Decision-making without Probabilities

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Decision-making without Probabilities

• FUR XII
• Rome, 26th June, 2006
• Jack Stecher, Radhika Lunawat
• Kira Pronin, John Dickhaut

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Issue

• How do agents make choices when they only have
  information in the form of ranges?
• Motivation historically, individuals have kept
  track of and compared ranges of outcomes, even
  before probability was part of anyones
  vocabulary
• We test two models of individual choice behavior
  where information is in the form of ranges

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Experiment

• 1 seller, 4 potential buyers, bid for a
  financial asset where possible return given in
  form of a range

1 2 3 4 5
Seller has 1000 fr to invest Possible return (-0.1, 0.5) Seller invests S0 New information to seller Possible return (?, ?)?(-0.1, 0.5) Seller decides reservation price based on information received in step 2 Buyers learn ?and S0 Possible return (?, 0.5) Buyers privately decide what to bid in a first-price sealed bid auction. Buyers can bid up to 1500 fr.
Note 4 fr 1 Canadian cent
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Claims

• 3 types of behavior
• Consistent with expected utility maximization
• Consistent with interval-based preference theory
• Inexplicable
• Results most often consistent with
  interval-based preference theory

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Expected Utility Theory

• Simplest case Risk-neutrality (can be
  generalized)
• Seller decides on initial investment all or
  nothing, depending on sign of E(?)
• Seller sets reservation price to expected value
• Buyer learns ?? (?, 0.5)
• Buyer foresees that any winning bid will have
  negative expected value ? Bids in 0, (1?) S0
• 4. Market prediction NO TRADE

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Interval-based preference theory

• General idea Choices and market prices are based
  on intervals
• Sellers can invest anything in the interval
  between 0 and 1000
• Reservation price is in the interval between
  (1?) S0 and (1?) S0, with ? lt 0.5
• Bids are in the interval between (1 ?)S0 and
  (1.5)S0
• Trade can occur in this range.

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Bid Intervals
Expected utility - Buyer
Interval-based Pref. - Buyer
Inexplicable
0.9S0
(1?)S0
0
1.5S0
1500
(1?)S0
Lowest possible ex ante value
Ex post lower bound for buyer/seller
Highest possible ex ante value
Highest possible bid
Ex post upper bound for seller
Sellers reservation price
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Remarks about the Experiment

• The experiments were run in Canada at CIRANO
  Research Institute, with 20 subjects in 4 groups
  of 5, who played this game for 20 rounds per
  group. Subjects earned from C20.75 C30, plus
  C10 show-up.
• The sellers average investment was typically NOT
  all or nothing
• Sellers investment was 0 only once (1.4)
• Sellers invested their full endowment, 1000 fr,
  14 times (19.7)
• This was consistent with Interval-based
  Preference Theory but not with risk-neutral
  Expected Utility maximization.

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Results Buyers Bids
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Results Market Prices
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Summary

• When given information in the form of ranges,
  individuals tend to behave consistently with
  interval-based preference theory rather than how
  expected utility theory predicts
• However, a core group behaved consistently with
  expected utility maximization