Issues on the border of economics and computation נושאים בגבול כלכלה וחישוב

1. Issues on the border of economics and computationנושאים בגבול כלכלה וחישוב INTRODUCTION

2. Instructors • Dr. LiadBlumrosenד"ר ליעד בלומרוזן • Department of economics, huji. • Dr. Michael Schapiraד"ר מיכאל שפירא • School of computer science and engineering, huji. • Office hours: by appointment.

3. Course requirements • Attend (essentially all) classes. • Solve 3-4 problem sets. • The final problem set might be slightly bigger. • Problem sets grade is 100% of the final grade. • No exam, no home exam.

4. Computer science and economics ?!? Today: • Introduction and examples • Game theory 1.0.1.

5. Classic computer science What a single computer can compute?

6. Classic Economics Analyzing the interaction between humans, firms, etc.

7. New computational environments Electronic markets Information providers • Properties: • Large-scale systems, belong to various economic entities. • Participants are individuals/firms with different goals. • Participants have private information. • Rapid changes in users behavior. Social networks P2P networks Mobile and apps Internet

8. Algorithmic game theory • Which tools can we use for analyzing such environments? • Interactions between computers, owned by different economic entities and different goals. • New tools should be developed: algorithmic game theory • The theory borrows a lot from each field.

9. What tools should we use? “Classic” CS Economics/Game theory • Not handling, eg: • Incentives • Asymmetric information • Participation constraints • Not handling, eg: • Tractability • Approximation • Various objectives • Algorithmic Game Theory: • Design & evaluate systems with selfish agents. • Real need from the industry.

10. Few examples

11. Example 1: Single-Item Auctions Say that you need to sell a single (indivisible) item to a set of bidders. How can you do that? • 1st-price auction • Buyers submit bids • Highest bid wins • Winner pays his own bid • 2nd-price auction • Buyers submit bids • Highest bid wins • Winner pays the 2nd-highest bid In which auction would you bid higher? How do people behave in such auctions? Which one earns greater revenue for the seller?

12. Example 1: Single-Item Auctions • Auctions are part of the mechanism design literature. • Mechanism design: economists as engineers.Design markets with selfish agent to achieve some desired goals. • Relation to computer science is straightforward. • Once a niche field in economics, now mainstream. • See this year’s Nobel prize (+ 2007, 1994)

13. Example 2: Sponsored-search auctions • Bla Search results Advertisements

14. Example 2: Sponsored-search auctions • Selfish parties: • Google vs. Yahoo vs. MSN • Users • Advertisers • A real system: • A simple interface • short response time • robustness • Economic challenges, eg: • Which auction to use? • Private info – how much advertisers will pay? • Click Fraud • Attract new advertisers • payments per impression/click/action

15. Example 3: FCC spectrum auctions • Multi-billion dollar auctions. • Preferences for bundles of frequencies (Combinatorial auctions): • Consecutive geographic areas. • Overlaps, already owned spectrum. • Sophisticated bidders • At&t, Verizon, Google. • Again, asymmetric information. • Bottleneck: communication.

16. Example 4: selfish routing • Many cars try to minimize driving time. • All know the traffic congestion (גלגלצ, WAZE)

17. Externalities and equilibria • Negative externalities: my driving time increases as more drivers take the same route. • In “equilibrium”: no driver wants to change his chosen route. • Or alternatively: • Equilibrium: for each driver, all routes have the same driving time. • (Otherwise the driver will switch to another route…)

18. Efficiency, equilibrium. • Our question:are equilibriasocially efficient? • Would it be better for the society if someone told each driver how to drive? • We would like to compare: • The socially-efficientoutcome. • What would happen if a benevolent planner controlled traffic. • The equilibrium outcome. • What happens in real life.

19. Network 1 • c(n) – the cost (driving time) to users when n users are using this road. • Assume that a flow of 1 (million) users use this network. C(n)=1 (million) S T • Socially efficient outcome: splitting traffic equally • expected driving time: ½*1+½*1/2=3/4 • Exercise: prove this is efficient. • The only equilibrium:everyone use lower edge. • Otherwise, if someone chooses upper link, the cost in the lower link is less than 1. • Expected cost: 1*1=1 C(n)=n

20. Network 1 C(n)=1 (million) S T • Conclusion: • Letting people choose paths incurs a cost • “price of anarchy” • The immediate question:if we have a ratio of 75% for this small network, can it be much higher in more complex networks?Which networks? C(n)=n

21. Network 2 c(n)=n c(n)=1 • In equilibrium: half of the traffic uses upper routehalf uses lower route. • Expected cost: ½*(1/2+1)+1/2*(1+1/2)=1.5 S T c(n)=n c(n)=1

22. Network 3 Now a new highway was constructed! c(n)=n v c(n)=1 • The only equilibrium in this graph:everyone uses the svwt route. • Expected cost: 1+1=2 • Building new highways reduces social welfare!? c(n)=0 S T W c(n)=1 c(n)=n

23. Braess’s Paradox Now a new highway was constructed! c(n)=n v c(n)=1 • This example is known as the Braess’s Paradox:sometimes destroying roads can be beneficial for society. • The immediate question: how can we choose which roads to build or destroy? S c(n)=0 T W c(n)=n c(n)=1

24. Level3 AT&T Comcast Qwest Example 5: Internet Routing Establish routes between the smaller networks that make up the Internet Currently handled by the Border Gateway Protocol (BGP).

25. Level3 AT&T Comcast Qwest Why is Internet Routing Hard? Not shortest-paths routing!!! Always chooseshortest paths. Load-balance myoutgoing traffic. Avoid routes through AT&T if at all possible. My link to UUNET is for backup purposes only.

26. BGP Dynamics Prefer routes through 1 Prefer routes through 2 2 1 1, my route is 2d 2, I’m available 1, I’m available d

27. Two Important Desiderata • BGP safety • Guaranteeing convergence to a stable routing state. • Compliant behaviour. • Guaranteeing that nodes (ASes) adhere to the protocol.

28. We saw examples for modern systems that raise many interesting questions in algorithmic game theory. • Next:a quick introduction to game theory • Outline: • What is a game? • Dominant strategy equilibrium • Nash equilibrium (pure and mixed)

29. Game Theory • Game theory involves the study of strategicsituations • Portrays complex strategic situations in a highly simplified and stylized setting • Strategic situations: my outcome depends not only on my action, but also on the actions of the others. • A central concept: rationality • A complex concept. Many definitions. • One possible definition:Agents act to maximize their own utility subject to the information the have and the actions they can take.

30. Applications • Economics • Essentially everywhere • Business • Pricing strategies, advertising, financial markets… • Computer science • Analysis and design of large systems, internet, e-commerce. • Biology • Evolution, signaling, … • Political Science • Voting, social choice, fair division… • Law • Resolutions of disputes, regulation, bargaining… • …

31. Game Theory: Elements • All games have three elements • players • strategies • payoffs • Games may be cooperative or noncooperative • In this course, noncooperative games.

32. Let’s see some examples….

33. Example 1: “chicken” Chicken!!!

34. Example 2: Prisoner’s Dilemma • Two suspects for a crime can: • Cooperate (stay silent, deny crime). • If both cooperate, 1 year in jail. • Defect (confess). • If both defect, 3 years (reduced since they confessed). • If A defects (blames the other), and B cooperate (silent) then A is free, and B serves a long sentence.

35. Lecture Outline • What is a game? • Few examples.  Best responses • Dominant strategies • Nash Equilibrium • Pure • Mixed • Existence and computation

36. Notation • We will denote a game G between two players (A and B) by G[ SA, SB, UA(a,b), UB(a,b)] where SA = set of strategies for player A (aSA) SB = set of strategies for player B(bSB) UA: SA x SB R (utility function for player A) UB: SAx SB Rutility function for player B

37. Normal-form game: Example • Example: • Actions:SA = {“C”,”D”}SB = {“C”,”D} • Payoffs:uA(C,C) = -1, uA(C,D) = -5, uA(D,C) = 0, uA(D,D) = -3

38. A best response: intuition • Can we predict how players behave in a game? • First step, what will players do when they know the strategy of the other players? • Intuitively: players will best-respond to the strategies of their opponents.

39. A best response: Definition • When player B plays b. A strategy a* is a best response to bif UA(a*,b)  UA(a’,b) for all a’ SA (given that B plays b, no strategy gains Aa higher payoff than a*)

40. A best response: example Example:When row player plays Up,what is the best response of the column player?

41. Dominant Strategies(אסטרטגיות שולטות/דומיננטיות) • Definition: action a* is a dominant strategy for player A if it is a best response to every action b of B. Namely, for every strategy b of B we have: UA(a*,b)  UA(a’,b) for all a’ SA

42. Dominant Strategies: in the prisoner’s dilemma • For each player: “Defect” is a best response to both “Cooperate” and “Defect. • Here, “Defect” is a dominant strategy for both players…

43. Dominant Strategy equilibriumשווי משקל באסטרטגיות שולטות • Definition:(a,b) is a dominant-strategy equilibrium if a is dominant for A and b is dominant for B. • (similar definition for more players) • In the prisoner’s dilemma: (Defect, Defect) is a dominant-strategyequilibrium.

44. Dominant strategies: another example • Who has a dominant strategy in this game? • Dominant-strategy equilibrium? We allowed ≥ in the definition. “Weakly dominant”

45. Dominant strategies: pros and cons • Plus: Strong solution. • Why should I play anything else if I have a dominant strategy? • Main problem:Does not exist in many games….

46. Lecture Outline • What is a game? • Few examples. • Best responses • Dominant strategies (golden balls)  Nash Equilibrium • Pure • Mixed • Existence and computation

47. Nash Equilibrium • How will players play when dominant-strategy equilibrium does not exist? • We will define a weaker equilibrium concept: Nash equilibrium • Apair of strategies (a*,b*) is defined to be a Nash equilibriumif:a* is player A’s best response to b*, andb* is player B’s best response to a*.

48. Nash Equilibrium: Definition • A direct definition:A pair of strategies (a*,b*) is defined to be a Nash equilibriumif UA(a*,b*)  UA(a’,b*) for all a’SA UB(a*,b*)  Ub(a*,b’) for all b’SB

49. Nash Eq.: Interpretation • No regret: Even if one player reveals his strategy, the other player cannot benefit. • this is not the case with non-equilibrium strategies • Stability: Once we reach a Nash equilibrium, players have no incentive to alter their strategies. • Even after observing the strategies of the other players • Necessary condition for an outcome chosen by rational players. • If players think that there is obvious outcome to the game, it must be a Nash equilibrium

50. (Pure) Nash Equilibrium • Examples: Note: when column player plays “straight”, then “straight” is no longer a best response to the row player. Here, communication between players help.