Changing Game Theory to Reach Social Optimum

Many of the equilibrium on Game Theory turn out not to be the social optimum solution. For a society perspective, this is a problem.

This is an example of a couple having to cleaning the house:

Partner 2
Clean Dont Clean
Partner 1 Clean 4,4 -4,8
Dont Clean 8,-4 0,0

As you can tell the dominate strategy is to neither person to clean. And what is interesting is that the dominate strategy of 0,0 has a lot less value than the best value for the social optimum of 4,4. So the question is, how do you make it so both persons pick the social optimum solution?

The key is to shift the persons to from striving to maximize personal outcomes to strive to maximize relationship outcomes. (Relationship outcomes is both the outcomes added together). This what the matrix would be:

Partner 2
Clean Dont Clean
Partner 1 Clean 8,8 4,4
Dont Clean 4,4 0,0

Now the dominate strategy is for both people to clean which is also the social optimum solution. So the best way to change a game theory matrix to reach social optimum is to make the other person care about the results of the other person. Had we all cared about how many points everyone else got in the investment game in class, we would of all saved and we would have all been better off.

Here are the two matrix again.

		Partner 2
		Clean	Dont Clean
Parnter 1	Clean	4,4	-4,8
	Dont Clean	8,-4	0,0

		Partner 2
		Clean	Dont Clean
Parnter 1	Clean	8,8	4,4
	Dont Clean	4,4	0,0

However, if the relationship is bad a different matrix would come out. This would happen if each person rather than trying to striving to maximize their own personal outcomes but instead to get an outcome that is superior to the other person (own outcome minus partner's outcome).

This matrix would look like this:

		Partner 2
		Clean	Dont Clean
Parnter 1	Clean	0,0	-12,12
	Dont Clean	12,-12	0,0

This matrix once again leads to neither partner cleaning. So in term of the investment game in class, had we all only cared about getting more points than the person next to us, then everyone would have saved.