Economic Classroom Experiments/The Wallet Game

Hand Run Version
Students bid for an object in a first-price auction. Each receives an independently drawn signal of the value of the object. The actual value is the sum of the signal.

Objectives for learning (Intended Learning Outcomes)

 * 1) Strengthening understanding of rules behind first-price auction.
 * 2) Concept of common value auction but private information about value.
 * 3) Intuition behind Bayes’ Rule. (Given that you win, the value of the others’ signals are lower.)
 * 4) Understand of the Winner’s curse.

Suitable modules.
Financial Markets and Decisions, Advanced/MSc Micro.

Level (year of programme):
Third year or MSc or MBA.

Prerequisite knowledge:
Knowledge of first price auctions.

Procedures/tips for instructors
Divide students in three groups (or how many bidders you want). Give the students index cards with randomly drawn signals [0,10] written on them. (You can get these from random numbers excel file.) Write their group (A,B or C) on the card for them (they may forget). Have them write their bids on the cards. Collect the cards and show bids, signals on the board. Determine winner and profit of the winner. Repeat one or two times.

Tip. You may want to write 4 numbers per card and randomly choose one to count. Worthwhile to write all 4 bids on the board and chose the one that counts after all numbers are displayed. (The random selection process can be done by flipping a coin twice (HH is 1, HT is 2, TH is 3, TT is 4) or writing the numbers 1 to 4 on the slips of paper and have one student select the winner.

Tip. For excitement you can pay (or get paid) for the winner. Use a conversion such as winnings are divided by 10 and given in pounds.

Tip. Group sizes should not be larger than 3 to 4 students. For larger classes, either increase the number of groups in the game or randomly select a subset of groups that count in the experiment. For instance if the class size is 60, you can have 20 groups of 3 and select 4 of these 20 groups to count (writing the bids on the board and the value is the sum of only these 4 groups).

The equilibrium bidding is described by $$b=\frac{(N+2)(N-1)}{2N}\cdot V$$ (see slides for derivation). For N=2, this is just b=V.

Topics/questions for class discussion
Can be described as a takeover battles where bidder 1 knows the value of one of the target's divisions and bidder 2 knows the value of the other division.

Myopia would have one think the value is $$N \cdot V$$ and bid $$(N-1)/N$$ times this equals $$(N-1)\cdot V$$. Actual expected value is $$(N-1)\cdot {V\over 2}+V=(N+1)\cdot {V \over 2}$$. Another possibility is that expect everyone else’s signal to be ½ times highest possible signal. Then using the above analysis expected value is $$V+{1\over 2} \cdot 10\cdot (N-1). $$ Hence, in both cases there could be a winner’s curse.

As N increases, your information becomes less useful, however, the competition becomes fiercer. If true value were average of the signals (rather than sum), then a graph of bid/V vs. N looks like. The above graph shows that competition increases bids for smaller N, Winner’s curse hurts bids more for higher N.

What happens when N is large? Your bid approaches the expected value of the object if you win.

Instructions for students.

 * You know how much money is in your wallet.
 * You do not know how much money is in the wallet of others.
 * Each wallet has money is drawn uniformly on [0,10].
 * We will run a first-price auction on the sum of three wallets (including yours).

also see slides.

Results and feedback:
Most groups bid $$3+0.8\cdot V$$, i.e., overbidding for all signals but particularly for low signals.

Computerized Experiment
Students bid for an object in a first-price auction. Each receives an independently drawn signal of the value of the object. The actual value is the average of the signals.

Procedure
This experiment is run on Charlie Holt’s website. See tip sheet for his website.

For an introduction see http://veconlab.econ.virginia.edu/cv/cv.php

To set up a session http://veconlab.econ.virginia.edu/cv/cv_admin_login.php

The equilibrium bidding is described by $$b=\frac{(N+2)\cdot(N-1)}{(2N\cdot N)} \cdot V$$ (see slides for derivation). For $$N=2$$, this is just $$b=V/2$$.

Further reading:

 * Auctions with Almost Common Values: The "Wallet Game" and its Applications European Economic Review, 1998. Paul Klemperer. http://www.nuff.ox.ac.uk/economics/papers/1998/w3/wallwebb.pdf


 * Ch. 21 of Webgames and Strategy: Recipes for Interactive Learning, Charles Holt, forthcoming, Addison-Wesley, 2006.
 * Holt and Sherman (2000), ""Risk Aversion and the Winner's Curse,"," Working Paper, University of Virginia. http://www.people.virginia.edu/~cah2k/wincurse.pdf

This page was first created by Toddkaplan 10:07, 9 April 2007 (UTC)