Selfishness, Economics and Game Theory
How can we use revealed preferences to make predictions?
I am always surprised by how many people are convinced that economists are only interested in selfish behavior. I believe this comes from a misconception of self-interest and selfishness. To say that we are self-interested is not that controversial. If you are an incredibly charitable person and give up money and time for others, you are doing this because you rank this above all other uses of your time. You are doing what is best for yourself. It is of little consequence that as a result of your actions others benefit. Below, I will take you through a reveled preference exercise to construct payoffs. With those payoffs in hand, we will then analyze a new situation that involves strategic considerations.
Economics, as mentioned elsewhere, makes use of revealed preference. If a person chooses one thing over another, we ascribe a higher payoff to that option relative to all other available options. So, when we see Agent Smith decide to donate 90% of their income to charity, economists ascribe a higher payoff to this choice than all others. With this structure, we can provide a full map of how a person ranks outcomes. We can then make predictions about this person’s behavior. For example, we can make a pretty good guess what would happen to a massive cash donation to Agent Smith. Therefore, economics can deal with selfless agents and selfish agents. Let’s see how this works and how it can be used to extrapolate to new situations. First I will talk about selfish agents.
Imagine I observe a firm, call it Dinobots Inc. engage in price competition with one other firm. Imagine Dinobots can charge high prices (H) or low prices (L). Additionally, imagine that for the past years, Dinobots has only faced dumb competitors who do not consider the actions of their opponents and are born with a need to charge a specific price and cannot change their minds. Let’s make this more realistic. If you are the firm charging high prices and there is a competitor charging low prices, your competitor gets all the profits you get nothing. If both firms charge low prices they get lower profits but get to cut the market in half. If both charge high prices they both get half the market but get profits that are higher than when both charge low prices.
We might observe the following behavior over time from Dinobots when facing dumb (or fixed programme) opponents.
- At time=1 Dinobots faces firm that always charges price L. We observe Dinobots choose price L.
- At time=2 Dinobots faces firm that always charges price H. We observe Dinobots choose price L.
- At time=3 Dinobots faces firm that always charges price L. We observe Dinobots choose price L.
- At time=4 Dinobots faces firm that always charges price L. We observe Dinobots choose price L. ….
- and so on.
As an economist we could generate a set of rankings for the outcomes Dinobots faces. It seems that if Dinobots faces someone picking L, they will also pick L. That means when facing L, L is preferred to H, so the payoff from L must be greater than from H. When faced with someone charging H, Dinobots prefers to pick L. So again the payoff from L must be greater than picking H.
We could put numbers as well, if we just want to make predictions about the way in which Dinobots will behave in future and if we are not interested in dollar values. We just have to pick the payoffs to respect the rankings the revealed preferences have given us.
- Payoff when opponent H and Dinobot L: 10
- Payoff when opponent H and Dinobot H: 8
- Payoff when opponent L and Dinobot L : 4
- Payoff when opponent L and Dinobot H : 0
Notice that these payoffs respect what we said about revealed preferences but also take into account the fact that this is a pricing game. These are not dollar values but simply numerical representations of the payoffs that generate the observed behaviour.
Now imagine that Dinobot faces a new rival, Rhinobot, that is strategic and is known to have the same preferences as Dinobot. How do we deal with this situation? Rhinobot is going to think what Dinobot is going to do and so is Dinobot. Each player’s payoff depends on his own action and that of his opponent and each will consider carefully the incentives his opponent faces.
We can summarize the situation with a table. In each cell, I am going to put a pair of numbers. The first will be Dinobot’s payoff, the second is Rhinobot’s payoff. The letters on the left correspond to D’s move and the column headers are R’s move. The numbers are derived from the revealed preference exercise from above.
The question is what will each firm pick? How do we solve this situation? We use an equilibrium concept that requires each player to do the best for themselves whatever their opponent does. This is Nash Equilibrium. It is a deep concept that I will talk about elsewhere but for now let’s use it to solve this situation.
The easiest way to apply Nash it go through all possible outcomes and check if anyone wants to change their action, if so this is not an equilibirum. If no one changes their mind we have found an equilibrium. If we start with (H,H) (where the first component is Dinobot’s move and the second is Rhinobot’s) then each will get 8.
However, Dinobots would like to switch to a lower price. This is enough to rule (H,H) out as an equilibrium.
If we have outcome (H,L), then Dinobots would like to switch to L. So, again (H,L) is not a stable outcome. If we then look at (L,L), we see that no one wants to change their mind. This is the unique prediction of this game. Everyone charges low prices and that’s it.
This game is the prisoner’s dilemma. It has been used and abused to highlight how economists’ main suggestion is to screw your opponent over. However, we should now fully understand what this game is. This game has been constructed using observed behaviors. This game describes Dinobots and Rhinobots and not saints. The payoffs were constructed from revealed preferences. If two saints were playing this game we would have different revealed preferences and would therefore be analyzing a different game. The prisoner’s dilemma is a game about arch rivals who do not want to coordinate on anything. It is not a game describing behavior of two people who want to agree with each other.
We could write down a game of agreement between two people. Again we would use reveled preferences to do this. Imagine Alice and Bob want to meet for a date. They must decide to meet at the Cinema (C) or at the best restaurant in town (R).
On past dates, Bob has done the following when meeting with someone:
- When faced with someone who chooses C, Bob chooses C.
- When faced with someone who chooses R, Bob chooses R.
The same goes for Alice. An example payoff table would be:
In this setting, (R,R) and (C,C) are the two Nash equilibria (there is another one but that is a bit technical). Here the two people want to coordinate. Their revealed preferences generate the payoff table. And their self-interested behavior generates an equilibrium where they coordinate.
My point is this: economics makes no statement about people’s motivations. It simply treats them as given and uses observed actions as revealing preferences. With those preferences we can make predictions. In the pricing game we began collecting data on a firm that wanted to make high profits. In the dating game, we collected data on people who wanted to coordinate. The actions gave us those payoffs and not the other way around. The solution was found by making sure everyone got what they wanted. Notice how the coordination game had self-interested players but they were interested in meeting! Economics surprisingly is pretty free of value judgements. It is descriptive but can yield new insights with access to a full map of rankings.
