Difference‐Form Persuasion Contests

• DOI: http://doi.org/10.1111/jpet.12211
• Published date: 01 December 2016
• Date: 01 December 2016

DIFFERENCE-FORM PERSUASION CONTESTS

STERGIOS SKAPERDAS

University of California, Irvine

AMJAD TOUKAN

Lebanese American University of Beirut

SAMARTH VAIDYA

Deakin University

Abstract

We explore the equilibrium properties of two types of “difference-

form” persuasion contest functions derived in Skaperdas and Vaidya in

which contestants spend resources to persuade an audience. We find

that both types of functions generate interior pure strategy Nash equi-

libria unlike Baik and Che and Gale with characteristics different to

existing literature. For one type of function, we find that the reaction

function of each player is “flat” and nonresponsive to the level of re-

sources devoted by the rival so that the “preemption effect” as defined

by Che and Gale is absent. Further, the equilibrium is invariant to the

sequencing of moves. For the second type of function, which applies

when there is asymmetry among contestants with regard to the qual-

ity of evidence, we find that the reaction functions of the stronger and

weaker players have gradients with opposite signs relative to Dixit and

therefore their incentive to precommit expenditures in a sequential

move game is also different. For both types of functions, the extent of

rent dissipation is partial. From the equilibrium analysis, we are also

able to establish the potential effects of some specific factors affecting

persuasion such as evidence potency, the degree of truth, and bias on

aggregate resource expenditures and welfare.

1. Introduction

A large variety of economic activities can be thought to be about persuasion where

competing parties attempt to influence the opinions and hence the decisions of their

Stergios Skaperdas, Department of Economics, University of California, Irvine, CA 92697

(sskaperd@uci.edu). Amjad Toukan, Department of Economics, Lebanese American University of

Beirut, P.O. Box 13-5053, Chouran, Beirut 1102 2801, Lebanon (amjad.toukan@lau.edu.lb). Samarth

Vaidya, Department of Economics, Deakin Business School, Deakin University, Geelong, Victoria, Aus-

tralia (samarth.vaidya@deakin.edu.au).

Received May 16, 2016; Accepted June 26, 2016.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 18 (6), 2016, pp. 882–909.

882

Difference-Form Persuasion Contests 883

relevant audiences through costly production of “information” or evidence.1These

include, among many others, advertising (Schmalensee 1972), electoral campaigning

(Snyder 1989; Baron 1994; Skaperdas and Grofman 1995), marketing (Bell, Keeney, and

Little 1975), litigation (Farmer and Pecorino 1999; Bernardo, Talley, and Welch 2000;

Hirshleifer and Osborne 2001; Robson and Skaperdas 2008), and rent-seeking or

lobbying (Tullock 1980). In each of these settings, contest functions have often been

employed to translate the resources or costly efforts employed by the competing parties

into probabilities of their view prevailing over the relevant audience.2

However, until recently the persuasion process by which resources expended by the

contestants translate into the win probabilities governed by such functions has not been

clarified. In the lobbying context, resources expended by competing sides to influence

a decision maker are often considered venal—where they are interpreted as transfers

or bribes.3However, such an interpretation does not encompass lobbying activities that

can be naturally thought of as persuasion even when no bribes are exchanged.

Skaperdas and Vaidya (2012) explicitly derive the contest functions as win proba-

bilities in a game of persuasion where competing parties invest resources to produce

evidence from which an audience updates its priors using Bayesian inference. They

show that both ratio-form and difference-form contest functions can be derived as an

outcome of such a process. In this paper, we examine the equilibrium characteristics

of both the symmetric and asymmetric versions of the difference-form contest function

derived in their paper as reproduced in (1) and (2), respectively, as follows:4

p1(R1,R2)=1

2+α

2[h(R1)−h(R2)],(1)

p1(R1,R2)=(1 −γ)+γ−1

h(R1)−1−δ

δh(R2)

+1−δ

δ−−1

h(R1)h(R2).(2)

The form in (2) is more general relative to (1), where h(.) represents the probability

of a player finding favorable evidence, 0 1 represents the audience’s decision

threshold, and −1

and 1−δ

δrepresent the evidence potencies of the competing players.

Biases can arise when γ= 1

2so that the bar is relatively higher for one of the parties

or when there are differences in evidence potencies. Under symmetry, when evidence

potencies are identical and γ=1

2, (2) naturally reduces to the form in (1).

Since (1) and (2) are explicitly grounded in the persuasion context, the parameters

in the functions have natural inferential interpretations, thus making them particularly

suitable to contests aimed at persuading a relevant audience such as marketing, adver-

1For a recent survey on the quantitative impact of such persuasion activities in voting, marketing, and

financial markets, see DellaVigna and Gentzkow (2010).

2See Corchon (2007) and Jia, Skaperdas, and Vaidya (2013) for an overview of the theoretical founda-

tions and applications of contest functions.

3See, for example, Grossman and Helpman (1994).

4Tullock (1980) originally applied a ratio-form contest in the context of rent-seeking. Subsequently,

the equilibrium characteristics of the ratio-form contest have already been extensively examined in the

contest literature and are well known. See Perez-Castrillo and Verdier (1992) and Nitzan (1994).