Contests

Question 1

Which contests are supposed to create the most surplus?

Answer 1

• Rottenberg (1956) says that balanced contests create the most surplus

Question 2

What are the payoff and profit functions in the Tullock model of contests?

Answer 2

Question 3

How do you solve the tullock model to find the equilibrium level of effort?

Answer 3

1. Differentiate π_i with respect to e_i
2. Simplify this formula
3. Use symmetric equilibrium e_i* = e_j*

• ^prize (V) = ^ e
• ^ players = less e
• ^y = ^e
• equal chance of winning, p = 1/N

Question 4

How does the free market reach an equilibrium level of talent?

Answer 4

• two teams, big and small
• talent produces wins, wins produce revenue
• Therefore, MR of talent is combo of how talent impacts win prob. and how win affects revenue
• MR_i > MR_j - big team MR is higher
• talent flows from small to big till MR_i = MR_j = c*
• Rottenberg - talent should move to where its most productive even if its unbalanced

Question 5

What is the principle of the draft?

Answer 5

Allocates new talent to the weakest teams first to try and stop the dominance that can come around in free market

Question 6

How does the draft work in a free mobility model?

Answer 6

• When there is free mobility the draft won’t improve the balance of talent
• Coase theorum: Property rights will be employed in their most productive use
  
  • There is only a wealth transfer, MR hasnt been changed

Question 7

How does the draft work in a model with mobility resttrictions?

Answer 7

• Coase requires no transcation costs, even Coase himself didnt like this
• In the NFL there are mobility restrictions in the way of salary caps
• Salary caps transfer wealth from the players to the team owners
• can improve the balance when combined with the draft
• Efficiency cost - talent not employed at its most productive place

Question 8

What is the importance of the Symanski league model?

Answer 8

It implies there is an externality of talent

Reaches an equilibrium where MR_i is not equal to MR_j

It is not socially efficent

Question 9

How does the symanski model find the equilibrium level of talent?

Answer 9

1. Set up
2. Max π with respect to talent
3. Solve ^dw/_dt
4. Will need to use nash conjecture = 0
5. Solve equilibrium

Question 10

What are the implications of the symanski model?

Answer 10

1. Increasing talent for one team will increase the ratio of Marginal revenues
2. Not socially efficent
3. Captures the idea of strategic substitution
4. Increasing talent for i imposes an externality on j

Question 11

What is the empirical evidence for the competitive balance theory?

Answer 11

• US sports are more balanced but demand for non-US sports are higher - potentially deu to higher quality in Europe
• Knowles (1992) Used pre match probability of home victory as proxy for uncertainty/ balance
  
  • Expected value = 0.5 for peak attendance, actual value = 0.6
  • Limited by betting market imperfections and that it only used stadium attendance
• Borland & Macdonald (2003) 3 out of 18 studies support match day uncertainty
  
  • home fan effect: ^ prob of home win = ^ attendance