The Endowment Eect as a Blessing Sivan Frenkel (HUJI), Yuval Heller (Oxford), Roee Teper (Pittsburgh)

Lund (April, 2016)

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Introduction

Outline 1

Introduction

2

Basic Model

3

Results

4

Extended Model

5

Results (Extended Model)

6

Discussion

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Introduction

Background Evidence suggests that people have systematic deviations from payo maximizing behavior; these biases have economic implications. I The biases cannot be fully attributed to complexity costs.

Our model focuses on two specic biases: I Endowment eect - People place higher value on an object once they

own it (mugs, lotteries, housing market; Thaler, 1980; ...). I Winner's Curse - Individuals do not fully take into account the

informational content of other players' actions (e.g., common value auctions, lemon market;

Frenkel, Heller, Teper

Kahneman et al., 1990; Eyster & Rabin, 2005)

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Introduction

Background The evolutionary research approach: I Individuals base their choices on heuristics (rules of thumb). I Dierent heuristics compete in a process of cultural learning. I Understanding how biases survive competitive forces can help achieve

better understanding of the biases and their implications.

Most of the existing literature studies a single bias. I The stylized main result (e.g., Dekel, Ely, Yilankaya., 2007): Biases can

be stable only if an agent's bias is observed by the opponent.

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Introduction

Research Objectives 1

Studying how seemingly unrelated biases can be stable in a competitive environment by approximately compensating for the errors that any bias yields in isolation.

2

Showing that unobservable biases can be stable, and induce non-payo maximizing behavior.

3

Developing a plausible family of non-monotonic selection dynamics.

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Basic Model

Outline 1

Introduction

2

Basic Model

3

Results

4

Extended Model

5

Results (Extended Model)

6

Discussion

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Basic Model

Overview Large population of agents who interact in barter trade. Agent's type determines his (unobservable) biases: (1) perception bias, (2) cursedness. Agents subjectively best-reply to the aggregate behavior. Payo-monotonic dynamic: More successful types become more frequent (cultural learning or biological evolution). Rarely a few agents experiment with a new type (mutants). Objective: characterize stable states of the population in the long run.

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Basic Model

Barter Trade Interaction Each of two traders owns a dierent kind of indivisible good. Each trader I

x1 , x2

i ∈ {1, 2}

privately observes his valuation of the good

are i.i.d. continuous variables with a full support over

Public signal

α ≥1

xi .

[L, H].

represents surplus coecient of trade.

I Trader 1's good is worth

α · x1

to trader 2.

I A continuous distribution with a large support.

Goods are exchanged if both traders agree.

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Basic Model

Types (Biases) Each agent is endowed with a pair of biases:

χ ∈ [0, 1]

t = (χ, ψ) ∈ T .

- cursedness level (a la Eyster & Rabin, 2005):

I

χ =0

- fully-cursed agent expects to get a good of an average value.

I

χ =1

- no cursedness.

I Cursed agents underestimate adverse selection; thus trade too much.

ψ : [L, H] → [L, H]

- perception bias:

I If the agent's own good is worth I Endowment eect:

ψ (x) > x

x,

he believes it is worth

for every

x;

ψ (x).

induces too little trade, since

agents do not want to give up their goods.

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Basic Model

Strategies and Congurations Conguration

(η, b)-

the state of the population:

- distribution of types.

I

η

I

b : supp (η) → S

- strategy of each type: the values of

xi

and

α

for

which it agrees to trade.

Equilibrium conguration - all types (subjectively) best-reply to the aggregate behavior. I In equilibrium, each type

according to

Frenkel, Heller, Teper

χ,

(χ, ψ)

underestimates adverse selection

and mis-evaluates its own good according to

The Endowment Eect as a Blessing

ψ.

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Basic Model

Population Game Lemma

For each distribution η there is an equilibrium conguration (η, b).

An equilibrium selection function assigns to each population one of the possibly several equilibrium congurations. I All our results hold for any equilibrium selection function.

The barter trade and the equilibrium selection function jointly dene a population game

G = (T , u)

between the types:

I T - Set of actions = set of types. I

u (t, η)

- the payo of type

Frenkel, Heller, Teper

t

who faces population

The Endowment Eect as a Blessing

η.

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Basic Model

Dynamically Stable Populations

Denition (Notions of dynamic stability) η

is weakly (Lyapunov) stable if after any suciently small invasion, the

population composition remains close to

η.

It is strictly (asymptotically) stable if, in addition, the population converges back to

η.

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Results (Basic Model)

Outline 1

Introduction

2

Basic Model

3

Results

4

Extended Model

5

Results (Extended Model)

6

Discussion

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Results (Basic Model)

Set of Compensating Biases - Γ We characterize a set of types

Γ=

n

χ, ψχ∗



|0 ≤ χ ≤ 1

o

with the

following properties:

1

ψχ∗ (x)

is increasing in

2

(0, ψ0∗ )

is the unbiased type (ψ0

3

All other types in

4

Biases are perfectly correlated: larger

5

If all incumbents have types in

χ

and

x. ∗

Γ

≡ Id ). ∗ (x)

present the endowment eect (ψχ

Γ,

χ ⇔

> x ).

more endowment eect.

then they all play the same as-if 

rational behavior.

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Results (Basic Model)

Equilibria of the Population Game Proposition (Equilibria of the Population Game) Distribution η is a Nash equilibrium i supp (η) ∈ Γ. Moreover, such an equilibrium is strict with respect to types outside Γ.

Corollary (Relying on Taylor and Jonker 1978; Cressman, 1997) For any smooth payo-monotonic selection dynamics 1

A type is weakly stable i it is in Γ.

2

Γ is a minimal strictly stable set.

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Extended Model

Outline 1

Introduction

2

Basic Model

3

Results

4

Extended Model

5

Results (Extended Model)

6

Discussion

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Extended Model

Additional Interactions Biases may compensate for each other in a specic interaction, but be detrimental to decision making in other interactions where there is no perfect compensation. We study the robustness of the results in an environment with additional interactions: I Main interaction - barter trade (probability 1 I With probability

p:

− p ).

agents have some other interaction, in which biases

are harmful.

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Extended Model

Stability is not Robust with Payo-Monotonic Dynamics Proposition

For any p > 0, the unbiased type is the unique Nash equilibrium. Moreover, it is a strict equilibrium.

Corollary (Stability in payo-monotonic dynamics) For any p > 0, the unbiased type is strictly stable. Moreover, no other distribution of types is weakly stable.

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Extended Model

Hybrid-Replicator Dynamics Replicator dynamics is based on two assumptions:

1 Each new agent replicates a single incumbent. 2 The choice of which incumbent to replicate is proportional to the incumbents' payos.

Hybrid-replicator dynamics relax the rst assumption. Each new agent: I With probability 0

≤r ≤1

replicates each bias from a dierent

incumbent. I With probability 1

Frenkel, Heller, Teper

−r

replicates both biases from a single incumbent.

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Extended Model

Hybrid-Replicator Dynamics - Interpretations Biology

(Karlin, 1975; Eshel & Feldman, 1984; Waldman, 1994):

I Sexual inheritance: Ospring's genotype is a mixture of parents' genes. I Parameter

r

is the recombination rate. It is equal to 0.5 if each bias

is determined by a dierent chromosome. I We Ignore diploidy: makes the analysis tractable, while capturing all

the qualitative features (see, Maynard Smith, 1971; Nowak et al, 1997).

Cultural learning: I Some agents learn dierent strategic aspects from dierent mentors.

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Extended Model

Hybrid-Replicator Dynamics aren't Payo-Monotonic (r > 0)

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Results (Extended Model)

Outline 1

Introduction

2

Basic Model

3

Results

4

Extended Model

5

Results (Extended Model)

6

Discussion

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Results (Extended Model)

Example (Instability of Heterogeneous Populations) A population in which A mean mutant I

t 0 , t1 , t2

t1 , t2 ∈ Γ

t0 ∈ Γ

co-exist is unstable.

outperforms the incumbents:

fare (Approximately) the same.

I The hybrid ospring of

t0

are closer to

Γ⇒

Outperform the hybrid

ospring of the incumbents.

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Results (Extended Model)

Global Convergence Towards Γ Denition Type

t0

eliminates

t

if any mixture of both types converge to the state in

which everyone has type

t 0.

Proposition

Any type outside Γ can be eliminated by types strictly closer to Γ if p > 0 is suciently small.

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Results (Extended Model)

Stability of types in Γ Denition Type

t

is strictly stable against

mutants with type everyone has type

t 0,

t0

if after any suciently small invasion of

the population converges back to the state in which

t.

Proposition For any type t ∈ Γ and t 0 ∈ T , if p > 0 is suciently small, then t is strictly stable against t 0 .

Remark A xed small

p > 0:

types in

Γ

are quasi-stable: stable to all mutants

except nearby mutants with slightly smaller biases.

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Results (Extended Model)

Frenkel, Heller, Teper

Graphical Representation of Results

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Discussion

Outline 1

Introduction

2

Basic Model

3

Results

4

Extended Model

5

Results (Extended Model)

6

Discussion

Frenkel, Heller, Teper

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Discussion

Random Traits and Empirical Prediction Partially heritable biases: Agent of type

χ + εχ , ψ + εψ




, where

εχ

and

εψ

(χ, ψ)

exhibits behavior

are random noise.

I Cesarini et al. (2012): Experimental evidence suggesting that many

common behavioral biases are moderately heritable (20%-50%).

Our results remain qualitatively the same. Empirical prediction: I No correlation between the two biases within a specic society. I Strong correlation between the average cursedness and the average

endowment eect across societies.

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Discussion

Related Literature

Related Literature Indirect evolutionary approach literature (Guth and Yaari, 1992). I We contrast the main stylized result - With unobservable types all

agents are best replying to the material preferences. I Heifetz & Segev (2004) and Huck et al. (2005) explain the

evolutionary advantages of observable endowment eect in bargaining.

Papers that analyze joint inuence of biases: excessive risk-aversion & isolation eect (Kahneman & Lovallo, 1993), perception biases (Heifetz et al., 2007), evolutionary kludges for design ineciencies (Ely, 2011), dierent aspects of Prospect Theory (Herold & Netzer, 2011).

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Discussion

Related Literature

Evolutionary Dynamics with Sexual Inheritance Biology:

Karlin (1975), Eshel & Feldman (1984), Matessi & Di Pasquale (1996).

Economics: I Waldman (1994): Sexual inheritance can yield stable second-best

adaptations; demonstrating how it can induce overcondence; I Bergstrom & Bergstrom (1999): Sexual inheritance allow ospring to

successfully blackmail their parents into providing more resources.

Our contribution: (1) Analyzing seemingly-unrelated biases; (2) Introducing the tractable family of hybrid-replicator dynamics; (3) Extending analysis: global convergence and continuum of types.

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Discussion

Related Literature

Concluding Remarks A novel evolutionary foundation: Biases jointly and approximately compensate for the errors that any bias yields in isolation. I Example: the winner's curse and the endowment eect.

Behavior diers from best-replying although biases are unobservable. Introducing the plausible and tractable family of the hybrid-replicator dynamics, which are not payo-monotonic.

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