# PowerPoint Presentation - Economics - University of Pittsburgh by dfhdhdhdhjr

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```									Cohen and Sela (2005)
Cohen and Sela (2005)
Cohen and Sela (2005)
Cohen and Sela (2005)
Cohen and Sela (2005)
Cohen and Sela (2005): Review

The authors study the classical Tullock’s model and show
that by a simple non-discriminating rule the contest
designer is able to manipulate the outcome of the contest
such that the probabilities to win are not ordered according
to the contestant’s abilities.

2 players only?
N players?
The contest designer maybe able to manipulate?

Alexander Matros
Department of Economics
University of Pittsburgh
Plan
   Motivation
   Preliminary Results
   Model
   Results
   Examples
   Conclusion
Motivation
How to Raise Money?
How to reduce Rent-Seeking?

1.    Contest design
2.    Prize structure

What if the design and the prize structure are fixed?
Motivation: Example

Charity Lottery with a given prize.

Rent-Seeking activities
Motivation
This paper:

Consider transfers of players’ contributions
Preliminary Results

Winner-get-her-money-back contests
Example

The Amsterdam auction:
a loser gets premium which depends only on her own bid.
The Model: different values
   n ≥ 2 risk-neutral contestants
   One prize
   Contestants' prize valuations are commonly known

V1 ≥ … ≥ V n ≥ 0

   Player i exerts effort (buys lottery tickets of the amount) xi and wins the
prize and her contribution with probability          xi
n

x
j 1
j

   Cohen and Sela (EL, 2005): n = 2 and a particular case for n = 3.
Player i’s problem

xi
max   n
Vi  xi   xi
x
xi
j
j 1
Results
Based on the approach in (Hillman and Riley, 1989)
n
Define the total spending    s ( n)   xi
i 1

s n   xi
FOC
Vi  xi  2          
xi
1
s n      s n 
Results
FOC

x  Vi  2sn xi  sn sn   Vi   0,
2
i

Vi  Vi
xi  sn           .
2
Results
Proposition 1. ( 0,...,0,xi,0,...,0) is i-equilibrium, if

V1 , if i  1,
xi  
V2 , if i  1.
Cohen and Sela (2005)
Results
Results
Results
Cohen and Sela (2005)
Example: V1 ≥ V2 ≥ V3.
i-type equilibria

1-type: (x1, 0,0), where x1 ≥ V2;
2-type: (0, x2, 0), where x2 ≥ V1;
3-type: (0,0, x3 ), where x3 ≥ V1.
Example: V1 ≥ V2 ≥ V3.
Internal equilibria
(V2, V1, 0) and (V3, 0, V1).

If V1 ≤ V2 + V3, then

(0, V3, V2) and

1
V2  V3  V1 , V1  V3  V2 , V1  V2  V3 .
2
Results: Properties of equilibria

Proposition 4. The expected payoff of the active player i
in the equilibrium of i-type is Vi.

Proposition 5. The expected payoff of each player in any
internal equilibrium is zero.
Results: Properties of equilibria
Proposition 6. In each internal equilibrium with k active
players,
xi1  ...  xik
and
pi1  ...  pik
if and onlyif
Vi1  ...  Vik .
Results: Properties of equilibria

Corollary 2. A stronger player always has a smaller
chance to win the contest than a weaker player in any
internal equilibrium.
Cohen and Sela (2005)
Results: Total spending
Results: Rent Dissipation
Results: Rent Dissipation
Results: Rent Dissipation
Results: Rent Dissipation
Example: with or without reimbursement
Example: with or without reimbursement
Results: Rent Dissipation
Conclusion
1. All equilibria in asymmetric contests

2. Properties are discussed

3. A higher value (stronger) player always exerts less
effort than a lower value (weak) player

4. The expected net total spending might be higher

5. Applications: Lotteries, Charities

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