An experiment on deception, reputation and trust

An experiment is designed to shed light on how deception works. The experiment involves a twenty period sender/receiver game in which period 5 has more weight than other periods. In each period, the informed sender communicates about the realized state, the receiver then reports a belief about the state before being informed whether the sender lied. Throughout the interaction, a receiver is matched with the same sender who is either malevolent with an objective opposed to the receiver or benevolent always telling the truth. The main findings are: (1) in several variants (differing in the weight of the key period and the share of benevolent senders), the deceptive tactic in which malevolent senders tell the truth up to the key period and then lie at the key period is used roughly 25% of the time, (2) the deceptive tactic brings higher expected payoff than other observed strategies, and (3) a majority of receivers do not show cautiousness at the key period when no lie was made before. These observations do not match the predictions of the Sequential Equilibrium and can be organized using the analogy-based sequential equilibrium (ABSE) in which three quarters of subjects reason coarsely. Electronic supplementary material The online version of this article (10.1007/s10683-020-09681-9) contains supplementary material, which is available to authorized users.


Instructions -Senders (translation)
You are going to take part in an economic experiment. Depending on the decisions you make, you will be able to receive a certain sum of money which we will pay you at the end of this experiment.
This experiment will be conducted over five sessions which you will take part in one after the other. The participants in the experiment will have two different roles: experts or decisionmakers. You will be taking the role of expert and the participants joining us will be decisionmakers. In each of the sessions, each expert will be partnered with a decision-maker.
Each session is composed of 20 periods. During each of these 20 periods, your earnings will depend on which side a coin has fallen (0 on one side and 1 on the other) and on the choice made by the decision-maker you are matched with throughout the session (you are matched with the same decision-maker for the 20 periods of a session, but change your matched decision-maker every session). The further away the decision-maker's choice, a value between 0 and 1, is from the value obtained in the throw (0 or 1), the higher your earnings during a period.
Each period will be conducted as follows. The computer throws a virtual coin. On one side of this coin is a 0 and on the other a 1. This coin is not fixed -it has a ½ probability of falling 1 side up and a ½ probability of falling 0 side up. Furthermore, in each session the coin is thrown independently. As the expert, you are notified which side the coin has fallen on, whereas the decision-maker you are partnered with is not. After you have been notified which side the coin has fallen on, you must choose which of the following messages you are going to send to the decision-maker you are matched with: "The coin has fallen 0 side up" or "The coin has fallen 1 side up". So you can choose to send information which is either correct or incorrect. The system has been designed so that during each session, you will have to send correct information 9, 10 or 11 times throughout the 20 periods and, during the other periods, incorrect information. The computer will show you at the beginning of the session how many times you must send correct information for the current session.
The following procedure is carried out during a period: 1. The computer throws the coin. You, the expert, are notified which side the coin has fallen on, but the decision-maker you are matched with is not.
2. You choose a message to send to the decision-maker: "The coin has fallen 0 side up" or "The coin has fallen 1 side up". The correct information choice will appear on the screen in green and the incorrect information choice will appear in red. This screen will also show you the number of correct messages and incorrect messages you have left to send. 3. The decision-maker you are matched with makes a decision. This decision is the choice of a value between 0 and 1. 4. The decision-maker is notified which side up the coin has actually fallen (and finds out if you sent correct or incorrect information during this period). 5. The computer calculates the earnings for that period and the following period can begin (except during period 20 where it is necessary to wait until all the expert/decision-maker pairs have finished their 20 periods to be able to start the next session).
In order to better anticipate their decisions and reactions, here is some information about the decision-makers you may be matched with, and your earnings, too.
A decision-maker's earnings in tokens are calculated in such a way that, at the end of each period, the closer his decision is to the side the coin has fallen on, the higher his earnings. The earnings in tokens will be changed into earnings in Euros according to different rules for the experts and the decision-makers (Cf. below).
In each period, the amount of your earnings in tokens and that of the decision-maker you are matched with is equal to 100. So the closer the decision-maker's decision is to the value of the side the coin has fallen on, the higher his earnings in tokens and the lower your earnings. Vice versa, the further away the decision-maker's decision is to the value of the side the coin has fallen on, the lower his earnings in tokens and the higher your earnings.
To be more precise, the earnings during a period are calculated as follows. Let's suppose that the value of the decision made by the decision-maker you are matched with is "D". Finally, the expert/decision-maker pairings are formed as follows. During each session, there is a 4/5 probability of every decision-maker being matched with your type of expert, "human", who sends incorrect information on average 10 times over the 20 periods in a session, (without knowing the form of such an expert's earnings) or a 1/5 probability of being matched with a "machine" type of expert (a computer program) which will give him correct information about the side the coin fell on each period. The decision-makers know about these 2 partnership possibilities and the 2 probabilities (4/5 and 1/5).
As the "machine' type of expert always sends correct information, at the end of the first period during which you have sent incorrect information, when the computer notifies the decisionmaker that you have sent incorrect information (at the end of the period in question), it will reveal that you are your type of expert (sending an incorrect message on average 10 times out of 20) and not a "machine" expert always telling the truth. NB: the match for each period are anonymously and randomly formed. Neither you nor the decision-makers will ever know who you have been partnered with. At each new session, a new expert/decision-maker pairing is formed.

Final information:
Your earnings for each period are counted in units of account we will call tokens. At the end of the experiment, the amount of tokens you have won during all the periods will be calculated by the computer and your earnings in tokens will be converted into earnings in Euros, with an exchange rate of one token being equal to 0.45 centimes. NB: the value of the token for a decision-maker is 0.15 cents, so that the payments both decision-makers and experts receive are of the same order.
Not all the periods in a session have the same importance. A weighting is given to each period. All the periods have a weighting of 1 except one which has a weighting of 5 -Period 5. The earnings during a period are multiplied by the weighting of this period to determine the number of tokens won during this period. This period is therefore 5 times more important than the others from an earnings standpoint. Furthermore, during the sessions, the table at the bottom of the screen will display the weighting of every period, the messages that you have already sent (indicating if they are correct or not) and the decisions taken by the decision-maker you are matched with as well as the earnings you have received during the previous periods.

Instructions -Receivers (Translation)
You are going to take part in an economic experiment. Depending on the decisions you make, you will be able to receive a certain sum of money which we will pay you at the end of this experiment.
This experiment will be conducted over five sessions which you will take part in one after the other.
Each of these sessions is composed of 20 periods. During each of these 20 periods, your earnings will depend on the side on which a coin has fallen (0 on one side and 1 on the other) and on your decision. Your earnings during a period will be higher the closer your decision, D, is from the value obtained in the throw (0 or 1). Please note that the weighting of each of the periods is not the same (Cf. description below).
At the time you have to make your decision, you will not have been notified which side the coin has fallen on. Nevertheless, you will have a certain amount of information. The throws will take place as follows. During each of the periods, the computer throws a virtual coin. On one side of this coin is a 0 and on the other a 1. This coin is not fixed -it has a ½ probability of falling 1 side up and a ½ probability of falling 0 side up. The throws of the coin for each of the periods are independent (meaning that during a period, if the coin falls 1 side up, it does not make it more likely that it will fall 0 side up in the next period). In order to direct you, you are matched during each of the 20-period sessions by an "expert" (you will stay with the same expert during the 20 periods of a session but will change expert for each of the five sessions). An expert is always perfectly informed of the value of each period's throw. At the beginning of each period, before you make your decision, your expert will send you one of the two following messages: "The coin has fallen 0 side up" or "The coin has fallen 1 side up". There are two types of experts, Type A experts and Type B experts. A Type A expert is a computer program which has been programmed to always send you correct information. A Type B expert is an individual person and on average he sends correct information half of the time (he is obliged to do so). That means that he communicates the correct value of the throw 10 times out of 20, and an incorrect value the other 10 times (it is an average and it is not certain that over the 20 periods, a Type B expert lies exactly 10 times). At the beginning of each session, there is a 1/5 probability of you being matched with a Type A expert and a 4/5 probability of you being matched with a Type B expert. You do not know which type of expert you have.