Example - Game of Chicken | |
|
In this example, Superman and Batman have challenged each other
to a game where they run at each other, and they can choose to go
(G), and collide, or Swerve (S), and be called "chicken".
The payoffs are as follows:
As before, if we consider the strategy from Superman's point of view: Again, there is no dominant strategy for Superman, nor, by symmetry, for Batman. There are two Nash equilibrium points (G, S) and (S, G). |
|
Commitment | |
|
If there are two Nash equilibrium points, which one will come
true?
If both players start from the same position, either equilibrium point might be realised. However, if one player "moves first", he has an advantage. For example, suppose that Superman makes the first move. If he chooses G, Batman has two choices G and S. Batman will choose S for a payoff of -1. Similarly, if Superman chooses S, Batman will choose G for a payoff of 2. Now, Superman can compare his two payoffs. Clearly, it is to his advantage to choose G. This process of reasoning is known as backward induction. |
|
Reputation | |
|
Another device to make one equilibrium realised is "reputation".
If Superman is known as "the unstoppable man" because he has never swerved in this kind of game, Batman should assume that Superman will not swerve this time either. Then Batman's best strategy is "swerve". However, this is only a static aspect. If this game will be repeated in the future, Batman may "go" (and be injured, of course) this time to build up his reputation to maximise his lifetime payoff. This type of game with Nash equilibria can be applied to the field of international economics when discussing strategic trade practices. |