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8/6/2019 Game Theory Von Neuman and Morgenstern the Theory of Games3120
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Game Theory Von Neuman and Morgenstern (The Theory
of Games and Economic Behavior, 1944)
Conceptual Framework
Game strategy
Components of a game
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Two Person, Zero Sum Games Each person knows own and opponents
alternatives
All preferences are known
Single period game
Sum of payoffs zero
Equilibrium reached when neither of the
participants can improve payoff
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Strategies Dominant strategy
Best regardless what others do
Maximin strategy
Choice that maximizes across the set of
minimum possible payoffs
Best of the worst
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Unstable Games
No equilibrium found
Strategy chosen leads to solution
Each player then has incentive to switch
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Two Person, Non-Zero Sum
Games The Prisoners Dilemma
Bonnie and Clyde are caught
Dilemma: Confess or not
1 period game
Non-cooperative solution: Both confess Cooperative solution: Both do not confess
Off diagonal represents double cross
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Duopoly as a Prisoners Dilemma Even if both agree to a cooperative solution,
one may double cross
Two firms: decision on amount of output
{Small or Large}
{L,L} represents normal profits
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Repeated Games
Single period game predicts competition,
but there are likely to be multiple periods.
Multiple periods allow for retribution, not
found in single period games
Duopoly as a Multiperiod Game
More likely to collude
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N-Person Games Extend to more than 2 players
Complications:
Coalitions
Cooperation and duplicity
Solutions can be difficult
Still gives insight into nature of conflict,
posturing, and resolution
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Best Pricing Practices Shift attention to tactics and strategy to
achieve competitive advantage
Examine rival firm behavior as if it were a
game
First-mover advantages
Credible threats to alter rival behavior
Stresses interdependency in oligopoly
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Business Strategy Games When rivals alter products or pricing, react
or adapt
Anticipate actions; be proactive
Sequential game--specific order of play
E.g.; One firm announces a price cut; decision
is to respond or not respond
Simultaneous game--all players choose
actions at same time
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Business Rivalry as a Sequential
Game The first to introduce a product, lower price,
etc. often achieve recognition and
advantage--first-mover advantage
When games last several periods, actions
can be rewarded or punished in subsequent
periods Entry of a new firm often discouraged by threat
of existing firms dropping prices to
unprofitable levels.
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First-Mover Games Game with military and civilian markets for
Hum Vs.
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Game Tree--Illustrating
Sequential Games Game tree is like a decision tree
Schematic diagram of decision nodes (or
focal outcomes)
Solutions parallel board games like chess
One approach to solution--end-game
reasoning--start with the final decision and
use backward induction to find the best
starting point.
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1999 South-Western College Publishing
A Credible Threat
A credible threat--an action perceived as a
possible penalty in a noncooperative game.
Its existence sometimes induces cooperativebehavior.
A credible commitment--a mechanism for
establishing trust
Such as a reward for good behavior in a
noncooperative game.
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1999 South-Western College Publishing
Mechanisms for Credible Threats and
Commitments
Contractual side payments, but these may violate
antitrust laws.
Use of nonredeployable assets such as reputation.
Entering alliance relationships which may fall
apart if any party violated their commitments.
Using a "hostage mechanism--irreversible and
irrevocable can deter breaking commitments.
Examples: "double your money back
guarantees," and "most favored nation"
clauses.
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1999 South-Western College Publishing1999 South-Western College Publishing
Hostage Mechanisms in
Oligopoly
Best Buys offer: If you find a lower advertised
price, youll get the difference back
This makes Best Buy cut prices whenever local
stores cuts prices
Local stores realize they cant undercut Best Buy
Customers realize it is unlikely to find lower prices
If potential entrants think they can get a foothold in area,
they know that Best Buys pricing is a credible
commitment.
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1999 South-Western College Publishing
Excess Capacity, Scale of Entry,
and Entry Deterrence Building excess capacity can deter entry.
Potential entrants know that the price can
be driven down to unprofitable levels upon entryof new firms.
The building of extra capacity is an action in a
sequential game, often with the intent of
forestalling entry. This is called a
precommitment game.
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Size Barriers
Sometimes market entry requires large scale
Incumbents may accommodate entrant,
allowing a niche
Incumbents may take entry deterring
actions, such as cutting prices at the threat
of entry
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SortingR
ules
Brand loyalty
Efficient rationing
Random rationing
Inverse intensity rationing
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Theory of Contestable Markets
High prices encourage entry
When barriers are low, even monopolist
must be careful about raising prices too
high.
Contestable markets tend to have
competitive prices and low or zeroeconomic profits
Potential entry matters more than actual
number of firms
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Simultaneous Games A sealed bid auction is a simultaneous game
A dominant strategy is the best decision, no
matter what anyone else does.
When no Nash equilibrium exists, it is
useful to hide ones strategy by randomly
changing strategies. Called a mixed Nashequilibrium strategy
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Nash Equilibrium When all players make their best reply
responses (so changing their choices cannot
improve their situation) then the game is in
Nash Equilibrium
Since game trees have several branches, we
can examine the concept in each part of thetree, called a subgame.
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Repeated Games
Escape from the prisoners dilemma
If games are repeated, there is a greater
expectation that firms will achieve a
cooperative solution
Firms signal by their behavior whether they
want to cooperate or not
Firms that expand output show that they do
not want to cooperate
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Repeated Game Strategies
Grim trigger strategy--violations never
forgotten
Alternatively, punishment can be short-lived
For multiperiod games, usually some period of
punishment that can induce cooperation
Trembling hand trigger--when slightdefections go unpunished
One non-cooperative act may be forgiven, but
not two