

What must be the perfect bayesian equillibrium value of f?

What is the informed CIA payoff in this equillibrium?

The informed in the CIA payoff is

2*2

Not in period 1

3*3

Perfect bayesian equilibrium value is

3*3

informed in CIA payoff

4*4