Sporting Contests and the Coase Theorem. Stefan Szymanski. Tanaka Business School, Imperial College London. October 2005

Transcription

1 Sporting Contests and the Coase Theorem Stefan Szymanski Tanaka Business School, Imperial College London October 005 Paper presented at "Advances in the Theory of Contests and Tournaments", October -, 005, Hosted and organized by the Social Science Research Center Berlin WZB) in collaboration with the University of Tromsø.

2 Stigler: with zero transactions costs, private and social costs will be equal Coase: if private cost is equal to social cost, it follows that producers will only engage in an activity if the value of the product of the factors employed is greater than the value which they would yield in their best alternative use Dixit and Olson 000): arguably the single largest influence on thinking about economic policy for the last three decades Critics: Practicality: costless bargaining with full property rights not feasible, e.g. Canterbery and Marvasti 99) Tautology: with zero transaction cost efficiency guaranteed among maximising agents, regardless of whether property rights, e.g. Usher 998) Falsity: there exist initial allocations of property rights for which the core is empty, e.g. Aivazian and Callen 003)

3 Coase Theorem in the sports literature: Sports especially baseball) often cited as a natural test of the Coase Theorem Professional league sports: A form of multi-stage contest characterised by a) asymmetry, b) demand for competitive balance as well as demand for success Teams allocate annual budgets to player salaries plus player acquisition costs Strong correlation between a) spending and success e.g. percentage of matches won) and b) between success and income Property rights over players in a sports league: Reserve Clause of baseball, Retain and Transfer System of English soccer

4 Rottenberg 956) "the defense most commonly heard is that the reserve rule is necessary to assure an equal distribution of playing talent among opposing teams; that a more or less equal distribution of talent is necessary if there is to be uncertainty of outcome; and that uncertainty of outcome is necessary if the consumer is to be willing to pay admission to the game. This defense is founded on the premise that there are rich baseball clubs and poor ones and that, if the players' market were free, the rich clubs would outbid the poor for talent, taking all competent players for themselves and leaving only the incompetent for other teams." p. 46) But he claims a market in which freedom is limited by the reserve rule such as that which now governs the baseball labor market distributes players among teams about as a free market would p.55) = Invariance Principle Mathematical restatement Quirk and El-Hodiri 974)): market distribution of talent is equal to the joint-profit maximising distribution Conclusion: Invariance Principle + market efficiency = Coase Theorem 3

5 Natural experiments:. Free agency in baseball in 976 Six year veterans free to move team Balance of evidence that competitive balance improved- distribution of players changed. The rookie draft 965 in baseball) Weak teams given first choice of new players entering the league Balance of evidence that competitive balance improved- distribution of players changed Not very powerful tests 4

6 A simple model of talent allocation in a sports league A. Each team generates attendance according to the number of wins, represented by a concave function Q i w i ) with Q i > 0 and Q i 0; beyond some critical value it is possible that Q i < 0. A. Win production: Each team purchases talent t) in a competitive market. Talent is assumed to be measured in perfectly divisible units and sold at a constant marginal cost. w t i i w i 0) = 0, w i ) =, > 0 and < 0. i w t i A3. Teams maximize profits, and the league planner maximizes attendance. Suppose all teams constrained to charge the same price Proposition a) If the marginal revenue functions are identical, then the noncooperative Nash equilibrium for the league will be perfectly balanced planner s allocation coincides with the Nash equilibrium). b) With asymmetric marginal revenue functions, the planner s equilibrium is less balanced than the noncooperative Nash equilibrium. 5

7 Proof π i = piqi wi ) cti ) Q Q ' i ' j = w i j t j wi t for all i and j. Thus at the Nash equilibrium if t i > t j then Q i > Q j. At the planner s optimum ' Qi 3) = ' Q j for all i and j Competitive externality commonplace in IO contexts) Hirshleifer s paradox of power 6

8 Empirical test: Estimate for each team the relationship between winning and attendance over some sample period: 4) Attendance it = a t + b i wpc it + c i wpc it + ε it Use the coefficients b i and c i to estimate the optimal distribution of wins 7

9 Actual and maximum attendance for the English second tier, 00/03 Club Actual win percentage Actual average attendance Attendance maximising win percentage constrained attendance maximising win percentage Bradford City Brighton & Hove Albion Burnley Coventry City Crystal Palace Derby County Gillingham Grimsby Town Ipswich Town Leicester City Millwall Norwich City Nottingham Forest Portsmouth Preston North End Reading Rotherham United Sheffield United Sheffield Wednesday Stoke City Walsall Watford Wimbledon Wolverhampton Wanderers Total Standard deviation maximum average attendance

10 Table : Actual attendance and maximum feasible attendance, Season Sum of average attendance per club actual) Sum of average attendance per club constrained optimal) difference standard deviation of win percentages actual) standard deviation of win percentages constrained) sum of win percentages constrained) 993/ % / % / % / % / % / % / % / % / % / %

11 Second tier English football Sum of average attendance per club actual) Sum of average attendance per club constrained optimal) 993/94 994/95 995/96 996/97 997/98 998/99 999/00 000/0 00/0 00/03

12 You Cannot Be Serious. Similar empirical results for Major League Baseball. Do fans demand competitive balance per se? 3. Do owners maximise profit? 4. Would redistributive measures help? they are generally intended to create more competitive balance, not less 5. Delegating control and the integrity of the sport 6. Other considerations- TV? 7. The Abramovitch effect 3

13 Pre-emption through bidding The Abramovitch effect: bookmakers have paid out to bettors on Chelsea to win the Premier League after only nine games of a 38 game season: t A w =, w = w t + t A) π = - w ) w ct, π = - w ) w ct, > A3) π = - w ) w - ct D = 0, t π t = - w ) w - ct D = 0 where T D = t + t, so that at the Nash equilibrium A4) w * = / + ) 4

14 A5) c T c t c t D 3 3, + = => + = + = T D T S c* A6) S T c * + = A7) * * w R w w w R = = + > + = = 5

15 Joint profits A8) π + π = + )w - w ct, A9) w M = + )/4 > w * Inefficient result 6

16 The incentive to pre-empt At the interior equilibrium the profits of the dominant team is 4 + A0) π* = 3 + ) If team pre-empts by offering a wage rate c* + ε, it acquires all the talent T S = t * + t *) has a win percentage w = and obtains, for ε small enough, profits equal to 3 S A c * T = + ) Pre-emption can therefore be profitable if A 3 > + + > *.84 Note w M = + )/4 implies w M = for = 3) 7

17 Pre-emption and bidding for talent Under these conditions firm will start to bid up the price of talent A3) Pre-emption constraint: c = c** where π w =, c**) = π w = w *), c**) A4) Participation constraint: π w = w *), c**) 0 To solve for c** when 3) binds A5) + ) + 3 S c ** T = c* * T S From this we derive A6) c ** 3 + S T + ) = 8

18 Competition from firm The participation constraint requires A7) π w = w *), c**) = S c** T + ) + 0 From A6) and A7) we can see that both constraints bind when 3 A8) + + = 0 => = + + ) + 9

19 Contest wages and pre-emption 0.8 no pre-emption no pre-emption but wages rise to deter it pre-emption occurs but profit lower than under c* with no pre-emption 0.6 pre-emption occurs and is more profitable 0.4 wage rate 0. c* c** sigma competitive imbalance) 0

20 Conclusion: 3 regimes. < * interior equilibrium, pre-emption never profitable. * < < + pre-emption at c*, profitable, but wages bid up so that pre-emption does not occur 3. > + pre-emption occurs NB pre-emption occurs at values of < 3)