Elicited bid functions in (a)symmetric first-price auctions



Appendix 1 - Instructions

Brief Outline

Each of you is about to particpate in a series of 100 auctions.

In each auction, you are randomly matched with one other participant whose identity is unknown to you.

In each auction, a hypothetical item is sold either to you or to the other participant.

You receive the item if your bid is the higher bid submitted.

You make a gain (profit) if you receive the item and if your bid is smaller than your resale value.

The resale value for each of the 100 items that you will bid for is randomly drawn from a given range.

Bidder Types

Before the experiment starts, each participant draws a card that detrmines her/his type : You will either be a A-
type or a B-type bidder.

Your type remains the same throughout the experiment.

If you are a A-type, in each auction, your resale value is drawn with an equally likely chance from the range
[0 ;100].

If you are a B-type, in each auction, your resale value is drawn with an equally likely chance from the range [-
100 ;100].

A A-type bidder is always matched with a B-type bidder and vice-versa.

Submitting the Bid Function

A bid function specifies a bid for every possible resale value between 0 and 100. A bid cannot be greater than its
corresponding resale value.

Your bid function always consists of 2 lines connecting the 3 points B0, Bv and Bmax.

. The point B0 specifies the bid that you submit if you receive the resale value 0. This bid is always equal to 0.

. The point Bv specifies the bid you submit if you receive the resale value v, which is any arbitrary value
between 1 and 99.

. The point Bmax specifies the bid you submit if you receive the resale value 100.

. The bid that you submit if you receive a resale value between 0 and v is determined by the line connecting B0
and Bv. Similarly, the bidthat you submit if you receive a resale value between v and 100 is determined by the
line connecting Bv and Bmax.

Your task is to choose Bv and Bmax at the outset of each auction, before your resale value is drawn.

Each bidder knows his own bid function but not the one of the other participant.

Resale Values and Bids

After you have chosen your bid function, your resale value for the current auction is randomly drawn.

Once your resale value is drawn, one of the following two situations occurs :

If your resale value is smaller than 0 (which can happen only to B-type bidders), you cannot submit a bid.

If your resale value is greater or equal to 0, your bid is determined by your bid function and is automatically
submitted.

Awards

If only one of the bidders could submit a bid, she/he is awarded the item.

If both bidders could submit a bid, the one with the higher bid is warded the item.

If both bidders submit the same bid, one of them will be randomly chosen (each with probability of one half) to
be awarded the item.

The bidder who is awarded the item makes a gain which is equal to his resale value minus the bid.

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