Managerial Economics: Topic 5 Sequential Games & Bargaining

1. Managerial Economics: Topic 5Sequential Games & Bargaining Sequential Games Commitments Commitments in Bargaining

2. Some History • The tools of game theory are now common-place within economics. They were originally developed by John von Neumann and Oscar Morgenstern in their 1944 book, The Theory of Games and Economic Behavior. • Thomas Schelling in his 1956 book The Strategy of Conflict was the first to apply game theory to many contexts in social sciences. He won a Nobel Prize in 2005, along with Robert Aumann, another game theorist, for their work in addressing the question: why do some individuals/groups/countries succeed in cooperating, while others suffer from conflict? • The theory has developed to a high degree of mathematical sophistication. The importance of this development was signified by the award of the 1994 Nobel Prize to three game theorists: John Nash, John Harsanyi, and Reinhard Selten.

3. Topic 5a Introduction to Sequential Games Sequential Choices: Represented by games in extensive form (also called game trees)

4. Game Trees A game tree has choice nodes (squares) for each player, and chance nodes (circles) when Nature plays. Pull ball away Lucy Accept Let Charlie Brown kick Charlie Brown Reject

5. An Entry Game • Vacuum cleaner market currently has one incumbent (Fastcleaners) • Potential entrant (Newcleaners). It is deciding whether to enter the market or not. • If enters, Fastcleaners has 2 choices: • Accommodate: accept a lower market share • Price war

6. Newcleaner’s Payoffs $100,000 = TR - Entry Cost =$150,000 - $50,000 Accommodate Fastcleaners Enter Fight Price War Newcleaners -$25,000 = $25,000 - $50,000 Keep Out $0 to Newcleaners

7. What should it do? • Newcleaner needs to forecast Fastcleaner’s response • How does it do this? • Put themselves in Fastcleaner’s shoes • Work out Fastcleaner’s payoffs

8. Work Backwards N: $100,000 F: $150,000 Accommodate Fastcleaners Enter Fight Price War N:-$25,000 F: $25,000 Newcleaners Keep Out N: $0 F: $300,000

9. Work Backwards N: $100,000 F: $150,000 Accommodate Fastcleaners Enter Fight Price War N:-$25,000 F: $25,000 Newcleaners Keep Out N: $0 F: $300,000

10. Backwards Induction • The predicted outcome of extensive form games can be found by solving the game by rollback: • the decisionmaker at each node makes the decision that gives her the highest payoff • She doesn’t consider others’ payoffs, except to determine how others will act at their decision nodes. • In the entry game, the solution is found by finding Fastcleaners’ best response to entry. If Newcleaners enters, Fastcleaners would rather accommodate entry than fight a price war. (A threat of entry is not credible.) So entry is worthwhile. • Sequential Games: In-class exercises To notice for later: Sequential games do not necessarily lead to a surplus-maximizing outcome!

11. Games with Nature as a player: Uncertainty • Solving nodes with uncertainty is the same as before, except that there are now two payoffs to keep track of. • Should David Jones stock extra umbrellas this summer? DJ $10, $5 buy YOU -$5, -$10 don’t Rains often 0.2 Stocks extra umbrellas YOU $10, $2 Rains less 0.6 -$5, - $1 NATURE Drought 0.2 YOU $10, - $5 doesn’t $0, ? - $5, $0

12. Making Credible Threats:ex: controlling rotten kids Refuse to go (-1, -1) Punish Parent Relent (2, 0) Difficult Child Agree to go (1, 1)

13. Credibility • Problem: The parent threatens the child with a punishment that is not credible, because it hurts both the parent and the child.  The child will refuse to go.  Unless the parent can commit to punish if the child refuses to go, (s)he cannot convince the child to go. • Similarly, Lucy cannot commit not to pull away the ball  Charlie Brown should not kick • What are some of the ways to commit in this case? • reputation • delegation

14. Example: Nuclear Deterrence • What if the USA sets up an automatic nuclear response EARLY? (1 to USSR, -1 to USA) Accommodate USA Invade Europe Fight Nuclear War USSR (-100 to USSR, -100 to USA) Don’t invade (0 to USSR, 0 to USA)

15. Nuclear Deterrence in Dr. Strangelove Automaticresponse system is set up • “Accommodate” branch is ruled out BEFORE the game (1 to USSR, -1 to USA) Accommodate USA Invade Europe Fight Nuclear War USSR (-100 to USSR, -100 to USA) Don’t invade (0 to USSR, 0 to USA)

16. Nuclear Deterrence in Dr. Strangelove • “Accommodate” branch is ruled out BEFORE the game • USSR will not invade (1 to USSR, -1 to USA) Accommodate USA Invade Europe Fight Nuclear War USSR (-100 to USSR, -100 to USA) Don’t invade (0 to USSR, 0 to USA)

17. Role of Commitments • You commit to a future action that you would not normally want to take, in order to influence the choices of other players. (Preventing invasion,...) • (This is different from providing information to other players about what actions you’ll want to take: • if you don’t study at all, and don’t come to class, you’ll fail = information • if you work hard, but still don’t understand at all, you’ll fail = commitment to a performance standard.

18. Commitment Mechanisms(Dixit and Nalebuff, Thinking Strategically) • establishing a reputation • writing an enforceable contract • cutting off communication • burning bridges behind you • leaving the outcome out of your control • (3rd party arbitration, for example) • moving in small steps • developing credibility through teamwork • employing mandated negotiating agents

19. Application: Bargaining with a specific protocol Almost all bargaining is a series of offers and counter-offers • it’s a sequential game. Example: The value of commitments • ArgoSoft is negotiating the acquisition of B-tech, another software company that is facing bankruptcy. • The negotiations drag on, and approach the deadline by which B-tech must enter bankruptcy proceeding. • The CEO of ArgoSoft sends a (signed!) acquisition agreement to B-tech’s lawyers, at the same time as he disappears for a vacation that will last until after the deadline, and is unreachable. • Suppose $20 million is ArgoSoft’s Willingness-to-Pay (B-tech’s Willingness-to-Sell is probably $0)

20. The ultimatum game (one round) A: $19.9B: $0.1 Accept If B-tech’s lawyers do not sign the agreement, each gets nothing. B-tech Offer $0.1 A: $0B: $0 Reject $15, $5 A Offer $5 Argo R $0, $0 $10 A $10, $10 R $0, $0 A Offer $15 $5, $15 $0, $0 R

21. Solve by rollback A: $19.9B: $0.1 Accept If Argo offers $15m, B-tech’s best response is to accept. B-tech Offer $0.1 A: $0B: $0 Reject $15, $5 A Offer $5 Argo R $0, $0 $10 A $10, $10 R $0, $0 A Offer $15 $5, $15 $0, $0 R

22. Solve by rollback A: $19.9B: $0.1 Accept So we can eliminate the ‘reject’ branch in that situation. B-tech Offer $0.1 A: $0B: $0 Reject $15, $5 A Offer $5 Argo R $0, $0 $10 A $10, $10 R $0, $0 A $0, $0 Offer $15 $5, $15 R

23. Solve by rollback A: $19.9B: $0.1 Accept But the same holds for any other positive offer – so B-tech will always accept. B-tech Offer $0.1 A: $0B: $0 Reject $15, $5 A Offer $5 Argo R $0, $0 $10 A Remember – these are the complete payoffs and this is the complete game. $10, $10 R $0, $0 A $0, $0 Offer $15 $5, $15 R

24. Solve by roll back So now the game is simple – the Argo CEO should offer B-tech the minimum amount and he will expect B-tech to accept. Offer $0.1 Argo: $19.9B-tech: $0.1 Offer $5 Argo $5, $15 $10 $10, $10 Offer $15 $15, $5

25. So:Argo gets almost all the surplus WHY? • ArgoSoft gets to make a take-it-or-leave-it offer to B-tech, so it gets all the surplus. Question: Why can’t Argo make a take-it-or-leave-it offer without cutting off communication? • So bargaining power depends on the bargaining process • If you can dictate/influence the bargaining process, it’s worth doing! • These tactics will damage long-term relationships  don’t try this with a regular business partner!

26. Warning! Studies of our sense of fairness Fairness probably tends to make extreme results less likely: • The experiment is as follows: • Subject 1 is given a sum of money and ask to divide it between herself and Subject 2. • Subject 1 makes a take-it-or-leave it offer of a “split” • Subject 2 has the option of accepting 1’s offer or rejecting it. • If accepted, they get 1’s proposed division; if rejected, they get nothing. (E.g., Subject One proposes to divide $10 but keeping $7 and giving subject Two $3. If Two accepts, One gets $7 and Two gets $3, but if Two rejects they each get $0). • Note that theory predicts that subject 1 should offer subject 2 only one cent, and subject 2 should accept.

27. Actual Predicted Avg % of Total Demanded by 1 67.1 99+ % of Proposed 50-50 splits 25.5 0 % rejected by 2 21.5 0 Avg % Demanded by 1 in Rejected Proposals 85.3 Avg % Demanded by 1 in Accepted Proposals 61.0 99+ % of 1’s demands > 90% 11.8 100 Results: don’t push your luck!

28. 2 forces pushing results towards a fair split • Your ethics, sense of fairness • Risk that the other party get angry, will reject the offer even if it’s in their best interest to accept, for the satisfaction of lowering your profits.

29. Another example of fixed protocol • Parent gives Ben and Jerry a tub of ice cream to share; they must agree on a split before they can have any ice cream. • Ben is oldest, so he gets to make the first offer; then Jerry, then Ben again,... • The ice cream is gradually melting while they’re arguing: every time an offer is rejected, a third of the ice cream melts before they can make another offer and reach agreement. In-Class Exercise: • What will be the split, ignoring “fairness”? • How long does it take them to reach agreement? • (How would “fairness” affect the results?)