Sequential Games - PowerPoint PPT Presentation

1 / 18
About This Presentation
Title:

Sequential Games

Description:

'Life must be understood backward, but ... it must be lived forward.' - Soren ... Players: Current firm (F) with large market share faces a potential entrant (E) ... – PowerPoint PPT presentation

Number of Views:39
Avg rating:3.0/5.0
Slides: 19
Provided by: MikeS142
Category:
Tags: football | games | how | life | my | play | sequential | to

less

Transcript and Presenter's Notes

Title: Sequential Games


1
Sequential Games
  • Thinking What Theyre Thinking Part I
  • Some slides are adapted from Mike Shor, Owen
    School, Vanderbilt University

2
Sequential Games
  • Players make their decisions in a sequence where
    one decision is made after and with knowledge of
    prior decision(s)
  • Note lack of information may effectively turn a
    sequential decision process into a simultaneous
    one

3
Solving Sequential Games
  • Life must be understood backward, but it must
    be lived forward. - Soren Kierkegaard
  • (Consider Chess as Example)
  • Diagram the game tree simplify if needed
  • Start with the last move in the game
  • Determine the best course(s) of action for the
    player with the last move
  • Trim the tree -- Eliminate the dominated
    strategies
  • Repeat the procedure at the prior decision
    node(s) with the trimmed tree

4
An Example Market Entry
  • Players Current firm (F) with large market share
    faces a potential entrant (E)
  • Timing Potential entrant moves first
  • Moves Potential entrant (enter-stay out) Current
    firm (accept passively-fight)
  • Information full information
  • Payoffs (see game tree)
  • Rules Fixed (to simplify game for now)

5
Game in Extensive Form
Payoffs (E, F) expressed as profits (mil )
6
Looking Forward
  • Entrant makes the first move
  • Must consider how F will respond
  • If enter
  • Current Firm better off if accepts so trim
    fight branch from tree

7
And Reasoning Back
  • Now consider entrants move with tree trimmed
  • Solution (In, Accept Passively )

8
Games within Games NLCS
Payoffs (AZ, STL ) expressed as profits (mil
) L Tony LaRussa (Cardinals manager) BBob
Brenly (Diamondbacks manager)
9
Games within Games NLCS
Payoffs (outs hits)
(78,22)
RH-PH
Brenly
RH-Pitcher
LH-PH
LaRussa
(77,28)
RH-PH
(66,34)
LH-Pitcher
LH-PH
(85,15)
10
What Should LaRussa Do?
  • Would like the LH-LH matchup (85,15) payoff, but
    Brenly will not go this route
  • Brenly will not choose the top or bottom branches
    LaRussa should trim these
  • Given the middle two branches for Brenly, LaRussa
    should choose the RH pitcher to get the (77,28)
    payoff

11
THE POLITICS OF BUSINESS
  • Tom Hanks directed a 12 part HBO series-- From
    the Earth to the Moon dramatizing the U.S. space
    program from Mercury through the Apollo moon
    landings. One segment depicts the events of
    Apollo 1 in which three astronauts died in a
    capsule fire during a routine test. The fire
    resulted from a spark in wiring causing the
    highly pressurized, pure oxygen air in the
    capsule to ignite and reach temperatures over
    1000 degrees 15 seconds. The capsule contractor
    -- North American and its executive in charge of
    the Apollo learned that NASA would likely lay
    substantial blame on North American.  The NA
    executive, a hardworking and upstanding person,
    is outraged explains to his boss how NA should
    expose NASA by documenting the written warnings
    to NASAabout the dangers of a pure oxygen gas
    system as well as pressurized tests at sea level.
    His boss says , no,were not and goes on to
    respond. Can you make sense of the boss
    decision?
  • (Hint break into Expose/Not expose Congress
    involved)

12
Taking it Up a NotchPredatory Pricing
  • A large incumbent firm operates in three markets,
    and faces entry in each
  • Market 1 in year 1, Market 2 in year 2, etc.
  • With entry, incumbent firm can slash prices, or
    passively accept the new entry
  • What should incumbent do the first year?

13
Overview of the Game
E entrant M incumbent
E3
E2
out
out
E1
fight
fight
M
in
in
M
acc
acc
14
Payoffs in Given Year
  • The end of the tree in year 3 (payoffsE,M)
  • In year 3 ( In, Accommodate )

15
Rollback
  • Trim the tree

16
Predatory Pricing
  • Since the Incumbent will not fight Entrant 3, he
    will not fight Entrant 2
  • Same for Entrant 1 in First Period
  • Rollback Equilibrium
  • All entrants play In
  • Incumbent plays Accommodate
  • Does predatory pricing take place if so, why?
  • What issues may the game have missed?

17
First or Second Mover Advantage?
  • First Mover Advantage if manipulation of game
    possible through changing game or beliefs of
    rival
  • Princess Bride
  • Second Mover Advantage if information becomes
    available through sequence
  • Sailing NCAA Football Overtime

18
Take-Away Lessons
  • With sequential decisions, sound strategy
    requires looking to the end of the game and
    reasoning backwards
  • Even without formal game trees, this way of
    thinking will help eliminate irrelevant options
    and clarify relevant ones
  • Going first or second? Information v.
    manipulation tradeoff
Write a Comment
User Comments (0)
About PowerShow.com