Liability Insurance and Choice of Cars: A Large Game Approach

• DOI: http://doi.org/10.1111/jpet.12116
• Published date: 01 December 2015
• Date: 01 December 2015
• Author: SJUR DIDRIK FLÅM,ELMAR G. WOLFSTETTER

LIABILITY INSURANCE AND CHOICE OF CARS:ALARGE

GAME APPROACH

SJUR DIDRIK FL ˚

AM

University of Bergen

ELMAR G. WOLFSTETTER

Humboldt University at Berlin

Abstract

If a car, already on the road, is replaced by another one,

more expensive to collide with, a negative externality spills

over to other drivers. This paper studies such externali-

ties, relating them to insurance and incentives. It formal-

izes links from liability rules to choice of car. By assumption,

insurance is cooperative but car acquisition is noncooper-

ative. Construing drivers’ interaction as a large game, the

paper considers how a Nash equilibrium—and its efficiency

or fairness—is shaped by the underlying liability regime.

1. Introduction

As motivation for the present inquiry, consider the following somewhat

stylized story. Until the reunification of Germany, the East German car

pool was comprised of mostly inexpensive species such as the two-cylinder

“Trabbi.” Soon thereafter, many a well-to-do citizen replaced his Trabbi

with an expensive Mercedes Benz. As a result, the risk exposure of Trabbi

owners worsened; hence, their insurance rates went up. In contrast, any

Eastern owner of a new Mercedes Benz enjoyed low liability risk and thus

favorable insurance premiums. This implicit transfer from the first group

Sjur Didrik Fl˚

am, Economics Department, University of Bergen, Fossw gt 14, 5020 Bergen,

Norway (sjur.flaam@econ.uib.no). Elmar G. Wolfstetter, Institute of Economic Theory I,

Humboldt University at Berlin, Spandauer Str. 1, 10178 Berlin, Germany, and Korea Uni-

versity, Seoul (wolfstetter@gmail.com).

Support from Deutsche Forschungsgemeinschaft (DFG), SFB Transregio 15, “Gover-

nance and Efficiency of Economic Systems,” is gratefully acknowledged. Also, support

from Finansmarkedsfondet,CESIfo,andE.On Ruhrgas is gratefully acknowledged. Many

thanks are due an associate editor and referee for most useful comments.

Received November 5, 2013; Accepted December 6, 2013.

C2014 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 17 (6), 2015, pp. 943–963.

943

944 Journal of Public Economic Theory

to the second contributed to the speedy change of the East German car

pool—and to the accelerated extinction of the infamous Trabbi.

Albeit rather unique, these events evoke four issues. First,whencarscol-

lide, at least two are involved. So, there is no escape form externalities.Second,

money flows from good to bad risks, a frequent and troublesome feature

of insurance. Third, incentives are easily distorted. Established rules may fa-

vor special cars or conducts, prone to inflict or suffer great damage. Fourth,

there are perennial concerns with asymmetric information. On all four

accounts, any liability regime affects efficiency or fairness. Each instance mer-

its close analysis, and some might qualify for legal reform.

In most jurisdictions, liability insurance for cars is mandatory. Yet the

rules vary across countries and over time. Clearly, any specific form affects

drivers’ choice of car or driving behavior—hence their liabilities and losses.

This paper formalizes some of these links. Its main purpose is to place mani-

fold liability regimes within common frames, thereby opening up particular

designs for comparison and scrutiny.

Two designs are already prominent. One evokes the tort principle to judge

that the injurer should compensate the injured. Another applies no-fault in-

surance to cover only the damage to the driver’s own car—regardless of who

is at fault.

Tort law is usually justified by considerations of fairness and a desire to

discourage reckless driving. However, damage caused by a Trabbi driver is

partly due to the other driver’s brand of car. This and similar examples lead

one to question the efficiency and fairness of placing the full burden on the

responsible party. A no-fault arrangement is not only free from this defect,

it also avoids the litigation costs associated with establishing responsibilities.

The latter regime may, however, induce careless behavior or preference for

cars that suffer little loss.

Distortions of such sorts are easy to comprehend. However, formalizing

different liability structures and comparing them is far from trivial. Taking

some steps in that direction, this paper singles out two chief components and

assembles them into one equilibrium model. The first component deals with

risk sharing, basically a cooperative business that yields a core solution.Thesec-

ond component concerns agents’ choice of cars, essentially noncooperative—

hence part of a Nash equilibrium in a large, anonymous game where every

player behaves as though he does not affect insurance premiums. By integrat-

ing these two parts, we connect elements of cooperative and noncooperative

game theory, as in Fl˚

am and Jourani (2003).

While tractable in the small, the resulting model hinges on fixed

points in the large. Aggregation helps to establish existence of such points

at two different levels: first, in the sharing of pooled risks; second, in

affecting vehicle choice via insurance premiums and indemnities. At both

levels, the assumption of a large game plays a crucial role. In fact, the

risk exchange between numerous drivers—each contributing a moderate,

almost independent risk—is not plagued by potential ruin. And most likely,