20. Morals By Agreement, Chapter 3: Strategy (Game Theory)

Note: This post is the twentieth in a series. Click here for the full listing of the series.

This is the second of what should be a few posts on the book Morals by Agreement, by David Gauthier.

In the last post, we covered chapter 2 of Morals by Agreement, where Gauthier sketched out his view of what it meant for people to behave 'rationally' in situations which didn't involve other people who might themselves be trying to act rationally and whose actions might depend on our actions and vice-versa.

So in chapter 3, Gauthier extends his model of rational behaviour to cover what he refers to as 'strategic interaction' - that is situations where people are interacting with each other, rather than acting on their own. Basically, in the terms I used earlier in this series, he is moving from rational actions, to rational transactions.

The formal branch of knowledge that studies transactions is Game Theory. The most famous game in Game Theory is the Prisoner's Dilemma, which I introduced earlier in the series here.

For more background on game theory here is the Wikipedia entry on game theory and here is the excellent Stanford encyclopedia of philosophy entry on game theory.

When it comes to game theory, examples are the way to go to gain understanding.

Consider a simple game, where Harold and Kumar are trying to meet up at a local restaurant for a meal, but they are not in communication with each other. However, they both know that there are only two restaurants in town, White Castle and Black Castle. Furthermore, they know that Black Castle is closed.

                                        Harold
                            White                     Black
Kumar   White:      [5,5]                 [3,0]
                 Black :     [0,3]              [2,2]

The best outcome is if they both meet at the White Castle (5 for both). For both Harold and Kumar, the next best option is if they go to White Castle and the other person goes to Black Castle - they don't get to meet up, but at least they can eat. For both players, the third best is to meet at Black Castle and the worst option is to go to Black Castle while the other person has gone to White Castle (alone AND hungry).

Gauthier defines rational behavior in transactions, or 'strategic interaction' as follows:

A)Each person's choice must be a rational response (i.e. utility maximizing) to the choices she expects the others to make
B) Each person must expect every other person's choice to satisfy A
C) Each person must believe her choice and expectations to be reflected in the expectations of every other person.

So in the example above, Harold figures that if Kumar goes to White Castle, he (Harold) is better off going as well. But even if Kumar doesn't go to White Castle, Harold is still better off going to White Castle. So condition A sends Harold to White Castle. Condition B tells Harold that Kumar will follow a similar logic and also end up at the White Castle.

The outcome where Harold and Kumar both go to White Castle is what is known in game theory as an equilibrium outcome. What this means is that, given that both Harold and Kumar are choosing to go to White Castle, there is no reason for either of them to unilaterally change their choice. Compare that with the situation where Harold is going to White Castle and Kumar is going to Black Castle - this is not an equilibrium because in this situation, Kumar would be better off to change his strategy.

Now let's look at a different type of game. Consider the question of what side of the road to drive on. For now, imagine that only two people live on a road, Adam and Eve, and they need to agree on which side of the road to drive on and they both own British cars that were designed for driving on the left side of the road.

                                        Eve
                            Left                     Right
Adam   Left:      [2,2]                 [-10,-10]
            Right :    [-10,-10]            [1,1]

Note that there are 2 equilibrium outcomes in this game, One where both drive on the left and both drive on the right. Even though both Adam and Eve are better off if they both drive on the left, if for some reason they are currently both driving on the right, neither has an incentive to unilaterally change their strategy. Only by working together could they shift from the sub-optimal equilibrium to the optimal equilibrium. Unsurprisingly, this type of game is known as a coordination game, where the coordination needed has two parts: 1) making sure that both people pick the same outcome and 2) making sure the equilibrium they end up in is the optimal one.

But what if we change the game slightly so that Adam has a car that is designed to drive on the left and he has always driven on the left so strongly prefers driving on the left. Meanwhile, Eve has a car that is designed to drive on the right, but she just got her license so she is less attached to driving on one particular side.

                                        Eve
                            Left                     Right
Adam   Left:      [5,2]                 [-10,-10]
            Right :    [-10,-10]            [2,3]

Again there are 2 equilibriums and Adam and Eve need to coordinate to make sure they drive on the same side of the road. But the situation is complicated now by the fact that Adam prefers the 'drive on the left' equilibrium and Eve prefers the 'drive on the right' equilibrium.

This now becomes a bargaining problem, one that has been much studied and argued over in the history of game theory. The reason I bring it up here is because Gauthier himself brings it up in chapter 3 - because it will be useful to him later on in the book.


Finally, I won't go over the Prisoner's Dilemma again, but it is worth noting (as Gauthier does) that in the Prisoner's Dilemma, the equilibrium that Gauthier's rules for rational behavior lead to is different from the (Pareto) optimal outcome. In other words, if people pursue their own utility maximization it will lead to sub-optimal outcomes where there are possibilities to make people better off without making anyone worse off, but these possibilties are placed out of reach by people's self-interested behaviour.

Gauthier will argue that morality consists of the constraints necessary to generate optimal outcomes for 'rational' people.