MS&E246:GameTheorywithEngineeringApplicationsLecture 1Ramesh JohariOutline• Administrative stuff• Course introduction•A gameAdministrativedetails• My e-mail: [email protected]• Course assistant:Christina Aperjis, [email protected]•Website:eeclass.stanford.edu/msande246All students must sign up there,and keep up with announcementsAdministrativedetails•6-7 problem setsAssigned Thursday, due following Thursday in box outside Terman 319No late assignments accepted• Midterm to be held February 8 (in class)BigpictureEconomics and engineering aretied together more than everGame theory provides a set of tools we can use to study problems at this interfaceMotivatingexamples• Electronic marketplaces•eBay auctions:Fixed termination time•Amazon auctionsTerminate after 10 minutes of inactivityWhich yields higher revenue?Motivatingexamples• Internet resource allocation• TCP: regulates flow of packets through the Internet• Malicious users can grab much more than “fair” share• How do we design “fair”, “efficient”allocation protocols that are robust to gaming?Motivatingexamples•Electricity markets• Electricity can’t be stored, andmust be reliable• Market failure is disastrous(e.g., California in 2000)• How do we design efficient, sustainable markets?Internetprovidercompetition• Internet = 1000s of ASes (autonomous systems)• Bilateral contracts between ASes:•Transitvs. peer contractsA BISPcontracts•Transitvs. peer contracts•Transit:If A pays B, thenA agrees to carry all traffic to/from B•Peer:A and B are of similar size,and agree to exchange trafficterminating in each other’s networkProblemsintheISPindustry• In 2002, seven dominant players:• Sprint•AT&T• MCI/UUnet•Qwest•C&W• Level3• GenuityProblemsintheISPindustry• In 2002, seven dominant players:• Sprint (subsidized by wireless)•AT&T ACQUIRED (SBC)• MCI/UUnet ACQUIRED (Verizon)•Qwest $18B debt•C&W R.I.P. (in U.S.)• Level3 (merged w/Genuity)• Genuity ACQUIRED (Level3)Econ101,pt.1:warofattrition•Pricing below marginal cost⇒ War of attrition (repeated game):Lose money now in hopes of being last firm standingEcon101,pt.2:Bertrand• Example:• If p1< p2, then ISP 2’s profit = zeroCNNISP 1 ISP 2peer“eyeballs”p1p2Thefuture• Econ 101 captures the essence:• cutthroat pricing• massive financial losses• “last firm standing” mentality• Question: Is a regulated monopoly the only endgame?EngineeringWhat is the problem in Bertrand example?ISP 2 receives no credit for the value generated.Current protocols don’t expedite transmission of value information.⇒ How do we build economically robust, informative protocols?ThiscourseWe will develop the basics of noncooperative game theory……but with an eye towards connection with engineering applications.OurfirstgameTwo players each have a budget of $4.00.I have $8.00.Each player i puts $wiin an envelope.I give player i a fraction wi/(w1+ w2) of the $8.00 that I have.Whatever they did not put in the envelope, they keep for themselves.Reasoningaboutthegame• What is the “best” a player can do?• What is the best they can do together?• Should they ever bid zero?• Is there any bid a player should nevermake?• What is the minimum a player can guarantee himself or herself?• What will happen when the game is played?ReasoningaboutthegamePlayer 1’s payoff = 8 x w1/(w1+ w2) + 4 - w1$4$3$2$1$0$4.00$4.57$5.33$6.40$8.00$4$4.43$5.00$5.80$7.00$9.00$3$4.67$5.20$6.00$7.33$10.00$2$4.60$5.00$5.67$7.00$11.00$1$4.00$4.00$4.00$4.00$4.00$0Player 2’s bidPlayer 1’s bidReasoningaboutthegameNote that bidding $2 is always better than bidding $0, $3, or $4:$4$3$2$1$0$4.00$4.57$5.33$6.40$8.00$4$4.43$5.00$5.80$7.00$9.00$3$4.67$5.20$6.00$7.33$10.00$2$4.60$5.00$5.67$7.00$11.00$1$4.00$4.00$4.00$4.00$4.00$0Player 2’s bidPlayer 1’s bidReasoningaboutthegameIf we anticipate player 2 will not bid $0, $3, or $4…$4$3$2$1$0$4.00$4.57$5.33$6.40$8.00$4$4.43$5.00$5.80$7.00$9.00$3$4.67$5.20$6.00$7.33$10.00$2$4.60$5.00$5.67$7.00$11.00$1$4.00$4.00$4.00$4.00$4.00$0Player 2’s bidPlayer 1’s bidReasoningaboutthegame…then we should always bid $2…$4$3$2$1$0$4.00$4.57$5.33$6.40$8.00$4$4.43$5.00$5.80$7.00$9.00$3$4.67$5.20$6.00$7.33$10.00$2$4.60$5.00$5.67$7.00$11.00$1$4.00$4.00$4.00$4.00$4.00$0Player 2’s bidPlayer 1’s bidReasoningaboutthegame…and so should player 2.$4$3$2$1$0$4.00$4.57$5.33$6.40$8.00$4$4.43$5.00$5.80$7.00$9.00$3$4.67$5.20$6.00$7.33$10.00$2$4.60$5.00$5.67$7.00$11.00$1$4.00$4.00$4.00$4.00$4.00$0Player 2’s bidPlayer 1’s bidReasoningaboutthegame• Does this way of reasoning about the game make sense?• Thought experiments:What if the budgets are different?What if the size of the common pool