Strategic Bidding for Risky and Ambiguous Lotteries

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Strategic Bidding for Risky and Ambiguous
Lotteries

• Stefan Trautmann (Erasmus U Rotterdam)
• June 29, 2007

joint with Martin Kocher (CREED, Amsterdam)
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motivation

• ambiguity aversion
• prefer prospect involving known probabilities
  (risky) to prospect with unknown probabilities
  (ambiguous), even if normatively equivalent
  (Savage)
• strong ambiguity aversion in individual decision
  experiments (choice, valuation)
• in real life decision few probabilities are known

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motivation

• Individual decision phenomenon
• Effect on market outcomes?
• Zeckhauser 2006 effect on market size and
  prices. low competition-excess returns
• Easley-OHara 2005 AA investors do not
  participate in market, effect on prices and
  risk-sharing
• But little empirical evidence of the effects of
  market structure under AA

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motivation

• existing literature
• second-price auctions strong AA (eg
  DiMauro-Maffioletti 2004)
• Sarin-Weber 1993, first-price auctions/ double
  auctions, repetition, still strong AA
• not surprising if preference, nothing to learn
  and indiv. dec. tasks used incentive compatible
  as well (BDM)
• surprising short selling doesnt help (Roca et
  al 2006, pessimism other way)

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motivation

• What about participation/selection issue?
• design market with selection
• ambiguity neutral can easily gain
• ambiguity averse also have incentive to buy
  ambiguous option
• look at expectations, effect of heterogeneity,
  correlation RA-AA

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experiment design (1)

• first unrelated experiment risky choice, social
  allocation choices, random lottery incentives
• before Ss learn their payoffs auction off one
  risky and one ambiguous lottery option to group
  of 20-24 Ss (Ellsberg two-color urn lotteries,
  risky50/50, bet on color)
• Ss could submit bid for either risky lottery or
  ambiguous lottery from own cash

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experiment design (2)

• 8 sessions, 176 subjects
• Prize in both lotteries 30 Euro, show-up 5 Euro,
  no advances from first part (17E)
• Risk attitude of save choices in six pairs of
  gambles from part I of experiment (3x gamble vs
  EV and 3x Wakker et al. 2007 population split
  gambles)
• Instructions/screens counterbalanced

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experiment results (1)

• 37 ambiguous choices, strong AA
• indiv markets 7x ambiguous market smaller, equal
  in one session, 14-50 amb, significant effect
  of AA
• Average transaction prices were equal risky
  lottery 9.30 vs ambiguous lottery 8.90
• Four times risky higher, four times ambiguous
  higher

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experiment results (2)

• equality of prices (176 obs)
• mean bids 4.30 (amb) vs 3.43 (risky),
• median bids 4.00 (amb) vs. 3.05 (risky)

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experiment results (3)

• Different market sizes, equal prices?
• Segmentation in terms of risk aversion?
• gt Subjects in risky market are more risk averse

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experiment results (4)

• Segmentation in terms of risk aversion
• Probit of market choice on risk attitude
  significant positive effect of risk attitude
• gt7-points less likely to take ambiguous for
  each risk averting choice in part I
• OLS of Bid on risk attitude significant negative
  effect
• gt 0.40 Euro less per risk averting choice

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experiment results (5)

• Winners risky market 3.375 risk averting
  choices, ambiguous market 1.75 risk averting
  choices (expected competition 77.5 vs 40)
• Market size higher transaction prices in larger
  markets for one lottery
• Expectations about competition well calibrated
  on average
• inverse effect on market choice, driven by
  highly RA (highly AA?) subjects

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discussion

• How do our results relate to Sarin-Weber 93
• Market segmentation with heterogeneous ambiguity
  attitudes
• Bidders in our ambiguous market (low RA-AA) would
  drive up prices for risky lottery in S-W
• Bidders in our risky market (high RA-AA) unlikely
  to affect prices for ambiguous lottery
• Small markets

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discussion (2)

• Correlation RA-AA in the literature
• gt Some find it (Bossaerts et al 2006,
  Lauriola-Levin 2001, Potamitis-Zhang 2007)
• Many find no correlation
• problems measurement error, mutual
• effects (ambiguous option may affect price
• of risky option for RA-AA if pos correlation)
• Market incentive for relatively amb. neutral
• no correlation found if second order prob
  instead of Ellsberg ambiguity !!?

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conclusion

1. ambiguity aversion persists in markets and has an
   effect on market size
2. heterogeneity in ambiguity attitude matters if
   market institution supports segmentation (budget
   constraints, cost of information collection)
3. found evidence for correlation between risk
   aversion and ambiguity aversion