  Intelligent Databases / Game Theory Peter van Emde Boas INTELLIGENT DATABASES GAME THEORY PART 1 PREFACE Peter van Emde Boas ILLC-FNWI-UvA Bronstee.com Software & Services B.V See:

  Intelligent Databases / Game Theory Peter van Emde Boas AGENDA

  Intelligent Databases / Game Theory Peter van Emde Boas Games in Computer Science Evasive Graph properties ( ) Information & Uncertainty (Traub ea ) Pebble Game (Register Allocation, Theory 1970+) Tiling Game (Reduction Theory ) Alternating Computation Model ( ) 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)

  Intelligent Databases / Game Theory Peter van Emde Boas Games in Computer Science Cryptography Scenario Analysis –Secure Information Transmission –Secure transactions Agent Technology Distributed Computation –Leader Election –Byzantine Agreement Robot Soccer

  Intelligent Databases / Game Theory Peter van Emde Boas SECURE COMMUNICATION ALICEBOB ELIAS

  Intelligent Databases / Game Theory Peter van Emde Boas SECURE TRANSACTIONS ALICE BOB’s BANK ALICE’s BANK BOB CROOKS

  Intelligent Databases / Game Theory Peter van Emde Boas Computer Science for Games Analysis Game trees (Checkers, Chess, Backgamon, Go, Othello,...) Theory of  -  pruning Artificial Intelligence and (also) Computer Games....

  Intelligent Databases / Game Theory Peter van Emde Boas Previous Ph.D. Research © Peter van Emde Boas Anette Bleeker: Modal Logic & Cryptographic Protocols Marc Pauly: Power of Coalitions © Peter van Emde Boas Hans van Ditmarsch: Knowledge Games Cluedo Analysis

  Intelligent Databases / Game Theory Peter van Emde Boas Game Theory Theory of Strategic Interaction Attributes –Discrete vs. Continuous –Cooperative vs. Non-Cooperative –Full Information vs. Incomplete Information (Knowledge Theory)

  Intelligent Databases / Game Theory Peter van Emde Boas Discrete / Continuous Combinatorial Analysis Backward Induction Number Theory (Conway Guy Berlekamp) Equilibria theory (Nash) Stochasitic Features Optimization Other names of importance: Von Neumann & Morgenstern Aumann Shapley Harsanyi

  Intelligent Databases / Game Theory Peter van Emde Boas © Games Workshop URGATTHORGRIM Introducing the Opponents

  Intelligent Databases / Game Theory Peter van Emde Boas STRATEGIC VOTING Alice Bob Boris Horace Maurice Genootschap voor de Verpoldering van de Cultuur Agenda: Proposition: Alice to become Member Amendment: Bob to replace Alice

  Intelligent Databases / Game Theory Peter van Emde Boas STRATEGIC VOTING (2) Boris Horace Maurice Genootschap voor de Verpoldering van de Cultuur AliceBob 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

  Intelligent Databases / Game Theory Peter van Emde Boas Auctions FOR SALE ALICE HORACE £ 3M or £ 4M MAURICE £ 3M or £ 4M

  Intelligent Databases / Game Theory Peter van Emde Boas Auctions Dogbert’s advice to Alice: Run a Second-Price Auction © Scott Adams

  Intelligent Databases / Game Theory Peter van Emde Boas Auctions Second Price Auction Incites Buyers to submit true bids: Winner: Had I bid something else, it wouldn’t matter for the price paid, except when I had bid less than my opponent, in which case I would have scored nothing..... Loser: Had I bid something else, it wouldn’t have made a difference, except when I would have bid more than my opponent, in which case I would have paid more than what I believe the house should cost......

  Intelligent Databases / Game Theory Peter van Emde Boas Expected Gain for Alice Horace’s bid£ 3 M £ 4 M Maurice’s bid £ 3 M £ 4 M ½ ½ ½ ½ £ 0 M £ 1 M Expected profit: ¾ * £ 0 M + ¼ * £ 1 M = £ ¼ M

  Intelligent Databases / Game Theory Peter van Emde Boas Auctions Dogbert’s advice to Alice: Run a Second-Price Auction Ratbert’s advice to Horace and Maurice in case of First-Price Auction: Use mixed strategy: if willing to pay £ 4M bid := £ cM with such a distribution that P( bid ≤ £ bM ) = (b-3) / (4-b) © Scott Adams

  Intelligent Databases / Game Theory Peter van Emde Boas AUCTION What Ratbert’s advice amounts to Alice sells to Horace Alice sells to Maurice Maurice’s Bid £ 3M £ 3.5M £ 4M Maurice’s Reservation Price £ 4M £ 3M £ 3.5M Horace’s Bid Horace’s Reservation Price © Scott Adams

  Intelligent Databases / Game Theory Peter van Emde Boas Ratbert’s Advice Expected 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))) = ½ I.E., constant which not depends on b !

  Intelligent Databases / Game Theory Peter van Emde Boas Ratbert’s Advice Expected gain Alice: E(gain A ) = E(gain A | H wins) * P( H wins) + E(gain A | M wins) * P( M wins) = E(gain A | H wins) = E(gain A | H wins, H:3) * P(H:3) + E(gain A | H wins, H:4) * P(H:4) = ½ * E(gain A | H wins, H:4) = ½ * (1 - E(gain H | H wins, H:4) ) = ¼ by symmetry This is exactly what Alice can expect if she follows Dogbert’s advice..... Can she hope to gain more ???

  Intelligent Databases / Game Theory Peter van Emde Boas PLATFORM SELECTION Constructing a Platform for the Haran Ghomarist Party ISSUEIn FavourAgainst Prohibition of Smoking Elimination Mobile Phones Sodomy Laws Proposition year Curriculum in Academia Praying in School

  Intelligent Databases / Game Theory Peter van Emde Boas PLATFORM SELECTION (2) Akalawite PartyHamatite Party 01  { Borg Hive }{ Ferengi Alliance }

  Intelligent Databases / Game Theory Peter van Emde Boas PLATFORM SELECTION (3) Akalawite PartyHamatite Party 01  { Borg Hive }{ Ferengi Alliance } Ghomarist Party 