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Managerial economics topic 5 sequential games bargaining l.jpg

Managerial Economics: Topic 5Sequential Games & Bargaining

Sequential Games

Commitments

Commitments in Bargaining


Some history l.jpg
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.


Topic 5a introduction to sequential games l.jpg

Topic 5a Introduction to Sequential Games

Sequential Choices:

Represented by games in extensive form (also called game trees)


Game trees l.jpg
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


An entry game l.jpg
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


Slide6 l.jpg

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


What should it do l.jpg
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


Work backwards l.jpg
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


Work backwards9 l.jpg
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


Backwards induction l.jpg
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!


Games with nature as a player uncertainty l.jpg
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


Making credible threats ex controlling rotten kids l.jpg
Making Credible Threats:ex: controlling rotten kids

Refuse to go

(-1, -1)

Punish

Parent

Relent

(2, 0)

Difficult Child

Agree to go

(1, 1)


Slide13 l.jpg

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


Slide14 l.jpg

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)


Slide15 l.jpg

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)


Slide16 l.jpg

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)


Role of commitments l.jpg
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.


Commitment mechanisms dixit and nalebuff thinking strategically l.jpg
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


  • Application bargaining with a specific protocol l.jpg
    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)


    The ultimatum game one round l.jpg
    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


    Solve by rollback l.jpg
    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


    Solve by rollback22 l.jpg
    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


    Solve by rollback23 l.jpg
    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


    Solve by roll back l.jpg
    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


    So argo gets almost all the surplus l.jpg
    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!


    Warning studies of our sense of fairness l.jpg
    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.


    Results don t push your luck l.jpg

    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!


    2 forces pushing results towards a fair split l.jpg
    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.


    Another example of fixed protocol l.jpg
    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?)


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