After talking with my mentor T. Elson last week, I was inspired by his comments because they shed new light on my independent project. We primarily talked about the segregation model where the method of randomization can help achieve Nash equilibrium and thus providing a fair result in some situations. However, there is a distinction between an optimal situation and Nash equilibrium. Nash equilibrium only indicates that people are playing the best response corresponding to their opponents’ strategy, while an optimal situation indicates that each person receives the highest possible payoffs. A game with three Nash equilibria might only have one optimal situation.
Let us go back to the situation I talked about in my segregation blog and consider about not only under which circumstances Nash equilibrium exists but also which situations lead to the highest playoff. Last time, my only assumption was that people tend to feel more comfortable sitting with people of the same ethnicity. This time, I will be using the same assumption and consider other factors which could potentially affect the payoff of the circumstance.
If I were to make a policy on seating locations at dining hall tables, I have three choices, for there are three Nash equilibra. They will be:
- Allowing students to make their own decisions on where to sit.
- Assigning each student a specific seating location so that each table will have an equal amount of representatives from each ethnicity group.
- Randomizing students’ seating locations at dining hall tables.
These choices, even though they are all potentially desirable outcomes, do not produce the same payoffs, and each choice can have the different payoff depending on the situation. For example, assigning each student a specific seating location should, in theory, have the maximum possible payoff because students from different ethnicities can communicate with each other. However, the situation could end up badly if none of the students at each table are friends with each other and simply choose to not talk. Therefore, assigning each student a specific seating location can reach the maximum payoff if and only if they are close friends with each other, then a potentially beneficial conversation might result.
This example was analyzed in the Yale game theory lecture, and the answer was surprisingly straightforward. By analyzing the game, we can achieve the best payoff when everyone is mingled with people of different backgrounds. When we randomize the students’ seating location, we achieve a fair result. However, if the payoff of a fair result is lower than the payoff of an unfair result, do we still opt for a fair one? If we randomize students’ seating location, and a group of students’ who are not communicative are arranged to one table, the payoff might even be lower than just allowing students’ to choose their own seating locations.
Does the game theory help in enacting a policy in our real life? It does, to some extent. It gives us a general direction of where we are heading. Does it tell us which policy is better? No necessarily. It presents us with a generalized situation, but if there are more variables or factors, which, is often the case in reality, we still have to get out of a theory’s protective bubble and use our minds to make a final decision.
See a real example of how game theory is used in social policy.
“Dining Room.” Westtown School. Westtown School, n.d. Web. 10 Nov. 2014.