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

Issues on the border of economics and computation נושאים בגבול כלכלה וחישוב. INTRODUCTION. Instructors. Dr. Liad Blumrosen ד"ר ליעד בלומרוזן Department of economics, huji . Dr. Michael Schapira ד"ר מיכאל שפירא School of computer science and engineering, huji .

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

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  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.

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