1 / 31

Game Theory

Game Theory. “ Necessity Never Made a Good Bargain . ” - Benjamin Franklin Mike Shor Lecture 11. The Bargaining Problem. If an owner of some object values it less than a potential buyer, there are gains from trade  A surplus is created

erv
Download Presentation

Game Theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Game Theory “Necessity Never Made a Good Bargain.” - Benjamin Franklin Mike Shor Lecture 11

  2. The Bargaining Problem • If an owner of some object values it less than a potential buyer, there are gains from trade A surplus is created • Example: I value a car that I own at $1000. If you value the same car at $1500, there is a $500 gain from trade • Well-established market prices often control the division of surplus • If such cars are priced at $1200: $200 to the seller $300 to the buyer Game Theory - Mike Shor

  3. The Bargaining Problem In the absence of markets  bargaining • Bargaining Problem Determining the actual sale price or surplus distribution in the absence of markets • Home sales “Comps” are rarely truly comparable • Labor/management negotiations Surplus comes from production Game Theory - Mike Shor

  4. The Bargaining Problem • Importance of rules: The structure of the game determines the outcome • Diminishing pies The importance of patience • Screening and bargaining Game Theory - Mike Shor

  5. Take-it-or-leave-it Offers • Consider the following bargaining game for the used car: • I name a take-it-or-leave-it price. • If you accept, we trade • If you reject, we walk away • Under perfect information, there is a simple rollback equilibrium Game Theory - Mike Shor

  6. Take-it-or-leave-it Offers p-1000 , 1500-p accept p reject 0 , 0 Game Theory - Mike Shor

  7. Rollback • Consider the subgame: • Accept: p-1000 , 1500-p • Reject: 0 , 0 • You will reject if p>1500, accept otherwise • Rollback: I will offer highest acceptable price of 1500 • What if you make the take-it-or-leave-it offer? Game Theory - Mike Shor

  8. Take-it-or-leave-it Offers • Simple to solve • Unique outcome • Unrealistic • Ignore “real” bargaining • Assume perfect information • We do not necessarily know each other’s values for the car • Not credible • If you reject my offer, will I really just walk away? Game Theory - Mike Shor

  9. Counteroffers and Diminishing Pies • In general, bargaining takes on a “take-it-or-counteroffer” procedure • Multiple-round bargaining games • If time has value, both parties prefer trade earlier to trade later • E.g. Labor negotiations – later agreements come at a price of strikes, work stoppages, etc. Game Theory - Mike Shor

  10. Two-stage Bargaining • Value of car: $1000 me, $1500 you • I make an offer in period 1 • You can accept the offer or reject it • If you reject, you can make a counteroffer in the second period. • Payoffs • In first period: p-1000,1500-p • In second period: (p-1000) , (1500-p) Game Theory - Mike Shor

  11. Rollback • What happens in period 2? • In the final period, this is just like a leave-it-or-take-it offer: You will offer me the lowest price that I will accept, p=1000 • This leaves you with 500 • (1500-p)= (1500-1000) and leaves me with 0 • What do I do in the first period? Game Theory - Mike Shor

  12. Rollback • Give you at least as much surplus • Your surplus if you accept in the first period is 1500-p • Accept if: Your surplus in first period  Your surplus in second period 1500-p  500  p  1500-500 • p = 1500-500 • Note: the more that you value the future, the less you pay now! Game Theory - Mike Shor

  13. Example • If =4/5 • Period 2: You offer a price of 1000 • You get (4/5) (1500-1000) = 400 • I get 0 = 0 • In the first period, I offer 1100 • You get (1500-1100) = 400 • I get (1100-1000) = 100 Game Theory - Mike Shor

  14. First or Second Mover Advantage? • In the previous example, second mover gets more surplus • What if =2/5? • Period 2: You offer a price of 1000 • You get (2/5)(1500-1000) = 200 • I get 0 = 0 • In the first period, I offer 1300 • You get (1500-1300) = 200 • I get (1300-1000) = 300 Game Theory - Mike Shor

  15. First or Second Mover Advantage? • Who has the advantage? • Depends on the value of the future! • If players are patient: • Second mover is better off! • Power to counteroffer is stronger than power to offer • If players are impatient • First mover is better off! • Power to offer is stronger than power to counteroffer Game Theory - Mike Shor

  16. Bargaining Games With Diminishing Pies • More periods with diminishing pies • Suppose the same player makes an offer in each period • Infinite number of periods • Same point: if players are fully informed, a deal should occur in the first round! Game Theory - Mike Shor

  17. Information • Why doesn’t this happen? • “Time has no meaning” • Lack of information about values! • Reputation-building in repeated settings! COMMANDMENT In any bargaining setting, strike a deal as early as possible! Game Theory - Mike Shor

  18. Examples • British Pubs and American Bars • Civil Lawsuits • If both parties can predict the future jury award, can settle for same outcome and save litigation fees and time • If both parties are sufficiently optimistic, they do not envision gains from trade Game Theory - Mike Shor

  19. Uncertainty I:Civil Trial • Plaintiff sues defendant for $1M • Legal fees cost each side $100,000 • If each agrees that the chance of the plaintiff winning is ½: • Plaintiff: $500K-$100K = $ 400K • Defendant: -$500K-$100K = $-600K • If simply agree on the expected winnings, $500K, each is better off Game Theory - Mike Shor

  20. Civil Trial • What if both parties are too optimistic? • Each thinks that their side has a ¾ chance of winning: • Plaintiff: $750K-$100K = $ 650K • Defendant: -$250K-$100K = $-350K • No way to agree on a settlement! • “Delicate Disclosure Game” Game Theory - Mike Shor

  21. Uncertainty II:Non-monetary Utility • Labor negotiations are often a simple game of splitting a known surplus • Company will profit $200K – how much of this goes to labor? • Rules of the bargaining game uniquely determine the outcome if money is the only consideration Game Theory - Mike Shor

  22. Non-monetary Utility • Each side has a reservation price • Like in civil suit: expectation of winning • The reservation price is unknown • One must: • Consider non-monetary payoffs • Probabilistically determine best offer • But – probability implies a chance that no bargain will be made Game Theory - Mike Shor

  23. Example: Uncertain Company Value • Company annual profits are either $150K or $200K per employee • Two types of bargaining: • Union makes a take-it-or-leave-it offer • Union makes an offer today. If it is rejected, the Union strikes, then makes another offer • A strike costs the company 20% of annual profits Game Theory - Mike Shor

  24. Take-it-or-leave-it Offer • Probability that the company is “highly profitable,” i.e. $200K is p • If offer wage of $150 • Definitely accepted • Expected wage = $150K • If offer wage of $200K • Accepted with probability p • Expected wage = $200K(p) Game Theory - Mike Shor

  25. Take-it-or-leave-it OfferExample I • p=9/10 • 90% chance company is highly profitable • Best offer: Ask for $200K wage • Expected value of offer: (.9)$200K = $180K • But: 10% chance of No Deal! Game Theory - Mike Shor

  26. Take-it-or-leave-it OfferExample II • p=1/10 • 10% chance company is highly profitable • Best offer: Ask for $150K wage • If ask for $200K Expected value of offer: (.1)$200K = $20K • If ask for $150K, get $150K Game Theory - Mike Shor

  27. Two-period Bargaining • If first-period offer is rejected: A strike costs the company 20% of annual profits • Note: strike costs a high-value company more than a low-value company! • Use this fact to screen! • Assume (for simplicity): A strike doesn’t cost the Union anything Game Theory - Mike Shor

  28. Screening in Bargaining • What if the Union asks for $170K in the first period? • Low-profit firm ($150K) rejects • High-profit firm must guess what will happen if it rejects: • Best case – Union strikes and then asks for only $150K • In the mean time – Strike cost the company $20K • High-profit firm accepts Game Theory - Mike Shor

  29. Separating Equilibrium • Only high-profit firms accept in the first period • If offer is rejected, Union knows that it is facing a low-profit firm • Ask for $150K in second period • Expected Wage: • $170K (p) + $150K (1-p) Game Theory - Mike Shor

  30. What’s Happening • Union lowers price after a rejection • Looks like “Giving in” • Looks like Negotiating • Actually, the Union is screening its bargaining partner • Different “types” of firms have different values for the future • Use these different values to screen • Time is used as a screening device Game Theory - Mike Shor

  31. Lessons • Rules of the game uniquely determine the bargaining outcome • Which rules are better for you depends on patience, information • Delays are always less profitable • But may be necessary to screen Game Theory - Mike Shor

More Related