Ecosel as an Example of
Subscription Games
Lecture 12 (5/24/2017)
Bundle 3
Old-Forest:
534.79 ac
Carbon:
25,087 MgC
Reserve Price:
$80
The ECOSEL Concept
Bundle 1
Bundle 28
Bundle 31
Bundle 43
Bundle 31
Old-Forest:
698.52 ac
Carbon:
76,743 MgC
Reserve Price:
$291
Bundle 3
The ECOSEL Concept (cont.)
Bundle 1 (Max Timber Profit)
Bundle 18
Bundle 31
reserve price
The Auction Component
Classification
ECOSEL is a multi-unit, multi-dimension,
public good subscription game
with incomplete information
and asymmetric preferences
Subscription games: Bagnoli and Lippman 1989
Mathematical Characterization
Notation:
• I = the set of bundles available in the auction (i
indexes I);
• K = the set of players who play the game (k
indexes K);
k
v
• i = valuation or utility that Player k assigns to
Bundle k;
k
b
• i = the final bid that Player k places on Bundle i;
and
• ri is the reserve price of Bundle i
Mathematical Characterization Cont.
Social Surplus:
SSi    vik  bik    bik  ri   vik  ri
kK
kK
kK
Note: Social surplus does not depend on the value of final bids
Mathematical Characterization Cont.
Theoretical Welfare Maximum:


k
v  ri  Max   v j  rj 

jI
kK
 kK

k
i
Mathematical Characterization Cont.
Winning Conditions and Efficiency:
(1)
k
b
 i  ri  0
kK


k
(2)  b  ri  Max   b j  rj 
jI
kK
 kK

k
i
Mathematical Characterization Cont.
Payoff Function for Player k :


uk v k , b k 
  k

 k

 
k
k
k
k
k
  vi  bi  p bi   bi  ri , bi   bi  ri  Max

  b j  rj    :
jI
 Max  iI 
 kK
 
kK \ k
kK \ k




k
k

b

B
,
b

R

i

I
i
i
k




Mechanism Design
• Design options
– Maximize social surplus
– Maximize seller revenue
• Methods
– Theoretical testing (game theory and
simulation)
– Empirical testing (experimental economics)
• Software development
Mechanism Design cont.
• Design variables:
– Reserve price disclosure
– Communication policy
– Bid withdrawal policy
– Refund policy
– Number of bundles
– Auction sequencing
– And many more….
Website
How it works
How it works
How it works