The Encyclopedia of Economic Principals

Chapter 21

Experimental Markets, Learning, and Preference Elicitation

What experience, institutions and elicitation methods do to measured behavior.

Four of the chapter's worked examples, made interactive: a valuation gap that shrinks with experience, level-k reasoning in a guess-the-average game, a double auction against a sealed round, and a preference reversal. Change one value at a time and watch the figure, the numbers and the hand calculation respond.

Every example here is a constructed teaching example: it uses the hypothetical numbers of the chapter's worked examples, plus a few values added for comparison and labelled as such in each panel. Nothing here measures a real market, firm or household.

Demonstration 1 of 4

Experience shrinks the valuation gap

How much does trading experience narrow the gap between what owners ask and buyers offer?

The shaded band is the valuation gap. While the ask sits above the offer, no posted price can satisfy both sides at once. Experience pulls the two quotes together, from $8 apart to $2 apart.

Equation, written in LaTeX: A(0)=\$16-\$8=\$8.

Equation, written in LaTeX: A(10)=\$12-\$10=\$2,

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A is the valuation gap, the owners' minimum ask minus the buyers' maximum offer for the same card. Round 1 is novices; round 11 follows ten paid rounds with feedback. A trade needs a price no lower than the ask and no higher than the offer.

Predict first. At a $12 posted price, do novices trade?

Your prediction

Choose an example

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Figure: Experience shrinks the valuation gap. A price line from $6 to $18 with the buyers' offer at $8, the owners' ask at $16 and the shaded gap of $8 between them; the posted price $12 is a dashed line.
Round: Round 1 (novices), Posted price ($): $12
Constructed example: the chapter's hypothetical card market (asks $16 and $12, offers $8 and $10, posted price $12, midpoint $11); the $9 posted price is added for comparison.

Calculated values

Owners' ask
$16
Buyers' offer
$8
Valuation gap A
$8
Trade at posted price (typical quotes)
No

Novices (round 1): A = 16 - 8 = 8 dollars. At $12 no trade happens: owners want at least $16 and buyers pay at most $8. With these typical quotes no single price satisfies both sides; trades near the $12 midpoint need traders whose own quotes are closer than average. Experience shrinks the gap from $8 to $2, a fall of $6, but the average alone cannot separate learning from selection.

Worked steps

  1. A = ask - offer = 16 - 8 = 8
  2. Owners sell if 12 >= 16: no
  3. Buyers buy if 12 <= 8: no
  4. Midpoint of offer and ask = (8 + 16) / 2 = 12

Use the idea

Before reading a valuation gap as a stable preference, ask whether participants had relevant, paid, repeated experience, and track each person's gap to separate learning from exit.

Where the conclusion applies

Every participant values the card at $10, there are no fees, and the quoted ask and offer are the same for everyone in a round. A falling average may reflect selection, not learning.

Check your understanding: After ten rounds, what midpoint price splits the remaining gap?
(12 + 10) / 2 = $11.

Chapter 21 source: section "Market-experience effect".

Demonstration 2 of 4

Guess two thirds of the average

How do choices fall when players reason more steps about a guess-p-of-the-mean game?

Each extra step of reasoning multiplies the choice by p. With p below 1 the sequence falls toward zero, and observed rounds move the same way. With p = 1 any common choice is stable.

Equation, written in LaTeX: \bar{x}_1=\frac{50+40+35+30+25+18}{6}=33,

Equation, written in LaTeX: \bar{x}_2=\frac{99}{6}=16.5, t_2=\frac{2}{3}(16.5)=11.

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Six players choose numbers from 0 to 100; the prize goes to the choice closest to p times the mean. A level-0 player picks 50; a level-k player best responds to level k - 1, choosing 50 p^k. x-bar is a round's mean and t its target.

Predict first. Which first-round choice wins with p = 2/3?

Your prediction

Choose an example

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Figure: Guess two thirds of the average. Level-k choices for p = 2/3 at depths 0 to 3: 50.00, 33.33, 22.22 and 14.81. The depth-3 choice 14.81 is marked.
Multiplier p: 2/3, Reasoning depth k: 3
Constructed example: the chapter's hypothetical six-analyst contest (p = 2/3, both rounds of choices, and the p = 1 counterfactual); p = 1/2 is added for comparison.

Calculated values

Level-k choice
14.81
Round 1 mean
33
Round 1 target
22
Round 1 winner
25
Round 2 mean
16.5
Round 2 target
11

A level-3 thinker best responds to level 2: 50 x (2/3)^3 = 14.81. With p = 2/3 the mean falls from 33 to 16.5 between rounds: choices move toward the zero equilibrium without reaching it.

Worked steps

  1. Level-0 choice = 50
  2. Level 3 choice = 50 x (2/3)^3 = 14.81
  3. Round 1 mean = (50 + 40 + 35 + 30 + 25 + 18) / 6 = 198 / 6 = 33
  4. Round 1 target = (2/3) x 33 = 22, so 25 (3 away) wins
  5. Round 2 mean = 99 / 6 = 16.5, target = (2/3) x 16.5 = 11

Use the idea

When others are reacting to your forecast of them, estimate how many steps they reason, not only the equilibrium: real groups stop after one to three steps.

Where the conclusion applies

Level-0 play is centred at 50 and each level best responds to the one below. Real players mix depths, so round means fall more slowly than the level sequence.

Check your understanding: With p = 1/2, what does a level-2 thinker choose?
50 x (1/2)^2 = 12.5.

Chapter 21 source: section "Beauty-contest convergence".

Demonstration 3 of 4

Double auction versus sealed round

Does the trading institution change how much of the available surplus is realized?

The step curves cross where the next buyer's value falls below the next seller's cost. The continuous double auction lets traders revise until they reach that crossing; a single sealed round lacks that feedback. Each dot is a traded unit, drawn midway between its value and cost.

Equation, written in LaTeX: \$70+\$40+\$5=\$115,

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Four buyers each want one unit (values in dollars) and four sellers each have one unit (costs). Q* is the number of efficient trades and the price band is the range of prices that supports exactly Q* trades. In the sealed round each trader submits one bid or ask with no revision.

Predict first. How much of the $115 surplus does the sealed round realize?

Your prediction

Choose an example

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Figure: Double auction versus sealed round. Step demand from values 100, 90, 80, 70 and step supply from costs 30, 50, 75 and 95. The curves cross after 3 units; the price band $75 to $80 is shaded and 3 realized trades are marked with dots.
Institution: Continuous double auction, Third seller's cost ($): $75
Constructed example: the chapter's hypothetical market (values 100, 90, 80, 70; costs 30, 50, 75, 95; sealed bids and asks); third-seller costs of $60 and $85 are added for comparison.

Calculated values

Efficient quantity Q*
3
Maximum surplus
$115
Trades in this institution
3
Realized surplus
$115
Competitive price band
$75 to $80

Pairing the highest values with the lowest costs gives gains 70, 40, 5, -25, so Q* = 3 and maximum surplus is 70 + 40 + 5 = 115 dollars. Repeated bids and asks reach all 3 efficient trades, so the realized surplus is the full $115, however prices split it.

Worked steps

  1. Gains by pair: 100 - 30 = 70, 90 - 50 = 40, 80 - 75 = 5, 70 - 95 = -25
  2. Q* = 3 pairs with positive gains; maximum surplus = 70 + 40 + 5 = 115
  3. Price band: from 75 to 80
  4. The double auction trades all 3 efficient units: surplus 115

Use the idea

When a market leaves gains unrealized, look at the institution as well as the values and costs: allowing revisions and visible offers can recover the missing trades.

Where the conclusion applies

One unit per trader, known values and costs, and efficient pairs trading in the double auction. Sealed bids and asks are the book's and are held fixed when the third seller's cost changes; with an $85 cost the fixed $76 ask would sit below cost, but it crosses no bid, so the sealed result is unchanged.

Check your understanding: If the third seller's cost were $85, how many efficient trades and what surplus?
80 - 85 < 0, so Q* = 2 and surplus 70 + 40 = $110.

Chapter 21 source: section "Double-auction convergence".

Demonstration 4 of 4

Choice and price disagree

Can the lottery a person chooses differ from the one she prices higher?

The bars are expected values and the diamonds are stated prices. A reversal occurs when the direct choice and the pricing task rank the same pair differently, whatever the expected values.

Equation, written in LaTeX: \operatorname{EV}(P)=0.80(\$30)=\$24,

Equation, written in LaTeX: \operatorname{EV}(D)=0.25(\$100)=\$25.

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Lottery P pays $30 with probability 0.80; lottery D pays $100 with the chosen probability. EV is expected value. CE is the stated minimum selling price, elicited with an incentive-compatible procedure. Elena chooses P in a direct choice.

Predict first. Does the higher-EV lottery also get chosen directly?

Your prediction

Choose an example

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Figure: Choice and price disagree. Bars for expected value: P $24, D $25. Diamonds mark stated selling prices $20 for P and $28 for D. A reversal is shown.
Win probability of D: 0.25, Stated selling price of D ($): $28
Constructed example: the chapter's hypothetical lotteries (P: $30 at 0.80; D: $100 at 0.25; stated prices $20 and $28; choice P); D probabilities 0.2 and 0.3 and a $18 price are added for comparison.

Calculated values

EV(P)
$24
EV(D)
$25
Direct choice
P
Pricing ranks first
D
Reversal
Yes

EV(P) = 0.80 x 30 = 24 and EV(D) = 0.25 x 100 = 25 dollars, so expected value favours D. Elena chooses P directly, but prices P at $20 and D at $28, so pricing ranks D first. Choice and pricing disagree: a preference reversal.

Worked steps

  1. EV(P) = 0.80 x 30 = 24
  2. EV(D) = 0.25 x 100 = 25
  3. Stated prices: CE(P) = 20, CE(D) = 28, so pricing ranks D first
  4. Direct choice ranks P first: reversal

Use the idea

When designing a survey or a valuation, check whether choice questions and price questions rank options the same way before treating either as the true preference.

Where the conclusion applies

Elena's direct choice and her price for P are fixed at the book's responses; only D's win probability and stated price vary. Expected value is shown for reference, not as her utility.

Check your understanding: If D's selling price were $18, would there still be a reversal?
CE(P) = 20 > 18, so pricing ranks P first, agreeing with choice; no reversal.

Chapter 21 source: section "Preference reversal".