4. The Theories and the Real World

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 Auctions Negotiation 4.2 Alternative approaches Psychology Evolution Artificial intelligence 4.3 What the theory does not reflect? (Back to The experiment)

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 Auctions Negotiation 4.2 Alternative approaches Psychology Evolution Artificial intelligence 4.3 What the theory does not reflect? (Back to The experiment)

Strategic Behavior in Business and Econ What is an Auction? auction 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]

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: Wine Art Flowers Fish Electric power Treasury bills IPOs Emissions permits Radio Spectrum Import quotas Mineral rights Procurement

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 10 th, 2007 Cellular phone licenses in Europe – Germany 84 billion € – United Kingdom62 billion € – France33 billion € – Spain...

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

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

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

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

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

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

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

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!

Strategic Behavior in Business and Econ Bidding Strategy  Each bidder has a “private” valuation of the item  Bidding above your valuation is a bad choice (Dominated Strategy)  Hence, the choice is to either bid your valuation or below your valuation

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

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

Strategic Behavior in Business and Econ Bidding Strategy  Each bidder has a “private” valuation of the item  Bidding above your valuation is a bad choice (Dominated Strategy)  Hence, the choice is to either bid your valuation or below your valuation  Thus, the optimal strategy (weakly dominant) is to bid “slightly” below your valuation (bid shading)

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

Strategic Behavior in Business and Econ Bidding Strategy  Each bidder has a “private” valuation of the item  Bidding above your valuation might not a bad choice in this case since this this is not the price you will have to pay ! (and might increase your chances of winning)  Hence, we have to take into account the three possibilities:  Bidding your valuation  Bidding above your valuation  Bidding below your valuation

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

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

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

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

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

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

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

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

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

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?

Strategic Behavior in Business and Econ Number of Bidders Two bidders – Each has a value of 20 or 40 – There are four value combinations: Bidder 1 Bidder 2Prob. 20 ¼ 40¼ 20¼ 40 ¼

Strategic Behavior in Business and Econ Number of Bidders Two bidders – Each has a value of 20 or 40 – There are four value combinations: Bidder 1Bidder 2Prob.Outcome (revenue) 20 ¼ 40¼ ¼ 40 ¼

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 Bidder 1Bidder 2Prob.Outcome (revenue) 20 ¼ 40¼ ¼ 40 ¼

Strategic Behavior in Business and Econ Number of Bidders Three bidders – Each has a value of 20 or 40 – There are eight value combinations: Bidder 1Bidder 2Bidder 3Prob 20 1/ / / / / / /8 40 1/8

Number of Bidders Three bidders – Each has a value of 20 or 40 – There are eight value combinations: Bidder 1Bidder 2Bidder 3ProbOutcome (revenue) 20 1/ / / / / / /840 1/840

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 Bidder 1Bidder 2Bidder 3ProbOutcome (revenue) 20 1/ / / / / / /840 1/840

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

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!

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

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

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 Auctions Negotiation 4.2 Alternative approaches Psychology Evolution Artificial intelligence 4.3 What the theory does not reflect? (Back to The experiment)

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)

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=r 2 ·x (discounted value)... If x is accepted in round “t”, then it has a value of only r (t-1) ·x (discounted value)

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 ·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

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

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 reject it 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)

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

Strategic Bahavior in Business and Econ The Game (Solution) 0 1 Accept Reject s, (1-s) 0 1 Accept Reject s', (1-s') r·s', r·(1-s') 0, 0 P 1P 2 P 1 P 1 will accept any Proposal

Strategic Bahavior in Business and Econ The Game (Solution) 0 1 Accept Reject s, (1-s) 0 1 Accept Reject s', (1-s') r·s', r·(1-s') 0, 0 P 1P 2 P 1 P 1 will accept any proposal P 2 will propose s'=0 (hence, (1-s')=1)

Strategic Bahavior in Business and Econ The Game (Solution) 0 1 Accept Reject s, (1-s) 0 1 Accept Reject 0, 1 0, r 0, 0 P 1P 2 P 1 P 1 will accept any proposal P 2 will propose s'=0 (hence, (1-s')=1)

Strategic Bahavior in Business and Econ The Game (Solution) 0 1 Accept Reject s, (1-s) 0, r P 1P 2 This will be the solution if the game reaches this point, that is, if Player 2 Rejects the initial offer by Player 1

Strategic Bahavior in Business and Econ The Game (Solution) 0 1 Accept Reject s, (1-s) 0, r P 1P 2 This will be the solution if the game reaches this point, that is, if Player 2 Rejects the initial offer by Player 1 P 2 will accept any proposal such that (1 - s) ≥ r That is, 1 - r ≥ s

Strategic Bahavior in Business and Econ The Game (Solution) 0 1 Accept Reject s, (1-s) 0, r P 1P 2 This will be the solution if the game reaches this point, that is, if Player 2 Rejects the initial offer by Player 1 P 2 will accept any proposal such that (1 - s) ≥ r That is, 1 - r ≥ s P 1 will propose s = 1 – r, and P 2 will Accept right away

Strategic Bahavior in Business and Econ The Game (Solution) 0 1 Accept Reject s, (1-s) 0, r P 1P 2 This will be the solution if the game reaches this point, that is, if Player 2 Rejects the initial offer by Player 1 P 2 will accept any proposal such that (1 - s) ≥ r That is, 1 - r ≥ s P 1 will propose s = 1 – r, and P 2 will Accept right away P 1 will get 1 – r and P 2 will get 1 – (1 – r) = r

Strategic Bahavior in Business and Econ The Game (Solution) 0 1 Accept Reject 1-r, r 0, r P 1P 2 This will be the final solution of the game P 1 will propose s = 1 – r, and P 2 will Accept right away P 1 will get 1 – r and P 2 will get 1 – (1 – r) = r

Strategic Bahavior in Business and Econ The Game (Solution) Solution: 1 – r for Player 1 r for Player 2

Strategic Bahavior in Business and Econ The Game (Solution) Solution: 1 – r for Player 1 r for Player 2 What would you prefer ? To be Player 1 (the Initiator) To be Player 2 (the respondent)

Strategic Bahavior in Business and Econ The Game (Solution) Solution: 1 – r for Player 1 r for Player 2 What would you prefer ? To be Player 1 (the Initiator) To be Player 2 (the respondent) Depends on r !!!!

Strategic Bahavior in Business and Econ The Game (Solution) Solution: 1 – r for Player 1 r for Player 2 If r is low (for instance r = 0.3 ) it is better to be the initiator (Player 1 gets 0.7 while Player 2 gets 0.3) If r is high (for instance r = 0.7 ) it is better to be the respondent (Player 1 gets 0.3 while Player 2 gets 0.7) This is another example in which “tweaking” the rules of the game may be profitable It also shows that the “first mover advantage” is not always the case

Strategic Bahavior in Business and Econ Comments: Theoretical Bargaining Because the value of the item is decreasing (by r), Player 1 wants to strike an agreement as soon as possible Hence, Player 1 offers Player 2 a proposal Player 2 can not reject And Player 2 will not reject the proposal since the item will loose more value otherwise ! Thus, the prediction is that the negotiation will end in the first round (if the initial proposal is carefully computed) If the negotiation involved more than 2 rounds, the result would be the same: agreement right away. The only difference would be the proposal by Player 1 If r is low it's better to be Player 1, and vice versa

Strategic Bahavior in Business and Econ Comments: Bargaining in the Real Life Why this does not happen in real life ? Reputation building Lack of information Different “r” for different players But some lessons are useful in real life Civil lawsuits: If both parties can predict the future jury award, can settle for same outcome and save litigation fees and time What is your best strategy depends on information and Patience (r) Delays are always less profitable