On the Equilibrium Effects of
“Nudging”
Ran Spiegler (TAU & UCL)
UCL Conference on Behavioral I.O. and Consumer Protection
October 2014
Libertarian/Asymmetric/Soft Paternalism
(Nudging)
• Designing features of consumers’ choice problem that would
only affect boundedly rational ones (Camerer et al. 2003,
Thaler-Sunstein 2008, Bar-Gill 2012)
– Default options
– Disclosure
My (Semi-Conventional) Critique
•
To evaluate (theoretically) the welfare consequences of
nudges, we should take into account:
–
Firms’ equilibrium response.
–
An explicit psychological story (“procedural model”)
behind the consumer bias that called for the nudge.
• I make the claim with an example (more in the paper).
My (Semi-Conventional) Critique
• The same methodology is relevant for other regulatory
interventions (e.g., competition policy)
• But nudging is special – it targets parameters that are relevant
only because of consumers’ bounded rationality
Default Bias
• Default architecture: organ donation, retirement saving,
automatic contract renewals
• Default bias may originate from limited comparability.
• In market settings, comparability is endogenous; default
architecture may affect firms’ incentive to manipulate it.
Price Competition with Limited Comparability
• An extension of Carlin 2009, Piccione-Spiegler 2012,
Chioveanu-Zhou 2013 (all variants on Varian 1980)
• Two revenue-maximizing firms compete for a measure one of
consumers who value the firms’ products at 1 and have an
outside option of value 0.
Price Competition with Limited Comparability
• Each firm simultaneously chooses a pair (p,x), where
– p∈[0,1] is the product’s price.
– x∈{0,1} indicates the firm’s “obfuscation strategy”.
• The probability that each consumer makes a price
comparison is 1 – ½(x1+x2).
• In this model, obfuscation = reducing comparison probability.
Limited Comparability
• When consumer makes comparison, he chooses cheapest firm.
• When consumer cannot make a comparison:
– A fraction λ∈(0,1] of consumers are “decisive” – they choose
each firm with probability ½.
– A fraction 1-λ of consumers are “indecisive” – they choose by
default when possible (otherwise, they act “decisively”).
Default Architecture
• I examine three “default rules”:
– Opt in: The default is the outside option.
– Opt out: The default is one of the firms (each firm gets half
the consumer population, for symmetry).
– Active choice: Consumers cannot choose by default.
Firms’ Market Share Function
• Each firm maximizes its price × market share.
• Firm 𝑖𝑖’s market share under “opt in” is
𝑥𝑥1 +𝑥𝑥2
2
𝑥𝑥1 +𝑥𝑥2
2
𝑥𝑥1 +𝑥𝑥2
2
𝜆𝜆
2
𝑥𝑥1 +𝑥𝑥2
)�
2
1
if 𝑝𝑝𝑖𝑖 < 𝑝𝑝𝑗𝑗
𝜆𝜆
2
𝑥𝑥1 +𝑥𝑥2
)�
2
0
if 𝑝𝑝𝑖𝑖 > 𝑝𝑝𝑗𝑗
� + (1 −
𝜆𝜆
2
� + (1 −
� + (1 −
𝑥𝑥1 +𝑥𝑥2
1
)�
2
2
if 𝑝𝑝𝑖𝑖 = 𝑝𝑝𝑗𝑗
• Under “opt out” or “active choice”, the market share function
is the same, except that we plug 𝜆𝜆 = 1.
Symmetric Nash Equilibrium
Proposition: There is a unique symmetric Nash equilibrium.
With probability
𝜆𝜆
2
𝜆𝜆
2
, the firm plays 𝑝𝑝 = 𝑥𝑥 = 1. With
probability 1 − , it plays 𝑥𝑥 = 0 and randomize over 𝑝𝑝 < 1
according to the cdf 𝐹𝐹 𝑝𝑝 = 𝑀𝑀 + 1 −
interval
𝑀𝑀
[
, 1)
𝑀𝑀+1
, where 𝑀𝑀 =
𝜆𝜆(2+𝜆𝜆)
4(2−𝜆𝜆)
.
𝑀𝑀
𝑝𝑝
defined over the
Interpreting the Equilibrium
• Assume “opt in”. When consumers get more decisive, firms
obfuscate more because they benefit more from limited
comparability. This enables them to charge higher prices.
• For the same reason, a switch from “opt in” to “opt out”
results in more obfuscation and higher prices. The effect
increases with consumers’ indecisiveness.
Welfare Analysis
• The equilibrium fraction of consumers who make a comparison
𝜆𝜆
2
𝜆𝜆
2
𝜆𝜆
2
1
2
(1 − )2⋅1 + 2⋅ (1 − )⋅ = 1 −
𝜆𝜆
2
• Big difference between potential / observed default bias
• Under “opt in”, the equilibrium market participation rate (=
gross consumer welfare) is U-shaped
𝜆𝜆
𝜆𝜆 + (1 − 𝜆𝜆)(1 − )
2
Welfare Analysis
• Calculate a firm’s payoff when it plays 𝑝𝑝 = 𝑥𝑥 = 1 against the
equilibrium strategy:
1�
𝜆𝜆
2
𝜆𝜆
2
� + 1−
𝜆𝜆
2
𝜆𝜆
2
� �
1
2
=
1
𝜆𝜆(𝜆𝜆+2)
8
• Subtract industry profits from gross consumer welfare to get
1
4
net consumer surplus: 1 + 𝜆𝜆2 − 𝜆𝜆
Welfare Effects of Default Rule
• Net consumer welfare decreases with 𝜆𝜆.
• “Opt out” and “active choice” are dominated by “opt in”. The
effect is large when consumers tend to be indecisive.
• A rationale for banning auto-renewals (empirical question:
are contracts simpler when auto-renewals are banned?)
• Relevance for retirement saving programs…?
When else is in the Paper…
• Product-use disclosure is counter-productive if non-linear
pricing results from underestimation of future self-control
problems (extending DellaVigna-Malmendier 2004)
• Product-attribute disclosure reduces true quality if consumers
have intrinsic “attention deficit” / “trade-off aversion” (based
on Gabaix-Laibson 2006, Bachi-Spiegler 2014)
Conclusion
• Echoes of “structural” vs. “reduced form” debates
• Which type of story do firms tell themselves about
consumer biases?
• Related works: Heidhues-Koszegi 2010, Armstrong-Vickers
2012, Handel 2013, De Clippel et al. 2013, Grubb 2014