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