Economics of Betting Markets David Peel
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Introduction: Economics of Betting Markets David Peel To cite this version: David Peel. Introduction: Economics of Betting Markets. Applied Economics, Taylor & Francis (Routledge), 2008, 40 (01), pp.1-3. 10.1080/00036840701728773. hal-00582279 HAL Id: hal-00582279 https://hal.archives-ouvertes.fr/hal-00582279 Submitted on 1 Apr 2011 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Submitted Manuscript For Peer Review Introduction: Economics of Betting Markets Journal: Applied Economics Manuscript ID: APE-07-0713 Journal Selection: Applied Economics Date Submitted by the 03-Oct-2007 Author: Complete List of Authors: Peel, David; University of Lancaster, Economics C72 - Noncooperative Games < C7 - Game Theory and JEL Code: Bargaining Theory < C - Mathematical and Quantitative Methods C72 - Noncooperative Games < C7 - Game Theory and Keywords: Bargaining Theory < C - Mathematical and Quantitative Methods Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Page 1 of 6 Submitted Manuscript 1 2 3 Introduction: Economics of Betting Markets 4 5 by D.A.Peel 6 7 Economists have long been interested in the economics of betting markets as 8 9 exemplified by the excellent survey articles by Sauer (1998) and Vaughan Williams 10 11 (1999). This is perhaps not surprising give n that in many countries the majority of 12 persons gamble often with large stakes. 1 For instance 68% of the population of the 13 14 UK had participated in some form of gambling activity within the past year in the 15 16 UK (48% excluding people who had only gambled on the National Lottery Draw). 17 18 (See British Gambling Prevalence Survey 2007). Also the amount of money spent 19 on gambling activities is increasing in many countries. For example the amount 20 For Peer Review 21 retained by gambling operators in the UK after the payment of winnings, but before 22 23 the deduction of the costs of the operation was £9.8 billion a 36% increase in 24 25 nominal terms since 1999. See British Gambling Prevalence Survey 2007). 26 The last few years has seen an increase in academic literature on the economics 27 28 of gambling with new specialist journals formed. This probably reflects the 29 30 availability of data sets and the increasing importance of the gambling sector. 31 32 This issue of Applied Economics is given up to 11 papers that reflect current work 33 34 in this area. 35 The standard expected utility model is of course inconsistent with gambling at 36 37 actuarially unfair odds. Some still add a non -pecuniary motive (such as excitement or 38 39 entertainment), that compensates for the expected negative pecuniary returns to that 40 41 model to explain ga mbling. However whilst it is undoubtedly the case that non - 42 pecuniary returns are relevant for some who engage in gambling, the hypothesis per 43 44 se is unattractive, because it is inconsistent with apriori reasoning 2, with the fact that 45 46 a majority say they gam ble to make money 3 and with other experimental evidence 4. 47 48 49 1 For instance, Bruce and Johnson (1992) report average stakes of £22.63 on race horse 50 favorites. Strumpf (2003) reports that average bet size averaged in excess of $1000 in a 51 study of six illegal bookmak ers. 52 2 53 Friedman and Savage (1948) and Markowitz (1952) in their seminal papers provide a 54 critique of the entertainment rationale. For instance, Markowitz notes that if the utility of 55 56 a gamble is the expected utility of the outcomes plus the utility of play ing the game then, 57 58 for given fair odds, the smaller the amount bet, the higher the expected utility. This 59 60 implies millionaires should play poker for pennies and no one should purchase more than one lottery ticket. 1 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript Page 2 of 6 1 2 3 Cumulative Prospect theory (CPT) developed by Kahneman and Tversky (1979) 4 5 and Tversky and Kahneman (1992) can explain a variety of experimental results 6 7 inconsistent with expected utility theory and also optimal gambling on long shots. 8 9 In the first paper Cain, Law and Peel show that an alternative parametric 10 11 specification of CPT enables the CPT model to explain gambling on all outcomes 12 including odds on favorites. 13 14 One possibly problematic feature o f CPT is that betting on long shots at unfair 15 16 odds is induced by “extreme” probability distortion. This probability distortion 17 18 implies that the subjective expected returns sometimes run into hundreds of 19 percent. In order to explain the famous Allais (1953) paradox it is necessary to 20 For Peer Review 21 assume probability distortion. In paper two Peel, Zhang and Law introduce a small 22 23 degree of probability distortion into the Markowitz (1952) model of expected utility, 24 25 of which the value function in CPT is a special case. They show that this model can 26 explain the Allais experiments as well as gambling outcomes without assuming 27 28 subjective rates of return run into hundreds of percent. 29 30 In paper three Bhattacharyya and Garrett develop a model based on an extension 31 32 of that of Fried man and Savage (1948) model to explain state lottery games. The 33 34 utility function proposed by Bhattacharyya (2003) is concave for wealth below the 35 current wealth of the agent and it is convex above the current wealth of the agent. 36 37 Their model implies that l ottery players trade -off expected return for skewness of 38 39 return. Carefully carried out empirical analysis of two interesting data sets appears 40 41 to give support to their model. 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 3 59 When surveys ask gamblers why they gamb le, a majority (approximately 42% -70%) cite 60 financial reasons: ‘to make money’ (see, for example, The Wager (2000).) 4 Many experimental results conflict with the standard expected utility model. An excellent discussion of some of this experimental evide nce can be found in Starmer (2000). 2 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Page 3 of 6 Submitted Manuscript 1 2 3 However the precise structure of a lottery ticket implies a relationship betwee n 4 5 expected return and the higher moments. 5 Such a relationship can also be derived 6 7 from the utility function. Both should perhaps be explicitly included in future 8 9 analysis. Also their model is similar to a restricted version of the Markowitz model 10 11 and appe ars to imply unbounded stakes and preference for one -prize lottery 12 tickets. It would surely be interesting to build on their analysis employing alternative 13 14 models of utility, which do not have these implications. 15 16 In paper four Deck, Lee, and Reyes estimat e the degree of risk aversion of 17 18 contestants appearing on Vas o No Vas , the Mexican version of Deal or No Deal . 19 They find substantial evidence of risk aversion. However their estimates are lower 20 For Peer Review 21 than previous estimates based on game shows. They also find a considerable 22 23 variation in risk attitudes, with a few people being extremely risk averse while 24 25 others are risk loving. It would perhaps be interesting to rework the analysis 26 employing a non -expected utility approach. 27 28 In paper five Farrell and Forrest cons ider the interesting issue of the extent of 29 30 displacement effects across gaming products. Employing Australian data they 31 32 estimates a state level (fixed effects) panel data model, exploiting the intra -state 33 34 differences in the portfolio of gaming products ava ilable, to estimate the extent of 35 displacement effects across the gaming sector. In particular they examine whether 36 37 sales of lotto and lotto -style products in Australia were displaced by the 38 39 introduction and growth of large casinos and by the spread of cas ino -style machine 40 41 gaming within neighborhood hotels (pubs) and clubs. Their evidence suggests a 42 potential for local casinos to divert significant sums from lotto and the causes it 43 44 45 5 46 See Brockett and Garven (1998) and Cain and Peel, (2004). For instance for a 1 unit bet 47 with odds o win probability p the relationship between the moments is given by 48 49 µ22 + µs − () 22= 0 50 51 µ2()1− p where expe cted retur n=µ =p(1 + o), variance = 2 = , 52 p 53 54 µ3 (112−−pp)( ) skewness ==s 55 p2 56 57 58 59 60 skewness , s, is negative ly related to expected return but there is no behavior implied. 3 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript Page 4 of 6 1 2 3 funds. Their results are of relevance to the current policy debate in other countries 4 5 such as the UK. 6 7 In paper six Benar and Jenkins develop a model that focuses on the implications 8 9 for economic welfare of different taxation schemes for casinos, though it is 10 11 assumed that casinos cater exclusively to foreign tourists.