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Game Theory and

Applications

A Friendly Tutorial

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

Talk Based on

Y. Narahari, Dinesh Garg, Rama Suri, Hastagiri Prakash

Game Theoretic Problems in Network

Economics and Mechanism Design

Solutions

Monograph Published by Springer, London, 2009

Inspiration: John von Neumann

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

Nobel 2005^ Excitement: The

Nobel Prizes in

Economic Sciences

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)

MOTIVATING PROBLEMS

Problem 1: Direct Materials Procurement at IISc

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

KEY OBSERVATIONS

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)

Example 1: Matching Pennies

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}

Example 2: Prisoner’s Dilemma

No Confess NC

Confess

C

No Confess

NC - 2, - 2 - 10, - 1

Confess

C -1, - 10 - 5, - 5

Dominant Strategy Equilibrium

No Confess NC

Confess

C

No Confess

NC - 2, - 2 - 10, - 1

Confess

C -1, - 10 - 5, - 5

(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