Intelligent Databases / Game Theory 2003. Peter van Emde Boas INTELLIGENT DATABASES GAME THEORY PART

Intelligent Databases / Game Theory 2003. Peter van Emde Boas

INTELLIGENT DATABASESGAME THEORY PART 1

PREFACE

Peter van Emde Boas

ILLC-FNWI-UvABronstee.com Software & Services B.V.

2003

See: http://staff.science.uva.nl/~peter/teaching/idb03.html


AGENDA


Games in Computer Science• Evasive Graph properties (1972-74)• Information & Uncertainty (Traub ea. - 1980+)• Pebble Game (Register Allocation, Theory 1970+)• Tiling Game (Reduction Theory - 1973+)• Alternating Computation Model (1977-81)• Interactive Proofs /Arthur Merlin Games (1983+)• Zero Knowledge Protocols (1984+)• Creating Cooperation on the Internet (1999+)• E-commerce (1999+)• Logic and Games (1950+)• Language Games, Argumentation (500 BC)


Games in Computer Science

• Cryptography Scenario Analysis– Secure Information Transmission– Secure transactions

• Agent Technology• Distributed Computation

– Leader Election– Byzantine Agreement

• Robot Soccer


SECURE COMMUNICATION

ALICE BOB

ELIAS


SECURE TRANSACTIONS

ALICE

BOB’s BANKALICE’s BANK

BOBCROOKS


Computer Science for Games

• Analysis Game trees (Checkers, Chess, Backgamon, Go, Othello, ...)

• Theory of - pruning

• Artificial Intelligence

• and (also) Computer Games....


Previous Ph.D. Research

© Peter van Emde Boas © Peter van Emde Boas

Anette Bleeker:Modal Logic & Cryptographic Protocols

Marc Pauly:Power of Coalitions

© Peter van Emde Boas

Hans van Ditmarsch:Knowledge GamesCluedo Analysis


Game Theory

• Theory of Strategic Interaction

• Attributes– Discrete vs. Continuous– Cooperative vs. Non-Cooperative– Full Information vs.

Incomplete Information(Knowledge Theory)


Discrete / Continuous

Combinatorial AnalysisBackward InductionNumber Theory(Conway Guy Berlekamp)

Equilibria theory (Nash)Stochasitic FeaturesOptimization

Other names of importance:Von Neumann & MorgensternAumannShapleyHarsanyi


© Games Workshop © Games Workshop

URGAT THORGRIM

Introducing the Opponents


STRATEGIC VOTING

Alice Bob

Boris Horace Maurice

Genootschap voor deVerpoldering van de

Cultuur

Prefs Boris Horace Maurice1 Alice Nobody Bob2 Nobody Alice Alice3 Bob Bob Nobody

Agenda:

Proposition: Alice to become Member

Amendment: Bob to replace Alice


STRATEGIC VOTING (2)

Boris Horace Maurice

Genootschap voor deVerpoldering van de

Cultuur

Alice Bob

Prefs Boris Horace Maurice1 Alice Nobody Bob2 Nobody Alice Alice3 Bob Bob Nobody

Agenda:

Proposition: Alice to become Member

Amendment: Bob to replace Alice

Procedural Proposal: First Vote on adding a new member at all !!!

1: Horace: Bob Alice in Amendment

2: Maurice: Alice Bob in Amendment


Auctions

FOR SALE

ALICE HORACE

£ 3M or£ 4M

MAURICE

£ 3M or£ 4M


Auctions

Dogbert’s advice to Alice:

Run a Second-Price Auction© Scott Adams


AuctionsSecond Price Auction Incites Buyers to submit true bids:

Winner: Had I bid something else, it wouldn’t matter forthe price paid, except when I had bid less than myopponent, in which case I would have scored nothing.....

Loser: Had I bid something else, it wouldn’t have madea difference, except when I would have bid more than myopponent, in which case I would have paid more thanwhat I believe the house should cost......


Expected Gain for AliceHorace’s bid £ 3 M £ 4 M

Maurice’s bid

£ 3 M

£ 4 M

½

½

½ ½

£ 0 M £ 0 M

£ 0 M £ 1 M

Expected profit: ¾ * £ 0 M + ¼ * £ 1 M = £ ¼ M


AuctionsDogbert’s advice to Alice:

Run a Second-Price Auction

Ratbert’s advice to Horace and Mauricein case of First-Price Auction:

Use mixed strategy: if willing to pay £ 4Mbid := £ cM with such a distribution thatP( bid ≤ £ bM ) = (b-3) / (4-b)

© Scott Adams

© Scott Adams


AUCTION

What Ratbert’s advice amounts to

Alice sells to Horace

Alice sells to Maurice

Maurice’s Bid

£ 3M£ 3M £ 3.5M

£ 4MMaurice’s Reservation Price

£ 4M

£ 3M

£ 3M

£ 3.5M

Horace’s Bid

Horace’s Reservation Price

© Scott Adams


Ratbert’s AdviceExpected gain for Horace with reservation value £ 4 M

When bidding £ b M:

When Maurice has reservation value £ 3 M : £ (4-b) M (which happens with prob. ½ )When Maurice has reservation value £ 4 M : £ (4-b) M only in case he wins the auction (which happens with prob. ½ (b-3) / (4-b) )

in total: (4-b)* ( ½*(1 + (b-3) / (4-b))) = ½I.E., constant which not depends on b !


Ratbert’s AdviceExpected gain Alice:

E(gainA ) = E(gainA | H wins) * P( H wins) + E(gainA | M wins) * P( M wins) =

E(gainA | H wins) =E(gainA | H wins, H:3) * P(H:3) + E(gainA | H wins, H:4) * P(H:4) =

½ * E(gainA | H wins, H:4) =½ * (1 - E(gainH | H wins, H:4) ) = ¼

by symmetry

This is exactly what Alice can expect if she followsDogbert’s advice..... Can she hope to gain more ???


PLATFORM SELECTION

Constructing a Platform for the Haran Ghomarist Party

ISSUE In Favour Against

Prohibition of SmokingElimination Mobile PhonesSodomy LawsProposition 3696 year Curriculum in AcademiaPraying in School...........


PLATFORM SELECTION (2)

Akalawite Party Hamatite Party

0 1

{ Borg Hive } { Ferengi Alliance }


PLATFORM SELECTION (3)

Akalawite Party Hamatite Party

0 1

{ Borg Hive } { Ferengi Alliance }

Ghomarist Party

Documents

Intelligent Databases / Game Theory 2003. Peter van Emde Boas INTELLIGENT DATABASES GAME THEORY PART