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A tutorial on game theory and its applications in e-commerce. It covers strategic form games, mechanism design, cooperative games, and their solutions. The document also discusses the inspiration behind game theory and its relevance to various fields such as microeconomics, sociology, and computer science.
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June 2, 2009
Y. NARAHARI (IISc), DINESH GARG (Yahoo! Labs) ,
RAMASURI NARAYANAM (IISc)
E-Commerce Laboratory Computer Science and Automation Indian Institute of Science, Bangalore
Y. Narahari, Dinesh Garg, Rama Suri, Hastagiri Prakash
Monograph Published by Springer, London, 2009
Founded Game Theory with Oskar Morgenstern (1928-44)
Pioneered the Concept of a Digital Computer and Algorithms
60 years later (2000), there is a convergence ; this has been the inspiration for our research
John von Neumann (1903-1957) created two intellectual currents in the 1930s and 40s
Robert Aumann
The Nobel Prize was awarded to two Game Theorists in 2005 – Aumann visited IISc on January 16, 2007 The prize was awarded to three mechanism designers in 2007 Myerson has been one of our heroes since 2003
Eric Maskin visited IISc on December 16, 2009 and gave a talk in the Centenary Conference
Thomas Schelling Nobel 2005
Leonid Hurwicz Nobel 2007
Eric Maskin Nobel 2007
Roger Myerson Nobel 2007
Optimal solutions translate into significant benefits
Indirect Materials Procurement at Intel (2000)
Direct Materials Procurement at GM (2002)
Network Formation Problems at GM (2003) Infosys (2006), and IBM (2006)
Sponsored Search Auctions on the Web (2006-09)
Buyer 1,00, units of raw material
SUPPLIER 1
SUPPLIER 2
SUPPLIER 3
Incentive Compatible Procurement Auction with Volume Discounts Even 1 percent improvement could translate into millions of rupees
Supply Curves
Abstraction: Shortest Path Problem with Incomplete Information
S B
C
T
SP1 SP
SP3 SP
SP3 SP
A
The costs of the edges are not known with certainty
PROBLEM 3: Sponsored Search Auction
CPC^ Advertisers
1
2
n
Paid search auction is the leading revenue generator on the web
Players are rational, Intelligent, strategic
Both conflict and cooperation are “issues”
Some information is “common knowledge”
Other information is “private”, “incomplete”, “distributed”
Our Goal: To implement a system wide solution (social choice function) with desirable properties
Game theory is a natural choice for modeling such problems
Game Theory
Mathematical framework for rigorous study of conflict and cooperation among rational, intelligent agents
Market
Buying Agents (rational and intelligent)
Selling Agents (rational and intelligent)
Social Planner (Mechanism Designer)
Two players simultaneously put down a coin, heads up or tails up. Two-Player zero-sum game N = {1, 2}; S 1 = S 2 = {H,T}
No Confess NC
No Confess
No Confess NC
No Confess
(C,C) is a dominant strategy equilibrium
A dominant strategy is a best response whatever the strategies of the other players
Pure Strategy Nash Equilibrium
A profile of strategies is said to be
a pure strategy Nash Equilibrium if is a best
response strategy against s * i i^ ^1 ,^2 ,..., n
s 1 * , s 2 *,..., sn *
s i