Question

The issue of who takes care of the elderly parents is modeled as a game of chicken with asymmetrical preferences as follows;

Table 1

	Husband
Wife		Take care	Don’t take care
	Take care	2,2	1,3
	Don’t take care	3,1	0,0

Table 1 - who should care for the elderly parents as a chicken game?  

For each player it is best to do the opposite of what the other player does, and there is no obviously dominant outcome.

a. Identify the best and worst strategy in the game described in table above.

  

b. The payoffs would be different for a wife and husband living in Beijing China, both of them having career and they are the generation of One Child Policy. The different payoffs may result from difference in the value placed on having the elderly parents be cared for at all (wife care more), or in the burden associated with taking care (peer pressure), or both. This changes the payoffs for wife (if they are her parents in law, she married to the only child) but not for husband.

Draw and explain the new payoffs matrix.

Answer 1

a) IN THE GIVEN MATRIX BEHAVIOUR OF HUSBAND AND WIFE ARE GIVEN. THEY HAVE TWO CHOICES, EITHER THEY CARE FOR PARENTS OR THEY DON'T CARE FOR PARENTS. IF BOTH OF THEM CARE FOR PARENTS THEY WILL HAVE PAYOFF OF 2 EACH WHERE BOTH WILL BE BETTER OFF AND PARETO OPTIMALITY WILL BE ACHIVED.THIS IS THE NASH EQUILIBRIUM OF THE GAME.  AGAIN IF HUSBAND CARE AND WIFE DON'T CARE THEN HUSBAND WILL BE BETTER OFF AND WIFE WILL BE WORSE OFF AND THAT WILL NOT SATISFY PARETO OPTIMALITY. THE REVERSE WILL HAPPEN WHEN WIFE CARE AND HUSBAND DON'T CARE. THEN OLSO PARETO OPTIMALITY IS VIOLATED. IN LAST CASE IN BOTH DOES'T CARE BOT WILL RECIEVE A PAYOFF OF 0 EACH AND BOTH WILL BE WORSE OFF.

THUS THE BEST STRATEGY WILL BE TO TAKE CARE AND BOTH WILL BE BETTER OFF.
THE WORST STRATEGY WILL BE DON'T CARE AND BOTH WILL BE WORSE OFF.

b) IN CASE THEY BOTH LIVE IN BEIJING AND ARE SINGLE CHILD THEY HAVE TO TAKE CARE OF THEIR PARENTS. NOW THE HUSBAND WILL SURELY TAKE CARE BUT THE WIFE WILL TAKE CARE MORE FOR TWO REASONS: 1. SINCE THEY ARE FROM THE GENERATION OF ONE CHILD POLICY THEY ARE VALUED TO TAKE CARE OF ELDERS. 2. WIFE MAY TAKE CARE OUT OF PEER PRESURE.
FOR ANY OF THE REASON OR BOTH WIFE HAS TO TAKE CARE AND AS A RESULT HER PAYOFF WILL INCREASE. TO BE NOTED HUSBAND'S PAYOFF WILL BE THE SAME. THE EXECTED PAYOFF MAY BE AS FOLLOWS:

	HUSBAND
WIFE		CARE	DON'T CARE
	CARE	3,2	1,4
	DON'T CARE	4,1	0,0