Game Theory
• Von Neuman and Morgenstern (The Theory
of Games and Economic Behavior, 1944)
• Conceptual Framework
– Game strategy
– Components of a game
Two Person, Zero Sum Games
• Each person knows own and opponent’s
alternatives
• All preferences are known
• Single period game
• Sum of payoffs zero
• Equilibrium reached when neither of the
participants can improve payoff
Strategies
• Dominant strategy
– Best regardless what others do
• Maximin strategy
– Choice that maximizes across the set of
minimum possible payoffs
– Best of the worst
Unstable Games
• No equilibrium found
• Strategy chosen leads to solution
• Each player then has incentive to switch
Two Person, Non-Zero Sum
Games
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The Prisoner’s 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
Duopoly as a Prisoner’s 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
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
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
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
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
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.
First-Mover Games
• Game with military and civilian markets for
Hum Vs.
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.
A Credible Threat
• A credible threat--an action perceived as a
possible penalty in a noncooperative game.
– Its existence sometimes induces cooperative
behavior.
• A credible commitment--a mechanism for
establishing trust
– Such as a reward for good behavior in a
noncooperative game.
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.
1999 South-Western College Publishing
Hostage Mechanisms in
Oligopoly
• Best Buy’s offer: If you find a lower advertised
price, you’ll get the difference back
• This makes Best Buy cut prices whenever local
stores cuts prices
– Local stores realize they can’t 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 Buy’s pricing is a credible
commitment.
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 entry
of 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.
1999 South-Western College Publishing
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
Sorting Rules
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Brand loyalty
Efficient rationing
Random rationing
Inverse intensity rationing
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 zero
economic profits
• Potential entry matters more than actual
number of firms
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 one’s strategy by randomly
changing strategies. Called a “mixed Nash
equilibrium” strategy
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 the
tree, called a subgame.
Repeated Games
• Escape from the prisoner’s 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
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 slight
defections go unpunished
– One non-cooperative act may be forgiven, but
not two