Ecosel as an Example of Subscription Games

Lecture 12 (5/20/2015)

Bundle 3

Bundle 28

The ECOSEL Concept

Bundle 31

Bundle 43

Bundle 1

Bundle 31

Bundle 3

Bundle 3 Old-Forest: 534.79 ac Carbon: 25,087 MgC Reserve Price: $80

Bundle 31 Old-Forest: 698.52 ac Carbon: 76,743 MgC Reserve Price: $291

The ECOSEL Concept (cont.)

Bundle 31

Bundle 1 (Max Timber Profit)

reserve price

Bundle 18

The Auction Component

Classification

ECOSEL is a multi-unit, multi-dimension,

public good subscription gamewith incomplete informationand 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);

• = valuation or utility that Player k assigns to Bundle k;

• = the final bid that Player k places on Bundle i; and

• ri is the reserve price of Bundle i

kiv

kib

Mathematical Characterization Cont.

k k k ki i i i i i i

k K k K k K

SS v b b r v r

Social Surplus:

Note: Social surplus does not depend on the value of final bids

Mathematical Characterization Cont.

Theoretical Welfare Maximum:

k ki i j j

j Ik K k K

v r Max v r

Mathematical Characterization Cont.

Winning Conditions and Efficiency:

(1)    0

(2)   

ki i

k K

k ki i j j

j Ik K k K

b r

b r Max b r

Mathematical Characterization Cont.

Payoff Function for Player :

\ \

,

  ,   : 

                                                                                              ,  

k k

k

k k k k k k ki i i i i i i i j j

j Ii I k Kk K k k K k

ki k

u v b

v b p b b r b b r Max b rMax

b B

  kib R 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