Dragon Slaying with Ambiguity: Theory and Experiments

• DOI: http://doi.org/10.1111/jpet.12185
• Author: SARA LE ROUX,DAVID KELSEY
• Date: 01 February 2017
• Published date: 01 February 2017

DRAGON SLAYING WITH AMBIGUITY:THEORY AND EXPERIMENTS

DAVID KELSEY

University of Exeter

SARA LE ROUX

Oxford Brookes University

Abstract

This paper studies the impact of ambiguity in the best-shot and weakest-

link models of public good provision. The models are first analyzed

theoretically. Then, we conduct experiments to study how ambigu-

ity affects behavior in these games. We test whether subjects’ percep-

tion of ambiguity differs between a local opponent and a foreign one.

We find that an ambiguity-safe strategy is often chosen by subjects.

This is compatible with the hypothesis that ambiguity aversion influ-

ences behavior in games. Subjects tend to choose contributions above

(respectively, below) the Nash equilibrium in the best-shot (respec-

tively, weakest-link) model.

1. Introduction

This paper reports some theoretical results on how ambiguity affects behavior in the

best-shot and weakest-link models of public good provision. We then proceed to study

experimentally the impact of ambiguity in these models.

Public goods are goods that once provided can be consumed by everybody. Westudy

situations where individuals make voluntary contributions to the provision of the public

good. Due to the collective nature of the good, everybody enjoys the same amount of

it, irrespective of their own contribution. The usual assumption is that the amount of

the public good available is a function of the sum of all individual contributions. Am-

biguity in the standard public goods model has been previously studied in Eichberger

and Kelsey (2002) and Bailey, Eichberger, and Kelsey (2005). These models have been

tested experimentally by Di Mauro and Castro (2011).

An alternative is the best-shot model, where production of the public good is de-

termined by the maximum contribution made by an individual in the community. This

may be represented as: ui(xi,x−i)=max {x1,...,xn}−cxi,where xidenotes the con-

tribution of individual iand cdenotes the marginal cost of a contribution. In this case,

David Kelsey, Department of Economics, University of Exeter, Exeter EX4 4PU, England (D.Kelsey@

exeter.ac.uk). Sara le Roux, Department of Economics, Oxford Brookes University, Wheatley Campus,

Oxford, OX33 1HX England (drsaraleroux@gmail.com).

Financial support from the University of Exeter Business School is gratefully acknowledged. We

would like to thank J¨

urgen Eichberger, Zvi Safra, Scott Mcdonald, Dieter Balkenborg, Miguel Fonseca,

and some anonymous referees for their comments and suggestions.

Received April 24, 2015; Accepted December 23, 2015.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 19 (1), 2017, pp. 178–197.

178

Dragon Slaying 179

making a large contribution, xi, results in a large cost, cxi, but the benefit accrues to

all members of the group. This model may be illustrated by a medieval village that is

besieged by a dragon. It is only the knight endeavoring to slay the dragon who bears the

cost—in this case, the chance that he will be burnt to a crisp by the dragon. However,

once the dragon is slain, the benefits of a dragon-free village are enjoyed equally by all

the village folk! A “whistle-blower” may be seen as a modern-day dragon-slayer. He bears

the burden that comes with the act of exposing corruption or incompetence, though

the benefit of his act accrues to the general public.

A third possibility is the weakest-link model, in which provision of the public good

is a function of the minimum of the individual contributions. It may be represented as

ui(xi,x−i)=min {x1,...,xn}−cxi. It may be noted that making a large contribution,

xi,would have a large cost, cxi,but does not guarantee a large payoff, since the mini-

mum contribution made within the group of individuals would determine the level of

the public good.

This model can be illustrated by the example of a small island community that

must build sea defenses to protect itself from flooding. The success in holding back the

storm waters will depend on the minimum height or strength of the different sections

of the dyke. As such, it is the weakest dyke that will succumb to the storm first, resulting

in the entire island being flooded. Similarly, a weakest-link problem may be observed

when trying to prevent the spread of infectious diseases such as ebola, combating the

entry of illegal drugs into a country, or controlling illegal immigrants. The weakest-link

model is also relevant for environmental problems. Consider a global pollutant such as

CO2where the damage to the environment depends on total emissions. If industries

can relocate easily, then the level of pollution would depend on the country with the

weakest environmental regulation.

Our analysis shows that although both models have multiple Nash equilibria

(henceforth NE), when ambiguity is sufficiently high equilibrium under ambiguity

(henceforth EUA) is unique. Ambiguity aversion will cause people to choose the highest

effort level in the best-shot model and the lowest in the weakest-link model. We proceed

to test our results in the laboratory. Our experimental hypothesis is that ambiguity will

decrease individuals’ contributions in the weakest-link model, whereas it will increase

contributions in the best-shot case.

Kilka and Weber (2001) conducted an experiment where they asked German sub-

jects to rate their competence when judging stock price changes of Deutsche Bank (Ger-

many’s largest banking group) and Dai-Ichi Kangyo Bank (one of Japan’s largest banks).

A majority of their subjects (51 of the 55 studied) reported that they felt less competent

when judging stock price changes of the foreign security as opposed to the domestic

security.

We test whether players in games feel a similar lack of competence when dealing

with foreign opponents. If the analogy were to hold, a subject would feel more anxious

when faced by a foreign opponent, than when he is faced by a local one. The rationale

behind this hypothesis is that he believes the local opponent has been raised in a similar

sociocultural background as himself. Thus, the behavior of a foreign opponent, about

whom there is limited knowledge, is less predictable.

We find that behavior of the subjects is consistent with our hypothesis and that am-

biguity does indeed lead subjects to decrease (respectively, increase) contributions in

the weakest-link (respectively, best-shot) game. However, though subjects display ambi-

guity aversion on the whole, the level of ambiguity does not become more pronounced

when they are matched against a foreign opponent.