Match‐Fixing in a Monopoly Betting Market

• Published date: 01 February 2017
• Author: Parimal Kanti Bag,Bibhas Saha
• DOI: http://doi.org/10.1111/jems.12172
• Date: 01 February 2017

Match-Fixing in a Monopoly Betting Market

PARIMAL KANTI BAG

Department of Economics

National University of Singapore, Faculty of Arts and Social Sciences

AS2 Level 6, 1 Arts Link Singapore 117570

ecsbpk@nus.edu.sg

BIBHAS SAHA

Durham University Business School

Mill Hill Lane, Durham DH1 3LB U.K.

b.c.saha@durham.ac.uk

A monopolist bookmaker may set betting odds on a fairly even contest to induce match-fixing

by an influential corrupt punter. His loss to the corrupt punter is more than made up for by

enticing enough ordinary punters to bet on the losing team. This result is in sharp contrast

to competitive bookmaking, where even contests have been shown to be immune to fixing. The

analysis also reveals a surprising result that the incidence of match-fixing can dramatically fall

when match-fixing opportunities rise. This is shown by comparing two scenarios—when only

one team is corruptible and when both are corruptible. For both teams corruptible, the bookmaker

is uncertain about to which team the influential punter will have access, so carefully maneuvering

the odds to induce match-fixing is too costly.

1. Introduction

Match-fixing and betting-related corruption seem widespread if one goes by media

headlines, and legal scholars are beginning to pay attention.1Yet formal research on

this issue is relatively lacking.2If a small group of bettors with financial muscles, to

be referred as the influential punter (in short, IP or fixer), can access player(s) who, by

We especially thank an anonymous reviewer and an associate editor for detailed comments and suggestions

on earlier drafts. We also thank Murali Agastya, Aditya Goenka, Satoru Takahashi, and participants at the

2011 (XXIst) Annual Conference on Contemporary Issues in Development Economics at Jadavpur University,

2012 SAET Conference in Queensland, 2013 AEI-Four Economic Theory Workshop hosted by Seoul National

University, 2014 APET Conferencein Seattle, and seminars at the Indian Institute of Management (Kolkata),

and Indira Gandhi Institute of Development Research, for various feedbacks. The project was partly funded

by a Singapore MOE AcRF Tier 1 grant (grant no. R-122-000-151-112). For any shortcomings, we remain

responsible.

1. See an edited volume (Haberfeld and Sheehan, 2013) titled, Match-Fixing in International Sports:

Existing Processes, Law Enforcement, and Prevention Strategies. Betting-related match-fixing makes frequent

headlines. Latest is the allegation of an entire soccer league being fixed in Canada (“Revealed: Entire

‘rogue league corrupted by match-fixing’”—October 14, 2015 news at The Telegraph, http://www.telegraph.

co.uk/sport/football/11932437/Revealed-Entire-rogue-league-corrupted-by-match-fixing.html). The high

profile Indian Premier League (or IPL) in which many top international cricketers participate was rocked

by betting and fixing allegations in the recent past—see the report “Fixing? It’s people like us doing it” on

May 22, 2013 at http://www.espncricinfo.com/magazine/content/story/637034.html. For fixing allegations

in other sports including soccer in Europe, ATP tennis tournaments, basketball, horse races, etc., see links to

various news reports in Bag and Saha (2011).

2. There are some empirical papers on sports corruption. Duggan and Levitt (2002) study corruption in

Sumo wrestling but not betting. Strumpf (2003), Wolfers(2006), Winter and Kukuk (2008), etc. study betting-

related corruption in sports. See also two very recent contributions on detecting match-fixing—De Muinck

and Quatacker (2013) for soccer, and Rodenberg and Feustel (2014) for tennis.

C2016 Wiley Periodicals, Inc.

Journal of Economics & Management Strategy, Volume26, Number 1, Spring 2017, 257–289

258 Journal of Economics & Management Strategy

underperforming, can tilt the outcome of a sports contest that has high visibility and on

which many people bet, the competitive show is hit at its foundation.

In an earlier work (Bag and Saha, 2011), we presented a formal model of match-

fixing in the context of a (Bertrand) competitive fixed odds betting market. There the

bookmakers’ desire to steal business by undercutting rivals’ odds exposes the contest

to fixing, whereby a favorite deliberately underperforms. Such destructive effects of

competition are felt mostly in uneven contests; even contests are generally safe. One

question then is what happens if a bookmaker has market power. Will he try to protect

the market and his profit from the corrupt punter? Or, will he abuse his power to steer

the market in the direction of odds rigging? Weaddress this question here, by restricting

our attention mainly to even or near-even contests.

In our model a monopolist bookmaker posts betting odds, or equivalently sets the

“prices” of bets, for a contest between two teams to attract bets from a mass of ordinary

bettors. An anonymous influential punter may be able to bribe some members of one of

the teams to underperform, and then place a large sum of bets on the other team. Such

possibilities as well as the ordinary bettors’ response are factored in by the bookie, at

the time of posting the odds.

Bettors’ responses (including IP’s) depend on their position in the information

hierarchy. Weassume that the ordinary bettors have exogenous and heterogenous beliefs

and are unaware of the risk of match-fixing. So they respond to market prices naively.

The bookie and the IP, on the other hand, have superior information; they both know

the teams’ true win probabilities. Further, the IP can rise to the top of the information

hierarchy, if he can fix the match.

Aware of the fact that IP will never have less information than him, the bookie

cannot expect to make profit from the IP. But he needs to be mindful of how IP’s

incentives will be affected by the prices he will set. If the prices are so high that IP’s

betting becomes unprofitable despite match-fixing, the integrity of the contest will be

protected, but only after sacrificing a sizeable chunk of the ordinary bettors’ market. On

the other hand, if the prices are set appropriately low,IP can find match-fixing profitable;

if he gets to bribe one team, his return from the bet on the other team will be large enough

to cover the cost of bribery.In this case, the bookie faces a clear loss to IP, but the loss may

be partially (if not fully) offset by attracting a significant number of ordinary bettors.

So his profits from these two alternative price regimes can go either way. Since which

price regime is his own choice, the question is whether he would go for the first regime,

which we call bribe prevention or the second regime, which we call bribe inducement.

In contests where teams are (near) evenly matched, which regime would he choose?

When only one team is corruptible, we find that he would choose bribe inducement

for any positive chance of secret liaison with the corruptible team (given some standard

assumptions).3This is because bribe prevention is too costly; it requires giving up too

much on the ordinary punters’ betting. In some extreme instances, when the probability

of accessing the corrupt team is very high, the bookie actually welcomes the fixing role

of the IP. With his tacit help he can drastically increase the losing chance of the corrupt

team and steer most of the ordinary bettors to bet on it. Here, the loss to the IP is much

smaller than the substantial gain of capturing (nearly) the whole of the unsuspecting

bettors’ market.

3. Weassume that the corruptible team’s identity is known. Teams with good reputation or regimentation

and discipline are likely to be immune to outside influence.

Match-Fixing in a Monopoly Betting Market 259

Surprisingly though, this perverse incentive loses its force when both teams are

corruptible. In that case, though match-fixing opportunities are greater, the bookie is

unsure of which team the IP will be able to bribe, and therefore, he needs to make

concession on the bet prices of both teams, which means yielding a much greater loss to

not only IP but also a section of ordinary bettors; lowering both prices does not help to

tilt the market in one way or other. Therefore, bribe inducement will be preferred less

frequently.

The finding of the monopoly setup is in sharp contrast to the competitive case

analyzed in Bag and Saha (2011), where even contests are generally immune. Either

the competitive prices are above the bribery threshold level, or the bookmakers (non-

cooperatively) coordinate on the threshold prices for fear of letting the IP in. Under

monopoly, despite his full market power, the bookie may not try to protect the market.

The underlying market microstructure of our model assumes that the median bettor

always believes the contest to be dead even. So when the contest is truly an even (or a

near even) contest, the bookie’s informational superiority disappears, and his expected

profit will be minimum. In such cases, an anonymous fixer can come handy to make the

contest lop-sided and in anticipation of that the bookie can induce the ordinary bettors

en masse to back the losing team. But whether this will be optimal depends on how

large is the expected cost of fixing, which can significantly vary depending on whether

one team or both teams are corruptible.

Though our main analysis is presented assuming “uniform” distribution of the

ordinary bettors’ beliefs, we show that our key insight that the bookie will be most

keen to orchestrate match-fixing in even or near even contests will hold under general

(but symmetric) belief distributions. However, the other assumptions regarding the

bettors, such as their exogenous beliefs and their naivety of not suspecting foul play,

are important. That bettors have diverse beliefs and less precise information than the

bookie are somewhat essential to organize betting.4There is also considerable evidence

on leisure betting, which is most likely to be based on naive beliefs (Saunders and Turner,

1987; Bruce and Johnson, 1992; Winter and Kukuk, 2008). But if we allow the bettors to

be suspicious of match-fixing, when they see the posted odds that are too good to be

true (based on their initial beliefs), market manipulation will backfire; the bookie will

be better off by driving the fixer out of the market. We accommodate this argument,

albeit less formally; but the message is clear: the more unsuspecting the bettors are, the

stronger the incentives to induce match-fixing.

At a theoretical level, our exercise is also useful for extending the literature from

insider betting to fixing and betting. The insider betting model of Shin (1991), from which

we adapt the basic setup, is similar to insider trading (Glosten and Milgrom, 1985; Kyle,

1985; Seyhun, 1992), where some agents use privileged information which might have

been randomly or costlessly acquired. Match-fixing on the other hand is about generating

privileged information at a positive cost and then using it.5This is also related to the

idea of market manipulation in finance where even an uninformed trader may buy a

stock to bid up its price with the intent of selling the stock at a later date and profit

from it (e.g., Allen and Gorton, 1992; Chakraborty and Yilmaz, 2004). Further, our study

provides insights into the extent by which sabotages can be controlled through market

prices—a relatively neglected issue so far in the industrial organization research.

4. Diversity of beliefs naturally follow from our assumption of exogenous beliefs; allowing correlated

beliefs will largely eliminate demand for bets.

5. A similar theme, namely sabotage, has been studied in contest models with completely different con-

cerns than ours. There the focus is on the saboteur’s incentives; see, for instance, Konrad (2000), Chen (2003).