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4. The Theories and the Real World

4. The Theories and the Real World. Outline. 1. Introduction 2. Individual Decision Making 3. Basic Topics in Game Theory 4. The Theories and the Real World 4.1 Applications 4.1.1 Auctions 4.1.2 Negotiation 4.2 Alternative approaches 4.2.1 Psychology 4.2.2 Evolution

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4. The Theories and the Real World

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  1. 4. The Theories and the Real World

  2. Strategic Behavior in Business and Econ Outline 1. Introduction 2. Individual Decision Making 3. Basic Topics in Game Theory 4. The Theories and the Real World 4.1 Applications 4.1.1 Auctions 4.1.2 Negotiation 4.2 Alternative approaches 4.2.1 Psychology 4.2.2 Evolution 4.3.3 Artificial intelligence 4.3 What the theory does not reflect? (Back to The experiment)

  3. Strategic Behavior in Business and Econ Outline 1. Introduction 2. Individual Decision Making 3. Basic Topics in Game Theory 4. The Theories and the Real World 4.1 Applications 4.1.1 Auctions 4.1.2 Negotiation 4.2 Alternative approaches 4.2.1 Psychology 4.2.2 Evolution 4.3.3 Artificial intelligence 4.3 What the theory does not reflect? (Back to The experiment)

  4. Strategic Behavior in Business and Econ What is an Auction? • auc•tion • 1. A public sale in which property or • merchandise are sold to the highest bidder. • 2. A market institution with explicit rules • determining resource allocation and prices • on the basis of bids from participants. • 3. Games: The bidding in bridge • [Latin: auctio, auction – from auctus, • past participle of augēre, to increase]

  5. Strategic Behavior in Business and Econ Examples of Auctions • Definition: • A market institution with rules governing resource allocation on the basis of bids from participants • Over 30% of US GDP moves through auctions: • IPOs • Emissions permits • Radio Spectrum • Import quotas • Mineral rights • Procurement • Wine • Art • Flowers • Fish • Electric power • Treasury bills

  6. Strategic Behavior in Business and Econ Real Figures • Currently, there are “open” opportunities in the US for 40 billion $ in 5 years (public facilities) La Vanguardia. April 10th , 2007 • Cellular phone licenses in Europe • Germany 84 billion € • United Kingdom 62 billion € • France 33 billion € • Spain ...

  7. Strategic Behavior in Business and Econ Real Figures • No Auction in Spain !! • The government issued licenses based on public examination/contest

  8. Strategic Behavior in Business and Econ Real Figures • The Spanish government raised • 880 million € • ( 35 times less than France !! )

  9. Strategic Behavior in Business and Econ Types of Auctions • Different auction mechanisms • sealed vs. open auctions • first vs. second price • Issues: optimal bidding & care in design • Different sources of uncertainty • private vs. common value auctions • Issue: the winner’s curse

  10. Strategic Behavior in Business and Econ Sources of Uncertainty • Private Value Auction • Each bidder knows his or her value for the object (not the value for others !) • Bidders differ in their values for the object • e.g., memorabilia, consumption items, fine arts • Common Value Auction • The item has a single though unknown value • Bidders differ in their estimates of the true value of the object • e.g., FCC spectrum, drilling off-shore, IPOs

  11. Strategic Behavior in Business and Econ Basic Auction Types • Open Auctions (sequential) • English Auctions • Dutch Auctions • Japanese Auctions • Sealed Auctions (simultaneous) • First Price Sealed Bid • Second Price Sealed Bid

  12. Strategic Behavior in Business and Econ English Auctions (Ascending Bid) • Bidders call out prices (English) • Bidders hold down button (Japanese) • Highest bidder gets the object • Pays his or her bid

  13. Strategic Behavior in Business and Econ Dutch (Tulip) Auction (Descending Bid) • “Price Clock” ticks down the price • First bidder to “buzz in” and stop the clock is the winner • Pays price on clock

  14. Strategic Behavior in Business and Econ First Price Auction • First price auction presents trade-offs • If bidding your valuation – no surplus • Lower your bid below your valuation • Smaller chance of winning, lower price • Bid shading • Depends on the number of bidders • Depends on your information • Optimal bidding strategy is complicated!

  15. Strategic Behavior in Business and Econ Bidding Strategy • Eachbidder has a “private” valuation of theitem • Biddingaboveyourvaluationis a badchoice (DominatedStrategy) • Hence, thechoiceistoeitherbidyourvaluationorbelowyourvaluation

  16. Strategic Behavior in Business and Econ Bidding Strategy You Win You Lose Your bid Others’ bids higher Your value

  17. Strategic Behavior in Business and Econ Bidding Strategy (valuation vs below valuation) Case 1 Case 2 Case 3 No difference No difference is better !!

  18. Strategic Behavior in Business and Econ Bidding Strategy • Eachbidder has a “private” valuation of theitem • Biddingaboveyourvaluationis a badchoice (DominatedStrategy) • Hence, thechoiceistoeitherbidyourvaluationorbelowyourvaluation • Thus, theoptimalstrategy (weaklydominant) istobid “slightly” • belowyourvaluation (bidshading)

  19. Strategic Behavior in Business and Econ First Price Auction • In a first price auction, always bid below your true valuation • bidding your own valuation is a Dominated Strategy • Winning bidder’s surplus: • Difference between the winner’s valuation and the winner's bid

  20. Strategic Behavior in Business and Econ Bidding Strategy • Eachbidder has a “private” valuation of theitem • Biddingaboveyourvaluationmightnot a badchoice in this case sincethis • thisisnotthepriceyouwillhavetopay ! (and mightincreaseyour chances • of winning) • Hence, wehavetotakeintoaccountthethreepossibilities: • Biddingyourvaluation • Biddingaboveyourvaluation • Biddingbelowyourvaluation

  21. Strategic Behavior in Business and Econ Optimal Bidding Strategy in Second Price Auctions You Win You Lose Your bid Others’ bids higher Your value

  22. Strategic Behavior in Business and Econ Bidding Higher Than My Valuation Case 1 Case 2 Case 3 No difference No difference Lose money !!

  23. Strategic Behavior in Business and Econ Bidding Lower Than My Valuation Case 1 Case 2 Case 3 No difference No difference Lose money !!

  24. Strategic Behavior in Business and Econ Why Second Price? • Bidding strategy is easy • Bidding one’s true valuation is a dominant strategy • Intuition: • The amount a bidder pays is not dependent on her bid

  25. Strategic Behavior in Business and Econ Second Price Auction • In a second price auction, always bid your true valuation • Winning bidder’s surplus • Difference between the winner’s valuation and the second highest valuation • Surplus decreases with more bidders

  26. Strategic Behavior in Business and Econ Which is Better for the seller ? • In a second price auction • bidders bid their true value • auctioneer receives the second highest bid • In a first price auction • bidders bid below their true value • auctioneer receives the highest bid

  27. Strategic Behavior in Business and Econ Revenue Equivalence • All common auction formats yield the same expected revenue (in theory) • In fact, any auction in which: • The prize always goes to the person with the highest valuation • A bidder with the lowest possible valuation expects zero surplus yield the same expected revenue

  28. Strategic Behavior in Business and Econ Which is Better for the bidder? • English and Second Price are equivalent • Dutch and First Price are equivalent • It's difficult to say in general

  29. Strategic Behavior in Business and Econ Revenue Equivalence in the Real World • Risk Aversion • Does not influence 2nd price auctions • Risk averse bidders are more aggressive in first price auctions • Risk aversion 1stprice or Dutch are better • Non-familiarity with auctions • More overbidding in second-price auctions • More overbidding in sealed-bid auctions • Inexperience 2nd price sealed bid is better

  30. Strategic Behavior in Business and Econ Number of Bidders • More bidders lead to higher prices • Example • Second price auction • Each bidder has a valuation of either $20 or $40, each with equal probability • What is the expected revenue?

  31. Strategic Behavior in Business and Econ Number of Bidders • Two bidders • Each has a value of 20 or 40 • There are four value combinations:

  32. Strategic Behavior in Business and Econ Number of Bidders • Two bidders • Each has a value of 20 or 40 • There are four value combinations:

  33. Strategic Behavior in Business and Econ Number of Bidders • Two bidders • Each has a value of 20 or 40 • There are four value combinations: Expected revenue = ¾ (20)+ ¼ (40) = 25

  34. Strategic Behavior in Business and Econ Number of Bidders • Three bidders • Each has a value of 20 or 40 • There are eight value combinations:

  35. Number of Bidders • Three bidders • Each has a value of 20 or 40 • There are eight value combinations:

  36. Number of Bidders • Three bidders • Each has a value of 20 or 40 • There are eight value combinations: Expected Revenue = ½ (20)+ ½ (40) = 30

  37. Strategic Behavior in Business and Econ Summary • Bidding: • Bid true valuation in 2nd price auctions • Shade bids in 1st price auctions • Designing: • Take advantage of inexperience • Take advantage of risk aversion

  38. Strategic Behavior in Business and Econ Sources of Uncertainty • Private Value Auction • Difficult to lose money • Do not bid more than your value (or less than your cost) • Common Value Auction • The item has a single though unknown value • Bidders differ in their estimates • The winner might be wrong!

  39. Strategic Behavior in Business and Econ Common Value Auctions • Example: Offshore oil leases • The true value of oil is roughly the same for every participant • No bidder knows value for sure • Each bidder has some information • Auction formats are not equivalent • Oral auctions provide information • Sealed-bid auctions do not

  40. Strategic Behavior in Business and Econ Avoiding the Winner’s Curse • Given that I win an auction … All others bid less than me … Thus the object’s value must be lower than I thought • Winning the auction is “bad news” One must incorporate this into one’s bid Assume that your estimate is the most optimistic

  41. Strategic Behavior in Business and Econ Outline 1. Introduction 2. Individual Decision Making 3. Basic Topics in Game Theory 4. The Theories and the Real World 4.1 Applications 4.1.1 Auctions 4.1.2 Negotiation 4.2 Alternative approaches 4.2.1 Psychology 4.2.2 Evolution 4.3.3 Artificial intelligence 4.3 What the theory does not reflect? (Back to The experiment)

  42. Strategic Bahavior in Business and Econ Sequential Negotiation Consider a situation in which two players must negotiate (bargain) about the distribution of a single item The negotiation proceeds by alternating offers and counteroffers until an agreement is achieved or a deadline is reached Usually, the value of the item decreases as the negotiation unfolds (by some factor r<1)

  43. Strategic Bahavior in Business and Econ The value of the item If x is accepted right away (first round) it has a value of x (full value) If x is accepted in round two, then it has a value of only r·x(discounted value) If x is accepted in round three, then it has a value of only r·r·x=r2·x(discounted value) . . . If x is accepted in round “t”, then it has a value of only r(t-1)·x(discounted value)

  44. Strategic Bahavior in Business and Econ The value of the item (Example if r=0.9) • If $10 is accepted right away (first round) it has a value of $10 (full value) • If $10 is accepted in round two, then it has a value of only 0.9·10=$9(discounted value) • If $10 is accepted in round three, then it has a value of only 0.92·10=$8.1(discounted value) • . . . • If $10 is accepted in round “t”, then it has a value of only 0.9(t-1)·10(discounted value) After each round the prize loses a 10% of its value

  45. Strategic Bahavior in Business and Econ The value of the item (Interpretation) • If the item is a commodity, it might lose “quality” over time (Ex: ice cream) • If the item is money, it looses value because of the inflation, or because of the interest rate that you are not earning • Psychologically, r might represent your degree of patience. The higher is r, the more patient you are

  46. Strategic Bahavior in Business and Econ The Game • Player 1 makes a proposal s, (1-s) of distribution of the item (s between 0 and 1) • Player 2 receives the offer by player 1 and decides whether to accept or to rejectit • If accepts, the proposal by player 1 is implemented: s, 1-s • If rejects, then is player 2's turn to make an offer s’,(1-s') • Player 1 receives the offer by player 2 and decides whether to accept or to reject it • If accepts, the proposal by player 2 is implemented: s', 1-s', but they get the discounted value: r·s' , r(1-s') • If rejects,then the game is over (for simplicity) and each player receives a disagreement payoff of 0 (for simplicity)

  47. Strategic Bahavior in Business and Econ The Game Accept s, (1-s) 0 s, (1-s) Accept r·s', r·(1-s') 0 P 1 P 2 s', (1-s') Reject 1 P 2 P 1 0, 0 Reject 1

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