I am facing a game theory problem which is as follows:
An experiment was designed to study individuals' propensity to be trusting and to be trustworthy in a task called the investment game. In this game two subjects are each given 3 dollars as a show up fee.
One of the subjects is told that he or she will be decision maker one (DM1), and can send an amount (0 dollar, 1 dollar, 2 dollar or 3 dollar) to the other subject (decision maker two, DM2). The rules are simple. Every dollar sent will be doubled by the experimenter before it reaches DM2, who then gets to decide how much of the doubled money to keep and how much to send back to DM1. After DM2’s decision the game is over and subjects leave. The experiment is double-blind meaning that neither the subjects nor the experimenter knew who was matched together, or what subject made what decision.
In order to analyze this problem, I have drawn the extensive and normal forms which are showed [here] and [here].
I find no matter what kind of choice each subject choose, they all choose to play either (0,0) or (3,3) in the Nash equilibrium.
Now the question is know how to find subgame-perfect Nash equilibrium in terms of normal form and extensive form?
Is the normal form of the Trust game a symmetric game?
normal form link http://farm9.staticflickr.com/8426/7814582114_02459a1ef8.jpg
extensive form link http://farm9.staticflickr.com/8304/7814582210_85db97fb45.jpg