Start of Part I
We will now go through the instructions for the experiment. This will be followed by a short quiz based on the information provided here.
This Instructions page will remain accessible throughout the session at the bottom of each page. You will have also been provided a printed version of the instructions.
Section 1. The experiment task
How each round works
Following the instructions (Part I), the experiment will progress in rounds. Part II will consist of 3 shortened practice rounds, followed by Part III which will consist of 6 full rounds.
Each full round will consist of 5 potential matches. In each potential match, you will be paired with another person who is selected at random, who we shall call your counterpart for that match. The identity of your counterpart will be different each time. For each potential match, you will be required to select a plan-of-action from two available options.
How each full round works:
After you have chosen a plan-of-action for each potential match, one of the 5 potential matches will be selected at random to be played out as the interaction for that round. The plan-of-action that you choose will determine how you behave in that interaction. Because you do not know which potential match will be chosen, you should treat each as if it could be the one that will be selected for the interaction that round.
The shortened practice rounds in Part II will contain only 1 potential match, which is then used as the interaction for that round.
Your counterpart
The counterparts that you will be matched with are not in this room. In fact, these counterparts have previously completed an experiment similar to this one. Today, you will be interacting with the pre-recorded decisions made by your counterparts in that previous experiment.
While there are some differences between the experiment that your counterparts completed and today’s experiment, the interactions that you will face today are materially the same across the two experiments. In each potential match, your counterpart will be a person randomly selected from the previous experiment, whose choices in the interaction will be represented by a plan-of-action, same as the plans-of-action that you will choose between today.
How your payment will be determined in each interaction
The outcome of each interaction results in Experimental Currency Points, which we will call simply as points. At the end of the experiment, you will receive a payment corresponding to the total points you earned across the interactions in Part III at an exchange rate of 50 points = $1.
Section 2. The interaction
Your actions and outcomes
The interaction is 5 sets, each time using the same counterpart and chosen plan-of-action for the match that was selected. These sets are played consecutively and start again from the beginning with each new set.
How each interaction works:
Each set is a series of games which are played consecutively. For each game, both players (you and your counterpart) will select from the same two actions of either A or B. The action you select in each game will be determined by the plan-of-action you chose for that potential match. The outcome of a game is the pair of actions that are played, which result in a payoff of points as follows:
| Your action | Counterpart action | Game outcome | Your payoff | Counterpart payoff |
|---|---|---|---|---|
| A | A | AA | 5 points | 5 points |
| A | B | AB | 0 points | 7 points |
| B | A | BA | 7 points | 0 points |
| B | B | BB | 2 points | 2 points |
- If you played A and your counterpart played A, you both receive 5 points
- If you played A and your counterpart played B, you receive 0 points, and your counterpart 7 points
- If you played B and your counterpart played A, you receive 7 points, and your counterpart 0 points
- If you played B and your counterpart played B, you both receive 2 points
Your payoff for a set is the sum of all points received across each game within that set.
A random number of games in each set
The number of games in a set is random. After each game, there is a 7/8 chance the set will continue to the next game, and a 1/8 chance the set will end. These chances remain the same across all subsequent games and does not change depending on how many games have already been played.
A chance that your choice is changed
When an action is chosen, there is a 7/8 chance that it will actually be played. But with a 1/8 chance, an error occurs and the choice is changed such that the opposite action is played. That is:
- If A is chosen, with 7/8 chance A is played, and with 1/8 chance an error occurs and B is played instead
- If B is chosen, with 7/8 chance B is played, and with 1/8 chance an error occurs and A is played instead
- With chance (7/8) * (7/8) = 0.766, no change occurs and AA is the game outcome
- With chance (7/8) * (1/8) = 0.109, your counterpart's action is changed and AB is the game outcome. Additionally, you do not know your counterpart's action was changed through error
- With chance (1/8) * (7/8) = 0.109, your action is changed and BA is the game outcome. Additionally, you know your action was changed through error but your counterpart does not
- With chance (1/8) * (1/8) = 0.016, both actions are changed and BB is the game outcome. Additionally, both players know their own action has had an error, but do not know their if their counterpart had an error
Section 3. A plan-of-action
Understanding a plan-of-action
Your actions are determined by which plan-of-action you choose. A plan-of-action is a complete description of what action to choose in each game of a set. It does so by specifying a collection of rules, which state the action to choose given the history of the set.
Example #1 is a simple plan-of-action that has two rules: one rule stating the action in the first game, and one rule stating the action for all subsequent games regardless of the history.
Most plans-of-action will have rules that take into account the history of the set thus far. Example #2 is a plan-of-action that chooses a different action depending on the outcome of the past two games.
Example #3 is a plan-of-action with a special action rule. When applied, it requires you to choose the same action for the remainder of the set, over the other rules in the plan-of-action.
Instruction diagrams
A plan-of-action will be accompanied by an instruction diagram. These are visual representations of the rules in a plan-of-action. Below are examples of how different types of rules are represented in instruction diagrams, each by an arrow pointing from the history with which a rule applies, and pointing to the action that should be played following that history.
For example, rules (a) and (b) together provide Example #1 from above.
Implementing a plan-of-action
A plan-of-action is a complete description of behaviour. This means it will always state an action to choose for any history of the set. As such, the history will always match one and only one rule in a plan-of-action's instruction diagram.
A plan-of-action is based on the set history. This means when an error occurs in one game (as described in Section 2), the plan-of-action in the next game responds to what was actually played as opposed to what was the intended choice.
Plan-of-action: Choose A in the first game. In subsequent games, choose A if in the last game you played B. Otherwise, choose B if in the last game you played A.
If you chose A in the first game, then:
- With 7/8 chance, no error occurs and A is what you played. The plan-of-action now states you should choose B in the following game
- With 1/8 chance, an error occurs that changes your action and B is what you played. The plan-of-action now states you should choose A in the following game
Section 4. Conditions across rounds
Each round, the conditions for the potential match and the interaction may change in the following two ways. You will be informed of the conditions at the start of each round.
Your counterpart's plan-of-action
In some rounds, your counterpart's plan-of-action is provided to you during the potential match. This means you will know how your counterpart will behave in the interaction, and you can choose a plan-of-action in response to this. In other rounds, your counterpart's plan-of-action will not be provided to you.
Your counterpart's plan-of-action is presented the same as your plan-of-action. For ease, your counterpart's instruction diagram will retain the same style as your instruction diagram. This means across both instruction diagrams, blue indicates your actions and red indicates your counterpart's actions.
Implementing your plan-of-action
In some rounds, your plan-of-action will be implemented automatically. This means in each set, you will choose your action each game by pressing a 'Next action' button that plays the next action as according to your plan-of-action.
In other rounds, you will be required to implement your plan-of-action yourself. This means in each set, you will be required to choose the correct action each game, by clicking on buttons or using keystrokes A or B. You will be required to implement your plan-of-action correctly. If you make a mistake by choosing an action different from your plan-of-action, you will receive a payoff of 0 points for that set (the other sets in the interaction will remain unaffected).
Summary
A brief summary will now be provided.
In Part II and Part III, the experiment is conducted in rounds. In Part III, each round has 5 potential matches which will pair you with a different, randomly selected counterpart each time. In each potential match you will choose a plan-of-action from two available options. One of these potential matches will then be selected as the interaction for that round.
The interaction consists of 5 sets played consecutively, with your actions determined by your chosen plan-of-action for that match. Each set is a series of games played consecutively, and the points for a set is the total points received in each game in that set. Your final payment for Part III is the total points across all 6 rounds, paid out at a rate of 50 points = $1.