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Game Theory
Life must be understood backward, but it must be lived forward.-
Soren Kierkegaard
Mike ShorLecture 4
Game Theory - Mike Shor
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ReviewRecognize dominant and dominated strategiesDominant
strategies are always playedDominated strategies are never
played
Equilibrium: likely outcome of a game
Dominance solvableIterated deletion of dominated strategies
Game Theory - Mike Shor
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Cell-by-Cell InspectionGames of Assurance
The good equilibrium is riskyNeed assurancesGames of
Coordination
Failure to agree leads to no profitsCant agree on what to agree
onGames of Chicken
Game Theory - Mike Shor
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Games of ChickenA monopolist faces a potential entrantMonopolist
can accommodate or fightPotential entrant can enter or stay out
Monopolist
PotentialEntrant
AccommodateFightIn50 , 50-50 , -50Out 0 , 100 0 , 100
Game Theory - Mike Shor
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EquilibriumUse best reply method
to find equilibriaMonopolistPotentialEntrant
AccommodateFightIn50 , 50-50 , -50Out 0 , 100 0 , 100
Game Theory - Mike Shor
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Importance of OrderTwo equilibria exist
( In, Accommodate )( Out, Fight )Only one makes temporal
sense
Fight is a threat, but not credibleNot sequentially
rationalSimultaneous outcomes may not make sense for sequential
games.
Game Theory - Mike Shor
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Sequential Games
The Extensive Form
Game Theory - Mike Shor
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Looking ForwardEntrant makes the first move:
Must consider how monopolist will respondIf enter:
Monopolist accommodates
Game Theory - Mike Shor
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And Reasoning BackNow consider entrants move
Only ( In, Accommodate ) is sequentially rational
Game Theory - Mike Shor
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Sequential Rationality
COMMANDMENTLook forward and reason back.
Anticipate what your rivals will do tomorrow in response to your
actions today
Game Theory - Mike Shor
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Solving Sequential GamesStart with the last move in the
gameDetermine what that player will doTrim the tree
Eliminate the dominated strategiesThis results in a simpler
gameRepeat the procedure
Game Theory - Mike Shor
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Voting Revisited Gore v. BushFour judges prefer: BtoGtoRThree
judges prefer: GtoRtoBTwo judges prefer: RtoBtoG
Majority rule results:
B beats G ; G beats R ; R beats B
What if you want Bush to Win?
R vs. G then winner vs. B B
Game Theory - Mike Shor
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Extensive Form
RGB vs. GBGR vs. GB vs. RBRBRBG
Game Theory - Mike Shor
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Looking Forward
B vs. GBGB vs. RBRBRBGA majority prefers R to BA majority
prefers B to G
Game Theory - Mike Shor
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Trim The Tree
RGB vs. GBR vs. GB vs. RRRB
Game Theory - Mike Shor
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Reasoning BackFirst stage, in effect vote between R & BGore
supporters prefer G>R>B, vote R
RGB vs. GBR vs. GB vs. RRRB
Game Theory - Mike Shor
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What Happened?Gore supporters have preferences
Gore > Remand > BushIn first round, vote between R and
GGore supporters prefer Gore
But vote for G is in effect a vote for B!So Gore supporters vote
for remand.
Guarantee themselves second best choice
Game Theory - Mike Shor
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Rollback in Voting and Being PoliticalNot necessarily good to
vote your true preferences
Amendments to make bad bills worseCrossing over in open
primariesCentrist voting in primariesSupporting your second-best
option
STILL Outcome predeterminedAGENDA SETTING!
Game Theory - Mike Shor
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Predatory Pricing
An incumbent firm operates in three markets, and faces entry in
eachMarket 1 in year 1, Market 2 in year 2, etc.
Each time, I can slash prices, or accommodate the new entry
What should I do the first year?
Game Theory - Mike Shor
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Predatory Pricing
E1outinMfightaccE2outinfightaccME3
Game Theory - Mike Shor
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Predatory Pricing
The end of the tree: year 3
In year 3: ( In, Accommodate )
Game Theory - Mike Shor
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RollbackTrim the tree:
Game Theory - Mike Shor
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Predatory PricingSince the Incumbent will not fight Entrant 3,
he will not fight Entrant 2 Same for Entrant 1Only one Rollback
Equilibrium
All entrants play In Incumbent plays AccommodateWhy do we see
predatory pricing?
Game Theory - Mike Shor
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Game Theory
Example
Sequential Entry
Game Theory - Mike Shor
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Market Opportunity AnalysisAssesses the potential of a
geographic market for a specific set of products, providing a
prioritization of market coverage voids and recommending market
entry strategies.
Game Theory - Mike Shor
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Market Analysis400 SBCs700 SBCs
Game Theory - Mike Shor
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Extended Market AnalysisIf enter 400 SBC market:Next entrant, to
break even,
must expect market share of 300/400Must expect market share of
75%If enter 700 SBC market:Next entrant, to break even,
must expect market share of 300/700Must expect market share of
43%Real decision:All of 400 or half of 700
Game Theory - Mike Shor
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Breakfast Cereals
600500400300200100000less sweetmore sweet1234567891011vertical
axis: sales (in thousands)product development costs: $1.2M per
product
Game Theory - Mike Shor
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First Product Entry
Profit = x base x height F= x 5 x 600 1200= 1500 1200=
300600500400300200100000less sweetmore sweet12345678910111
Game Theory - Mike Shor
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Second Product Entry
Profit = 2 x 300= 600600500400300200100000less sweetmore
sweet12345678910112
Game Theory - Mike Shor
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Third Product Entry
Profit = 600 + 1500 1200 480= 420600500400300200100000less
sweetmore sweet12345678910113
Game Theory - Mike Shor
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Competitor Enters
Profit = 600 - 240 = 360600500400300200100000less sweetmore
sweet12345678910114
Game Theory - Mike Shor
