Carmen Pasca and John Hey Social Choice Session 8 Carmen Pasca and John Hey

Experiments in Economics You may not yet have heard about experiments in economics. These are ways of testing economic theories ‘in the laboratory’ just like in the physical sciences. We take the theory as written by the theorists and reproduce it in the laboratory. We see if the theory works under its own conditions. If it does, good... ...if not we usually get some insight into how the theory needs to be modified.

Session 8: A public goods experiment Today we are going to try and implement a simple public goods experiment. This is going to be difficult because there are so many of you. We therefore need your cooperation and also we need you to imagine that all payments are for real. It is crucial that you remain quiet during the experiment and that you do not talk to anyone else... ... in a real experiment you would be sitting at screened computer terminals and would not be able to talk to each other. This is vital to the experiment as a test of the theory.

Session 8: A public goods experiment We therefore need your cooperation and also we need you to imagine that all payments are for real. We also need volunteers to be Row Captains who will record the decision of the students in that row. Row Captains will not actually participate in the experiment but they are important to its functioning. We give all Row Captains a form on which to record decisions. They are sworn to secrecy. How it works is that each student in a row tells the Row Captain what he or she wants to contribute to the Public Good by showing the Captain an entry on a form. This must be done privately and in silence.

Session 8: A public goods experiment Now we describe the experiment. We will play this five times. The same rules each time. Each participant (not the Row Captains) is endowed with 10 tokens. Each participant decides and tells the Row Captain privately how many of these 10 tokens he is going to keep for himself and hence how many he puts in the public pool. Each token kept for himself becomes 1 euro. The average amount put in the public pool is multiplied by 2 and given to all participants in euros. An example...

Session 8: A public goods experiment An example: suppose there are just 4 participants. Suppose they keep for themselves 0, 4, 6 and 10 and hence put into the public pool respectively 10, 6, 4 and 0. The average amount put in the public pool is 5 (=(10+6+4+0)/4). This multiplied by 2 is 10. Thus everyone gets €10 plus what they kept for themselves. So they respectively get €10, €14, €16 and €20. So person 1 put 10 in the public pool and got paid €10. So person 2 put 6 in the public pool and got paid €14. So person 3 put 4 in the public pool and got paid €16. So person 4 put 0 in the public pool and got paid €20.

Session 8: A public goods experiment How are we going to implement this? Each round each participant decides how to much to contribute to the public pool and privately tells his Row Captain – by showing the Captain the form filled in. The Row Captain adds up all the contributions of his/her row and tells us privately. We then work out what all participants will get from the public pool – which is twice the average contribution. All participants will fill in the form, that we have distributed, which records his contribution, the money he gets from the public pool and his earnings for each period. He can then work out his total earnings for each round.

Privacy Crucial to the theory and hence to the experiment is privacy: No participant knows what any other participant has contributed to the public good. The Row Captains may know but they are sworn to secrecy. On the Row Captain’s form there is a space for the name of the subject but we suggest you insert a pseudonym so that no-one knows what you contribute. Each participant should know his column number on the Row Captain’s form so that entries are correct. In a real experiment, the experimentalist would check that the earnings column is correct. Today we have to trust you.

This is the form subjects fill in Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Round Income Note: Column 2 must equal column 3 plus column 4 Amount kept for oneself Amount contributed to the public good Public Good – this is the average contribution multiplied by 2. You will be told this after everyone has decided Your Earnings = Amount kept for oneself + Public Good This column must equal column 3 plus column 5 1 10 2 3 4 5 6 7 8 9 11 12 13 14 15

This is the form Row Captains fill in Subject 1 2 3 4 5 6 7 Total contributions from Row = sum of columns Subject Name Round 8 9 10 11 12 13 14 15

An example of a subject form filled in Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Round Income Note: Column 2 must equal column 3 plus column 4. Amount kept for oneself Amount contributed to the public good Public Good – this is the average contribution multiplied by 2. You will be told this after everyone has decided. Your Earnings = Amount kept for oneself + Public Good This column must equal column 3 plus column 5. 1 10 6 4 16 2 8 5 7 3 15 25 18 The red column will be supplied by US!

Record Table of the experiment Round Total contributions to the Public Pool Average contributions (previous column divided by ???) Public Good (the previous column multiplied by 2). EVERYONE GETS THIS. 1 2 3 4 5 6 7 8 9 10

Session 8: A public goods experiment We expect playing this game in 5 rounds will take up to an hour of our time. We expect that contributions will get lower and maybe approach zero. This is not a good thing. We will discuss ways of getting contributions up... ... and perhaps try a couple of rounds with new rules... ...and see what happens. Suggestions?

Session 8: A public goods experiment Depressing?