Contests over joint production on networks

• Author: Serhat Doğan,Çağrı Sağlam,Kerim Keskin
• DOI: http://doi.org/10.1111/jems.12343
• Published date: 01 April 2020
• Date: 01 April 2020

J Econ Manage Strat. 2020;29:377–400. wileyonlinelibrary.com/journal/jems © 2020 Wiley Periodicals, Inc.

|

377

Received: 15 May 2019

|

Revised: 28 September 2019

|

Accepted: 3 January 2020

DOI: 10.1111/jems.12343

ORIGINAL ARTICLE

Contests over joint production on networks

Serhat Doğan

1

|Kerim Keskin

2

|ÇağrıSağlam

1

1

Department of Economics, Bilkent University, Ankara, Turkey

2

School of Business, ADA University, Baku, Azerbaijan

Correspondence

Kerim Keskin, School of Business, ADA

University, AZ1008, Baku, Azerbaijan.

Email: kkeskin@ada.edu.az

Abstract

We consider a network of heterogeneous agents where each edge represents a

two‐player contest between the respective nodes. In these bilateral contests,

agents compete over an endogenous prize jointly produced using their own

contest efforts. We provide a necessary and sufficient condition for the

existence of Nash equilibrium and characterize the equilibrium total effort for

every agent. Our model has insightful results regarding the network type, that

is, depending on whether the network is bipartite or nonbipartite. Finally,

considering the sum of all expected utilities as an efficiency notion, we

investigate the optimal network structure.

KEYWORDS

efficiency, endogenous prize, joint production, networks, optimal network, Tullock contests

JEL CLASSIFICATION

C72; D74

1|INTRODUCTION

Since the seminal works of Tullock (1980) and Lazear and Rosen (1981), contest‐like situations have been extensively

investigated in the literature. In any such conflict, the contending parties expend nonrefundable resources to increase

their chances of winning some prizes. Real‐life applications range from sports and warfare to firm competition and

political campaigns.

In the contest theory literature, the existing studies mostly concentrate on a single conflict with two or more

contenders while overlooking possible interdependencies between different conflicts. These models are insufficient to

explain complex real‐life situations such as wars between countries in which a country is fighting against several others

at the same time (because of different issues, over different territories, etc.) or market competitions between multi-

product firms in which a firm is simultaneously competing with several others at the same time (in different markets,

for different products, etc.). Arguably, the former situation is a pure conflict, whereas the latter situation includes some

sense of collaboration as there may be positive externalities attached to the firms' contest efforts (e.g., increased market

awareness or increased production efficiency). In this paper we are interested in the latter situation.

For a more concrete example of market competition, consider a set of firms deciding on their advertising

expenditures to promote their own products. Each firm produces different types of goods; and for each type of good a

firm produces, there is another firm producing a close substitute. Advertising a specific good increases the consumers'

willingness to pay for that good as well as for its close substitute; and whichever firm is more successful than its

competitor ends up with a higher market share and a higher expected revenue. Along similar lines, consider also a set

of political parties deciding on the content of their political campaigns for an upcoming election. Each political party

has certain opinions on different topics; and for each view explicitly supported by a political party, there is another

political party challenging that view. Expressing an opinion on a particular topic leads to a debate, which in turn

attracts the swing voters' attentions to that topic, so that whichever political party wins the debate ends up with an

increased number of supporters. From a game‐theoretic perspective, two firms competing in the same market or two

political parties debating over an issue are engaged in a contest game where they exert costly efforts to increase their

expected revenues or expected number of votes. Considering the set of all firms or political parties, the overall

interaction can be described as a network including a bilateral contest game on each edge.

In the sense that our interest is mostly in strategic conflicts between the agents of a network, our model is most

closely related to the model proposed by Franke and Öztürk (2015).

1

These authors model the structure of local

conflicts with strategic interdependencies as a network where nodes represent the conflicting parties and edges

represent the bilateral conflicts in which the winner collects a rent. Following an implicit characterization of Nash

equilibrium, they concentrate on conflict intensity in certain types of networks and investigate cases of peaceful conflict

resolution as a notion of efficiency. In the current paper, we analyze conflicts over joint production instead of studying

pure conflicts (e.g., war) as in Franke and Öztürk (2015). Accordingly, we capture a sense of collaboration between the

agents of a network. This calls for a new modeling, which comes with important analytical and intuitive differences.

Analytically, we study bilateral contests with endogenous prizes (increasing in both agents' effort levels) rather than

rent‐seeking contests.

2

Intuitively, the nature of competition is different since exerting more effort not only increases

one's winning probability, but also one's winning prize, as well as the winning prize for the other party. Attached is a

different efficiency implication: in contrast to rent‐seeking contests, in which efforts are usually considered social waste,

exerting more effort might increase social welfare in our model since efforts are now productive.

It is worth noting that there are other studies in the “crossroads”of contests and networks, focusing on the strategic

interactions between several conflicting parties. For example, Huremovic (2015) investigates network stability in a

model of strategic network formation, after generalizing the results by Franke and Öztürk (2015). In more recent

papers, Hiller (2017) analyzes a network with friendship and enmity links such that an agent tries to extract payoffs

from his/her enemies in different bilateral contests not by choosing efforts but only through the help of his/her friends;

and Grandjean, Tellone, and Vergote (2017) study an n‐player contest on a network that influences the winning prizes

directly through the number of neighbors. These papers explore different conflict situations that lack the sense of

collaboration our model captures. Furthermore, they are rather interested in a network formation analysis, hence are

missing a detailed characterization of equilibrium strategies for a fixed network.

Throughout this paper, we analyze Nash equilibrium. We first provide a necessary and sufficient condition for the

existence of equilibrium and then characterize the equilibrium total effort for every agent. Our results indicate that

the network type significantly influences the equilibrium characteristics. In particular,if the network is nonbipartite, then

the agents in each bilateral conflict exert the same amount of effort in an equilibrium; whereas if the network is bipartite,

then the agents in the stronger group are equally more advantagedin their contests as they exert a common multiple of the

equilibrium efforts exerted by their respective rivals. Afterward, we proceed to an optimal network analysis in which we

consider the sum of all expected utilities as an efficiency notion. When the agents are symmetric, we prove that any

nonbipartite network is optimal. For the asymmetric case, we numerically show that there are cases where any non-

bipartite network is optimal as well as cases in which there exists a certain type of bipartite network dominating all

nonbipartite networks. For the latter, our numerical analysis indicates that the optimal network is generally such that the

number of agents in the partitioned sets are close to each other, although strong asymmetries are also possible.

Our main contribution is twofold: (a) We contribute to the analysis of strategic conflicts (see Anderton &

Carter, 2009; Dechenaux, Kovenock, & Sheremeta, 2015; Konrad, 2009, among others). Unlike the conventional models

focusing on a single conflict between two or more parties, we analyze multiple simultaneous conflicts between a group

of heterogeneous agents. On top of that, as we investigate contests over joint production, our analysis is closely related

to the literature on contests with endogenous prizes (see Chowdhury & Sheremeta, 2011; Chung, 1996; Keskin &

Sağlam, 2018; Lee & Kang, 1998, among others). (b) We contribute to the analysis of games played on networks (see

Abreu & Manea, 2012; Bramoullé & Kranton, 2007,2014; Galeotti, Goyal, Jackson, Vega‐Redondo, & Yariv, 2010,

among others);

3

and in particular, to the emerging literature on the analysis of contests on networks. Our model

investigates potentially very complex conflict situations between heterogeneous agents of a given network. Interest-

ingly, with such interdependent conflicts embedded in a network, our model is missing a typical assumption in network

games: strategic complementarity or substitutability.

378

|

DOĞAN ET AL.