Line Game |  |
Description
1. Description of the game
Each game is called a "Line." A possibly infinite sequence of subjects play in a line. Players make their decision sequentially. All players face the same decision problem. Each player must decide whether to keep a token or invest it. The number of players in a line depend on the roll of a dice. After each decision an electronic dice is roll and the line ends if a six appears, otherwise the line continues for one more period (one more player makes the keep or invest decision) and the dice is roll again, and so on. If there is a total of T players in a Line, the final payoff for player t is:
Payofft =
kt + (1 + r)(1 − kt−1) +
T
β Σ (ks + (1 + r)(1 − ks−1))
s=t+1
where ks = 1 if the player s decided to keep his token and zero otherwise. That is, if I play today I get (1 + r) if the player before me invested. In addition, I get 1 if I keep my token. If I invest my token and the game does not end today I get β(1 + r) and I get β times all the incomes made in the future. In other words, my payoff has two parts:
1) Present (or direct) payoff: kt + (1 + r)(1 − kt−1)
2) Future (or indirect) payoff (which is β times the future payoffs of all the future players):
T
β Σ (ks + (1 + r)(1 − ks−1))
s=t+1
2. Matching and Number of Lines
Regardless of the fact that the expected length is of 6 players, each line may end with a very large number of players. Therefore, I am planning the experiment in the following way: We start with two or three lines simultaneously. Each one has its own dice. Players are randomly assigned to a line as the lines need new players. Each player only plays in one 1 line and he only plays once! When all the original lines end, we start a new set of lines if enough players are left. For example, if we have a total of 60 subjects and the first three lines all end, leaving between 8 and 16 players that haven’t played, then we open one new line. If the number of players that haven’t played is between 17 and 24, we open 2 new lines and if the number of players that haven’t played is greater than 24 we open three. If these lines end and we have some players that haven’t played, then we open new lines following the same formula. If less than 8 players are left at any point, we don’t open new lines. It may be the case that a line goes for so long that uses all the subjects. Then we need to continue the experiment another day with new subjects. Therefore the software should be able to start an experiment in which we enter a past history. For example, if yesterday we run out of subject with a line in which player 1 kept the token, player 2 invested and player 3 kept it, we should be able to write (1,0,0) in the parameter file of the new session and start a line directly at player’s 4 decision round (this player 4 would actually be the first player of the new session). In this way, if we run out of subjects in a session, we can complete a line in a later session.
Sample Parameter File
View line-sample.txt.
Download line-sample.txt.
