Appendix A: Instructions
You are about to participate in an experiment in decision making.
During the experiment you will be asked to participate in 3 auctions of different types.
In each auction, a fictitious commodity is offered for sale to two participants.
Your partner for each auction will be randomly selected (by the experiment program) from the pool of participants. Your identity and your partner’s identity will be kept anonymous. The identity of your partner may change with the auction-type.
At the beginning of each auction you will receive a number representing your private value.
Specifically, at the beginning of each auction, your private value will be independently drawn from the set {50, 51, 52… 149,150} with every integer number between 50 and 150 being equally likely.
Your (anonymous) partner will similarly receive a private value independently drawn from the set {50,51, … 150}. You will not be informed of your opponent’s private value. Similarly, he/she will not be informed of your private value.
Your will be asked to participate in three auctions of the following types:
Type 1: One-bid Auction
In this auction you and your partner have to submit one bid; i.e., offer a single price at which you are willing to buy the commodity.
The bidder that has submitted the highest bid (among the two bidders) would win the commodity, pay his own bid, and receive his private value (representing the value of the fictitious commodity). The other bidder will not pay or receive anything.
For instance, if the first participant has bid A and the second bidder has bid B>A, and the private value of the second bidder is V then the second bidder would win the auction ending up with a payoff of V-B. The first bidder will win nothing.
If both bidders have submitted the same bid, then the identity of the buyer would be randomly determined (by flipping a fair coin) by the experiment program.
Type 2: Two bid Auction
In this auction you and your partner have to submit two bids; a high-bid and a low-bid; i.e., offer two prices at which you are willing to buy the commodity.
The bidder that has submitted the highest bid (among all four bids) will win the commodity and receive her private value (representing the value of the fictitious commodity). The price she will pay will be determined as follows:
-If the winner’s low-bid was higher than the high-bid of the other bidder, the winner would pay his low-bid
- Otherwise, the winner will pay his high-bid
The other bidder (the loser) would not pay or receive anything.
For instance, if the first participant has made a low bid of A and a high bid of B and the second participant has made a low bid of C and a high bid of D and D>C>B>A (so that the low-bid of the winner is higher than the high-bid of the loser) then the second bidder would win the auction and pay C for the commodity (ending up with a payoff of V-C, where V represents his private value)
If on the other hand D>B>C>A (so that the low-bid of the winner is lower than the high-bid of the loser) then the second bidder would win the auction but pay D for the commodity (ending up with a payoff of V-D)
If both bidders have submitted the same high-bid, then the identity of the buyer would be randomly determined (by flipping a fair coin) by the experiment program.
Type 3: Auction-type selection
In this type of auction you willbe asked to choose your favorite auction type: One-bid auction (type 1) or Two-bid auction (type 2). You willbe randomly matched (by the experiment software) with another participant that has chosen the same auction-type. Again, the identity of your partner will be kept anonymous. You will then play the corresponding auction (one-bid auction or two-bid auction) with your randomly selected partner as described above.
The Experiment Process
After you finish reading the instructions you will be asked to fill in a questionnaire with personal details.Then, you will be asked to participate in a one-bid auction. You will observe your private value and asked to submit a bid. The experiment willthen move on to the two-bid auction. Again, you will observe your (new) private value and asked to submit two bids: A high-bid and a low-bid as explained above. Finally, you will be asked to participate in an auction with type-selection. You will first observe your private value and asked to choose your favorite auction-type; you will then be asked to bid according to the type of auction you have selected. [1]
Previous-Auctions Data
During the experiment you will not receive any immediate feedback on the results of the three auctions in which you participate. The results of the auctions will be sent to your email address when we end the experiment.
However, in the course of each auction you will be able to excess an on-line database that contains the results of previous auctions of the same type. In the course of the one-bid auction, you will be allowed to inspect the results of previous similar one-bid auctions. In the course of the two-bid auction, you will be able to excess a database with the results of previous two-bid auctions. Finally, when you participate in an auction with type selection, you will be able to inspect (again) both databases: The one-bid auctions database and the two-bid auctions database.
The data for each database was recently collected in previous similar experiments and may help you understand the rules of the auctions and participants’ behavior in similar auctions in the past.
Upon clicking the database link you will receive a complete report of the results of a completed auction of the corresponding type. The report willdisclose the private values of both participants, the bids submitted (one bid per participant in the one-bid auctions; two-bids per participant in the two-bid auctions), the winner’s identity and the payoff of the winner. You may inspect the report for as long as you wish. You may then choose to inspect the results of another auction of the same type or return to the current auction.
Previous auctions-inspection is completely free and optional. You may choose to inspect as many auctions as you wish (upto 20 new auctions in the one-bid and two-bid stages of the experiment and an additional 10 auctions of each type at the auction selection stage). On the other hand, you are not requested to inspect any minimal number of auctions. On your discretion, you will be able to examine a summarizing report of the inspected-data by clicking the “summary of inspected-data” link.
The auctions that you inspect will be randomly retrieved from the database by the experiment software. In particular, the reports retrieved by your partner will not necessarily be similar to the reports you will retrieve yourself (even if both of you have decided to retrieve the same number of reports).
Actual Payoff
At the end of the experiment we will sum-up your payoffs in the three types of auctions and give you a check for the corresponding amount. If this is lower than 15 NIS, we will pay a guaranteed minimum of 15 NIS. A report with the first name of each participant and the four last digits of the participant’s id will be published on this site at the end of the experiment.
Appendix B: Auction selection screen[2]
Auction with type selection
Rules: You are first requested to choose between the two auction types (one-bid or two-bid auctions). You may inspect the two databases again (retrieve up to 10 more histories from each databases) before you chose your favorite type of auction. The summary of inspected –auctions screen (see link below) will enable you to reexamine all the inspected histories of each auction-type and observe the average payoff earned in each type of auction. After choosing your auction-type, you will be randomly matched with an (anonymous) partner that has chosen the same type of auction. You will then have to submit your bids according to the rules of the auction that you have selected
(click for complete version of instructions)
Click database with the results of previous one-bid auctions
to inspect the results of (up to 10 more) similar auctions
Click database with the results of previous two-bid auctions
to inspect the results of (up to 10 more) similar auctions
Clicksummary of inspected auctions
to examine all auctions that you have inspected
Your private value is:______
If you prefer the one-bid auction enter your bid here: _____
If you prefer the two-bid auction
enter your high bid here ___
enter your low bid here__
Appendix C: Equilibria of the one-bid and two-bid auctions
This appendix presents the symmetric CRRAM equilibrium strategies for the one-bid and two-bid auctions for the case whereindividual private values are independently drawn from the interval [50,150] and the utility function of each bidder takes the form for some [3]
The equilibrium bidding strategy for the one-bid auction has been used as a benchmarkfor analyzing actual behavior in many experimental studies. The symmetric equilibrium bidding-strategy (see, for instance, Cox, Smith and Walker, 1988) is . The equilibrium bidding function of risk-neutral bidders is therefore;where risk-averse bidders bid more aggressively than risk-neutral types and risk-seeking bidders submit lower bids than risk-neutral types in equilibrium.
The symmetric equilibrium bidding-strategies for the two-bid auction (see, Ivanova-Stenzel and Sonsino, 2004) are presented by the following expressions: and where
and
In particular, the equilibrium bidding functions of risk-neutral bidders are and . The equilibrium-bids of risk-averse bidders are higher than the corresponding bids of risk-neutral agents while the equilibrium bids of risk-seeking bidders are lower than the corresponding bids of risk-neutral types.
Ivanova-Stenzel and Sonsino (2004) moreover prove (propositions 2 and 3 in the paper) that:
(I) In equilibrium, the expected revenue of the seller from the one-bid auction is higher (lower) than the expected revenue of the seller from the two-bid auction when agents are risk-averse (risk-seeking).
(II) In equilibrium, the expected utility of a bidder with given valuation v from the two-bid auction is higher (lower) than his expected utility from the one-bid auction when the bidder is risk-averse (risk-seeking).
1
[1]This section was adjusted accordingly for the subjects that have started with the two-bid auction.
[2] The screens for the one-bid auction and the two-bid auction were similar; subjects could only approach the one-bid (two-bid) auctions database when playing the corresponding auction.
[3]We concentrate on the symmetric equilibrium to shorten the representation; extensions to the asymmetric case can be found in the references provided below.