Question

2. Two travelers David and Mike has returned home from a trip to an exotic island where they each purchased the same antique for $1. Upon arrival they each discovered that the airline has managed to smash them! The airline manager assures the travelers of adequate compensation, but since he does not know the cost of the antiques he comes up with the following scheme: Each of the two travelers has to write down on a piece of paper the cost of the antique. David and Mike can each tell the truth or can choose to lie in order to get more than what they paid for the antique. See the payoff matrix for potential compensation options.

	Mike
David		Truth	Lie
	Truth	1,1	1+a, 1-b
	Lie	1-b, 1+a	2,2

The parameters “a>=0” and “b>=0” in the payoff matrix. Parameter “a” represents a reward given to a player for telling the truth when the other player lies. Parameter “b” on the other hand represents a penalty given to a player for lying when the other player tells the truth.

(a) What should be the value of “a” and “b” if the airline manager wants to make sure that both David and Mike tells the truth? Explain.

(b) Based on the payoff structure above, should the manager focus more on the reward system (setting ”a”), penalty system (setting “b”) or both? Explain.

Answer 1

		Mike
		Truth	Lie
David	Truth	1,1	1+a,1-b
	Lie	1-b,1+a	2,2

Ans A)

If Airline manager needs that David and Mike should say truth that is Truth, Truth be an outcome and this would be possible when 1>1-b for David when Mike chooses truth and for Mike too when David chooses Truth

As we need only Truth, truth as an outcome therefore we should have 1+a>2

hence values of 1<a and 0<b<1

Ans B)

We know that a>=0 and b>=0
then any value for b <1 would always make players to choose truth when other payer chooses truth.

Manager should take care that (Lie,Lie) wont be an outcome therefore he should take care of "a" more aggressively than "b" otherwise we have (Lie,Lie) as another outcome and this would reduce the welfare for manager.

Hence he should focus more aggressively to have a>1 always and a>1>b for sure to maintain (Truth,Truth) as only Nash Equilibrium of this game.