Game Theory

1
Game Theory

• Von Neuman and Morgenstern (The Theory of Games
  and Economic Behavior, 1944)
• Conceptual Framework
• Game strategy
• Components of a game

2
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

3
Strategies

• Dominant strategy
• Best regardless what others do
• Maximin strategy
• Choice that maximizes across the set of minimum
  possible payoffs
• Best of the worst

4
Unstable Games

• No equilibrium found
• Strategy chosen leads to solution
• Each player then has incentive to switch

5
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

6
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

7
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

8
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

9
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

10
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

11
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.

12
First-Mover Games

• Game with military and civilian markets for Hum
  Vs.

13
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.

14
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
15
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
16
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.

?1999 South-Western College Publishing
?1999 South-Western College Publishing
17
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
18
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

19
Sorting Rules

• Brand loyalty
• Efficient rationing
• Random rationing
• Inverse intensity rationing

20
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

21
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 Nash equilibrium
  strategy

22
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.

23
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

24
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