Endowment as a Blessing
1
Sivan Frenkel
Yuval Heller
2
Roee Teper
3
1 Center for the Study of Rationality, Jerusalem 2 Nu eld College & Dept. of Economics, Oxford 3 Department of Economics, Pittsburgh August 2012, Malaga
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Introduction
Outline
1
Introduction
2
Trade Game
3
2-Stage Game & Evolution A Basic 2-Stage Game Partial Cursedness and Co-Evolution of Biases
4
Concluding Remarks
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Introduction
Behavioral Biases
Evidence about systematic deviations from payo maximizing behavior with important economic implications.
Question
Why evolutionary competitive forces select sub-optimal behavior? How did these biases evolve?
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Introduction
The Endowment Eect
People place higher value on an object once they own it. I Observed in various experimental setups (mugs; lotteries...). F
Thaler, 1980; Kahneman, Knetsch & Thaler, 1990; Knetsch, Tang & Thaler, 2001
I Field evidence in housing market F
Genesove & Mayer, 2001; Bokhari & Geltner, 2011.
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Introduction
Winner's Curse Individuals do not fully take into account the informational content of other players' actions. Winners in common-value auctions tend to overpay I
Capen, Clapp & Campbell (1971), Bazerman & Samuelson, 1983; Kagel & Levine, 1986, 2002;
Bilateral trade with private information (lemon market) I
Samuelson & Bazerman (1985), Ball, Bazerman & Carroll (1991).
Field evidence in several contexts I
Corporate takeovers (Roll, 1986); real-estate auctions (Ashenfelter & Genesove, 1992).
Eyster & Rabin (2005): solution concept in Bayesian games.
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Introduction
Any Relation?
Endowment eect and cursedness seem unrelated. Our results: I Each eect corrects the errors caused by the other in various
interactions. I They correct each other in simple trade interactions that were common
in primitive societies. I Mutual compensation can explain why both biases survived natural
selection.
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Introduction
Trade in Primitive Hunter-Gatherer Societies
Anthropological literature suggests barter to be an important interaction: Trade was based on localization of natural resources and tribal specializations. Tribes devoted much eort in producing their own special goods and trading them. Barter had substantial in uence on consumption and tness Herskovits, 1952; Polanyi, 1957; Sahlins, 1972; Haviland et al., 2007.
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Introduction
Evolutionary Literature Evolutionary foundations for behavioral biases I
Samuelson (2004): consumption eect; Robson & Samuelson (2007, 2009), Dasgupta & Maskin (2005): time preferences; Heller (2011): overcon dence.
Indirect evolution of preferences I
Güth & Yaari (1992); Heifetz, Shannon & Spiegel (2007); Dekel, Ely & Yilankaya (2007); Winter et al. (2011).
Evolution of the endowment eect to improve toughness in bargaining I
Heifetz & Segev (2004); Huck, Kirchsteiger & Oechssler (2005).
Evolution yields only second-best adaptations: I
Kahneman & Lovallo (1993); Waldman (1994); Ely (2011). 8 / 29
Trade Game
Outline
1
Introduction
2
Trade Game
3
2-Stage Game & Evolution A Basic 2-Stage Game Partial Cursedness and Co-Evolution of Biases
4
Concluding Remarks
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Trade Game
The Trade Game
2 traders
N = {1, 2}.
Each trader owns an indivisible good. Each trader
i ∈ {1, 2} privately observes his valuation of the good xi .
,
I x1 x2 are independent uniform random variables.
I Notations:
µ ≡ E (x ) i
and
µ< ≡ E (x |x < y ) . y
i
i
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Trade Game
The trade game (cont.)
Public signal
α ≥1
represents surplus coe cient of trade.
I Independent of x and x 1 2
.
I Arbitrary distribution with large enough support.
Each trader
i ∈ {1, 2}:
I Values his own good by
x. i
I Values his partner's good by
α · x−
i
.
Traders simultaneously declare whether they would like to trade or not. Trade takes place if (and only if ) both choose to trade.
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Trade Game
Benchmark I: Nash Equilibrium Traders are fully rational.
Proposition (Nash Equilibrium) Unique equilibrium (except the Pareto-inferior no-trade equilibrium). Trader i accepts trade i xi < x ∗ (α), where: x ∗ (α) = α µ
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Trade Game
Benchmark II: Cursed Equilibrium Traders are fully cursed: believe that partenr's action & signal are independent.
Proposition (Cursed Equilibrium in Dominant Strategies) Unique fully-cursed dominant strategy. Trader i accepts trade i: xi < x c (α) = α µ. x c (α) = unconditional expected value of partner’s object. Cursed traders make a systematic mistake agree too much to trade.
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Trade Game
Benchmark III: NE with Endowment Eect Both traders have a speci c
endowment eect:
trader believes the value of his object to be
after observing a signal
ψ(x ),
where
x, a
ψ(x ) > x .
Proposition (Nash Equilibrium with Endowment Eect) Trader i accepts trade i xi < x e (α) where: ψ [x e (α)] = α µ
x e (α) is too low. 14 / 29
Trade Game
Conclusion from Benchmarks
x ∗ (α) = α µ
x e (α) = f −1 α µ
x ∗ (α) < x c (α) ⇒ cursedness results in excess acceptance of trade. x e (α) < x ∗ (α) ⇒ endowment eect results in excess rejection of trade. L
xe
x*
xc
H
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2-Stage Game & Evolution
Outline
1
Introduction
2
Trade Game
3
2-Stage Game & Evolution A Basic 2-Stage Game Partial Cursedness and Co-Evolution of Biases
4
Concluding Remarks
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2-Stage Game & Evolution
A Basic 2-Stage Game
Outline
1
Introduction
2
Trade Game
3
2-Stage Game & Evolution A Basic 2-Stage Game Partial Cursedness and Co-Evolution of Biases
4
Concluding Remarks
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2-Stage Game & Evolution
A Basic 2-Stage Game
2-Stage Game Two players in each stage: 1st stage:
rational
principals play a perception game
(interpretation: natural selection). Each principal is associated with a trader and bene ts from his payo. Principals choose a perception for their agents (inc. mixed strategies). 2nd stage:
fully cursed perception bias ψi
agents play a trade game endowed with a .
Then biased traders play the unique fully-cursed dominant strategy, given his perception bias.
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2-Stage Game & Evolution
A Basic 2-Stage Game
Equilibrium of the Perception Game Proposition (Equilibrium of the Perception Game) Symmetric Nash equilibrium: ψi∗ (x ) =
µ · x > x. µ
Moreover, this equilibrium is: (1) unique; (2) dominance solvable; Cursed traders + EE
⇒
as-if rational behavior.
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2-Stage Game & Evolution
A Basic 2-Stage Game
Evolutionary Interpretation A population of cursed agents. Each agent has a type = gene = perception bias. Each generation agents are randomly matched and play the trade game. Payo from trade = tness.
Heifetz, Shannon & Spiegel (2007, ET), Theorem 1 ⇒
if a game
is dominance-solvable, then the population converges to a unit mass at the unique dominance-solvable equilibrium.
Corollary Any distribution of perception biases (with full support) will converge in the long run to a unit mass on ψ ∗ . 20 / 29
2-Stage Game & Evolution
Partial Cursedness and Co-Evolution of Biases
Outline
1
Introduction
2
Trade Game
3
2-Stage Game & Evolution A Basic 2-Stage Game Partial Cursedness and Co-Evolution of Biases
4
Concluding Remarks
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2-Stage Game & Evolution
Partial Cursedness and Co-Evolution of Biases
Partial Cursedness and Co-Evolution of Biases
The model has two restrictive and unnatural assumptions: I Cursedness is not aected by evolution. I Final population is homogeneous.
We therefore extend the basic model, and allow both biases to evolve together.
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2-Stage Game & Evolution
Partial Cursedness and Co-Evolution of Biases
An Extended Two-Stage Game
1st stage each principal
(χi , ψi ) ψi
where
χi
i
chooses distribution
ζi
over pairs of biases:
is the cursedness level (Eyster and Rabin, 2005), and
is the perception bias. I Partially cursed agent underappreciates the relation between his
opponent's strategy and type.
2nd stage Traders play a
cursed-biased equilibrium:
I Given his biases, each trader
i
best-responds to the distribution
ζ−
i
.
I Opponent's biases are unobservable.
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2-Stage Game & Evolution
Partial Cursedness and Co-Evolution of Biases
Equilibrium of the Two-Stage Game
For each 0
≤χ ≤1
consider the speci c perception bias:
ψχ∗ (x ) = χ · ψ ∗ (x ) + (1 − χ) · x . ψχ∗ (x )
presents the endowment eect for all
χ;
The endowment eect is strictly increasing in A trader of type
χ, ψχ∗
χ;
uses the NE threshold
x ∗ (α) when facing
rational behavior.
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2-Stage Game & Evolution
Partial Cursedness and Co-Evolution of Biases
Equilibrium of the Two-Stage Game (cont.)
De ne:
Γ=
n
o χ, ψχ∗ : χ ∈ [0, 1] .
Proposition A symmetric pro le ζ is a n Nash equilibrium of the perception game i its o ∗ support is a subset of Γ = χ, ψχ : χ ∈ [0, 1] .
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2-Stage Game & Evolution
Partial Cursedness and Co-Evolution of Biases
Evolution of Both Biases Population with many agents. Each generation agents are randomly matched and each couple plays the trade game. Each type (gene) determines both perception (ψ ) bias and cursedness level ( χ ). Types are unobservable.
Corollary
Assume that the initial distribution of biases has full support, and that it converges in the long run to a distribution ζ . Then the support of ζ is a subset of Γ. Population is heterogeneous in the long run. Positive correlation between the levels of two biases.
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2-Stage Game & Evolution
Partial Cursedness and Co-Evolution of Biases
Evolution of Both Biases Example
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Concluding Remarks
Outline
1
Introduction
2
Trade Game
3
2-Stage Game & Evolution A Basic 2-Stage Game Partial Cursedness and Co-Evolution of Biases
4
Concluding Remarks
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Concluding Remarks
Concluding Remarks
Endowment eect can serve as a blessing that xes the Winner's Curse. An explanation why these biases have survived Natural Selection. Demonstrates that biases can't be studied only one at a time. Main prediction: Positive correlation between the intensity of endowment eect and the cursedness level that an individual exhibits. Future research: test this prediction experimentally.
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