# Risk dominance selects the leader.  An experimental analysis

### Antonio Cabrales

Walter García-Fontes

Massimo Motta

## Instructions for the Game

### General

You are going to participate in an experiment on an economic game. Just for participating you will receive 500 pesetas1. Besides that, if you follow the instructions carefully and you take adequate decisions you may win a considerable amount of money which will be paid to you in cash after the experiment. It is important that you do not communicate with your neighbors. If you have questions raise your hands and one of us will come to you and will answer your questions.

The experiment will consist of a series of decision periods. In each period you will be randomly and anonymously matched with another person and depending on the action you choose and the action chosen by the person with whom you are matched you will receive some points. After receiving those points they will be converted into an amount of pesetas which will depend on the number of points you have. We will begin by explaining the conversion of points into pesetas so that you understand the effect of the points obtained in the amount of pesetas earned. After that we will explain the choice of actions in detail so that you understand how to obtain the points.

### Conversion of points into pesetas

At the end of each period you will have obtained an amount of points between 0 and 1000 according to the system we will explain later. The computer will randomly choose an integer number between 1 and 1000 (giving all numbers the same probability). If the number of points you have is larger than or equal to the number obtained by the computer you win 50 pesetas. If the number of points you have is smaller than the number obtained by the computer you win 0 pesetas. For example, if you have 450 points you have a 45% probability of winning 50 pesetas. It is important that you realize that the larger the number of points you obtain, the larger the probability of winning.

### Choice of actions

There are two types of players. At the beginning of the experiment the computer will tell you which type of player you are. You will keep this type for the duration of the experiment.

The experiment will be composed of 30 decision periods. In each period you will be randomly matched with a player of the other type. In this way all pairs will be composed of a type A player and a type B player. The identity of you couple is unknown to you and it changes every period randomly.

Once the period begins each player can choose between two options: 0 and 1. The points obtained will be a function of your choice and the independent choice of your couple, as indicated in the following example:

 Choice of B 0 1 Choice 0 292, 164 612, 362 of A 1 364, 509 367, 346

For instance, to know the points you have obtained if you are type A and you choose 0 when the person you are matched with (therefore a type B) chooses 1, you look in the table for the cell corresponding to (A, 0), (B, 1) and you find the number 612. In this same situation your pair obtains 362, as one can see from the same cell (A, 0), (B, 1) of the table. You can find the table for this experiment at the end of these instructions.

Once you decide on your action you should enter you decision in the computer.

Once you and the player you are matched with have taken the decision, the computer will determine the number of points earned, using the corresponding table. The computer will tell you this information.

After that, the computer converts the point into pesetas. Once this is done the computer will tell you this information together with the history of your decisions and those of the player with whom you have been matched.

### History of decisions

The computer gives you a history of the decisions you have taken in previous periods, as well as those of the players you were matched with and how many points and pesetas you won.

### Development of the experiment

At the beginning of the experiment you will have two practice rounds to get used to the terminal and the game. The gains of those periods are fictitious and will not be paid at the end. Once the practice rounds are over the true experiment begins, where the gains are real. The experiment will consist of 30 true periods.

### Footnotes:

1 Spanish currency

File translated from TEX by TTH, version 1.67.