Game Theory and Competitive Strategy

1
Chapter 13

• Game Theory and Competitive Strategy

2
Topics to be Discussed

• Gaming and Strategic Decisions
• Dominant Strategies
• The Nash Equilibrium Revisited
• Repeated Games

3
Topics to be Discussed

• Sequential Games
• Threats, Commitments, and Credibility
• Entry Deterrence
• Bargaining Strategy
• Auctions

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Gaming and Strategic Decisions

• Game is any situation in which players (the
  participants) make strategic decisions
• Ex firms competing with each other by setting
  prices, group of consumers bidding against each
  other in an auction
• Strategic decisions result in payoffs to the
  players outcomes that generate rewards or
  benefits

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Gaming and Strategic Decisions

• Game theory tries to determine optimal strategy
  for each player
• Strategy is a rule or plan of action for playing
  the game
• Optimal strategy for a player is one that
  maximizes the expected payoff
• We consider players who are rational they think
  through their actions

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Gaming and Strategic Decisions

• If I believe that my competitors are rational
  and act to maximize their own profits, how should
  I take their behavior into account when making my
  own profit-maximizing decisions?(Text, p. 474)

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Noncooperative vs. Cooperative Games

• Cooperative Game
• Players negotiate binding contracts that allow
  them to plan joint strategies
• Example Buyer and seller negotiating the price
  of a good or service or a joint venture by two
  firms (i.e., Microsoft and Apple)
• Binding contracts are possible

8
Noncooperative vs. Cooperative Games

• Noncooperative Game
• Negotiation and enforcement of binding contracts
  between players is not possible
• Example Two competing firms, assuming the
  others behavior, independently determine pricing
  and advertising strategy to gain market share
• Binding contracts are not possible

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Noncooperative vs. Cooperative Games

• The strategy design is based on understanding
  your opponents point of view, and (assuming your
  opponent is rational) deducing how he or she is
  likely to respond to your actions. (Text, p. 475)

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Gaming and Strategic Decisions

• An Example How to buy a dollar bill
• Auction a dollar bill
• Highest bidder receives the dollar in return for
  the amount bid
• Second highest bidder must pay the amount he or
  she bid but gets nothing in return
• How much would you bid for a dollar?
• Typically bid more for the dollar when faced with
  loss as second highest bidder

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Acquiring a Company

• Scenario
• Company A The Acquirer
• Company T The Target
• A will offer cash for all of Ts shares
• The value and viability of T depends on the
  outcome of a current oil exploration project

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Acquiring a Company

• Project failure Ts value 0
• Project success Ts value 100/share
• All outcomes in between equally likely
• Ts value will be 50 greater with As management

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Acquiring a Company

• Scenario
• A must submit the proposal before the exploration
  outcome is known
• T will not choose to accept or reject until after
  the outcome is known only to T
• Company T will accept any offer that is greater
  than the per share value of the company under
  current management
• How much should A offer?

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Dominant Strategies

• Dominant Strategy is one that is optimal no
  matter what an opponent does
• An Example
• A and B sell competing products
• They are deciding whether to undertake
  advertising campaigns

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Payoff Matrix for Advertising Game
Firm B
Dont Advertise
Advertise
Advertise
Firm A
Dont Advertise
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Payoff Matrix for Advertising Game

• Observations
• A regardless of B, advertising is the best
• B regardless of A, advertising is best

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Payoff Matrix for Advertising Game

• Observations
• Dominant strategy for A and B is to advertise
• Do not worry about the other player
• Equilibrium in dominant strategy

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Dominant Strategies

• Equilibrium in dominant strategies
• Outcome of a game in which each firm is doing the
  best it can regardless of what its competitors
  are doing
• Optimal strategy is determined without worrying
  about the actions of other players
• However, not every game has a dominant strategy
  for each player

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Dominant Strategies

• Game Without Dominant Strategy
• The optimal decision of a player without a
  dominant strategy will depend on what the other
  player does
• Revising the payoff matrix, we can see a
  situation where no dominant strategy exists

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Modified Advertising Game
Firm B
Dont Advertise
Advertise
Advertise
Firm A
Dont Advertise
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Modified Advertising Game

• Observations
• A No dominant strategy depends on Bs actions
• B Dominant strategy is to advertise
• Firm A determines Bs dominant strategy and makes
  its decision accordingly

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The Nash Equilibrium Revisited

• A dominant strategy is stable, but in many games
  one or more party does not have a dominant
  strategy
• A more general equilibrium concept is the Nash
  Equilibrium introduced in Chapter 12
• A set of strategies (or actions) such that each
  player is doing the best it can given the actions
  of its opponents

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The Nash Equilibrium Revisited

• None of the players have incentive to deviate
  from its Nash strategy, therefore it is stable
• In the Cournot model, each firm sets its own
  price assuming the other firms outputs are
  fixed. Cournot equilibrium is a Nash Equilibrium.

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The Nash Equilibrium Revisited

• Dominant Strategy
• Im doing the best I can no matter what you do.
  Youre doing the best you can no matter what I
  do.
• Nash Equilibrium
• Im doing the best I can given what you are
  doing. Youre doing the best you can given what I
  am doing.
• Dominant strategy is a special case of Nash
  equilibrium

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The Nash Equilibrium Revisited

• Two cereal companies face a market in which two
  new types of cereal can be successfully
  introduced, provided each type is introduced by
  only one firm
• Product Choice Problem
• Market for one producer of crispy cereal
• Market for one producer of sweet cereal
• Each firm only has the resources to introduce one
  cereal
• Noncooperative

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Product Choice Problem
Firm 2
Crispy
Sweet
Crispy
Firm 1
Sweet
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Product Choice Problem

• If Firm 1 hears Firm 2 is introducing a new sweet
  cereal, its best action is to make crispy
• Bottom left corner is Nash equilibrium
• What is other Nash Equilibrium?

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Beach Location Game

• Scenario
• Two competitors, Y and C, selling soft drinks
• Beach is 200 yards long
• Sunbathers are spread evenly along the beach
• Price Y Price C
• Customer will buy from the closest vendor

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Beach Location Game

• Where will the competitors locate (i.e., where is
  the Nash equilibrium)?
• Will want to all locate in center of beach
• Similar to groups of gas stations, car
  dealerships, etc.

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The Nash Equilibrium Revisited

• Maximin Strategies - Scenario
• Two firms compete selling file encryption
  software
• They both use the same encryption standard (files
  encrypted by one software can be read by the
  other - advantage to consumers)
• Firm 1 has a much larger market share than Firm 2
• Both are considering investing in a new
  encryption standard

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Maximin Strategy
Firm 2
Dont invest
Invest
Dont invest
Firm 1
Invest
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Maximin Strategy

• Observations
• Dominant strategy Firm 2 Invest
• Firm 1 should expect Firm 2 to invest
• Nash equilibrium
• Firm 1 invest
• Firm 2 Invest
• This assumes Firm 2 understands the game and is
  rational

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Maximin Strategy

• Observations
• If Firm 2 does not invest, Firm 1 incurs
  significant losses
• Firm 1 might play dont invest
• Minimize losses to 10 maximin strategy

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Maximin Strategy

• If both are rational and informed
• Both firms invest
• Nash equilibrium
• If Player 2 is not rational or completely
  informed
• Firm 1s maximin strategy is to not invest
• Firm 2s maximin strategy is to invest
• If 1 knows 2 is using a maximin strategy, 1 would
  invest

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Maximin Strategy

• If Firm 1 is unsure about what Firm 2 will do, it
  can assign probabilities to each possible action
• Could use a strategy that maximizes its expected
  payoff
• Firm 1s strategy depends critically on its
  assessment of probabilities for Firm 2

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Prisoners Dilemma
Prisoner B
Confess
Dont Confess
Confess
Prisoner A
Dont Confess
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Prisoners Dilemma

• What is the
• Dominant strategy
• Nash equilibrium
• Maximin solution
• Dominant strategies are also maximin strategies
• Both confess is both Nash equilibrium and maximin
  solution

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Mixed Strategy

• Pure Strategy
• Player makes a specific choice or takes a
  specific action
• Mixed Strategy
• Player makes a random choice among two or more
  possible actions, based on a set of chosen
  probabilities

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Matching Pennies
Player B
Heads
Tails
Heads
Player A
Tails
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Matching Pennies

• Pure strategy No Nash equilibrium
• No combination of head and tails leaves both
  players better off
• Mixed strategy Random choice is a Nash
  equilibrium

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Matching Pennies

• Player A might flip coin playing heads with ½
  probability and tails with ½ probability
• If both players follow this strategy, there is a
  Nash equilibrium both players will be doing the
  best they can given what their opponent is doing
• Although the outcome is random, the expected
  payoff is 0 for each player

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Mixed Strategy

• One reason to consider mixed strategies is when
  there is a game that does not have any Nash
  equilibriums in pure strategy
• When allowing for mixed strategies, every game
  has a Nash equilibrium
• Mixed strategies are popular for games like poker
• A firm might not find it reasonable

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The Battle of the Sexes
Joan
Wrestling
Opera
Wrestling
Jim
Opera
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The Battle of the Sexes

• Pure Strategy
• Both watch wrestling
• Both watch opera
• Mixed Strategy
• Jim chooses wrestling
• Joan chooses wrestling

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Repeated Games

• Game in which actions are taken and payoffs are
  received over and over again
• Oligopolistic firms play a repeated game
• With each repetition of the Prisoners Dilemma,
  firms can develop reputations about their
  behavior and study the behavior of their
  competitors

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Pricing Problem
Firm 2
Low Price
High Price
Low Price
Firm 1
High Price
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Pricing Problem

• How does a firm find a strategy that would work
  best on average against all or almost all other
  strategies?
• Tit-for-tat strategy
• Repeated game strategy in which a player responds
  in kind to an opponents previous play,
  cooperating with cooperative opponents and
  retaliating against uncooperative ones

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Tit-for-Tat Strategy

• What if the game is infinitely repeated?
• Competitors repeatedly set price every month,
  forever
• Tit-for-tat strategy is rational
• If competitor charges low price and undercuts
  firm
• Will get high profits that month but know I will
  lower price next month
• Both of us will get lower profits if keep
  undercutting, so not rational to undercut

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Tit-for-Tat Strategy

• What if repeated a finite number of times?
• If both firms are rational, they will charge high
  prices until the last month
• After the last month, there is no retaliation
  possible
• But in the month before last month, knowing that
  will charge low price in last month, will charge
  low price in month before
• Keep going and see that only rational outcome is
  for both firms to charge low price every month

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Tit-for-Tat Strategy

• If firms dont believe their competitors are
  rational or think perhaps they arent,
  cooperative behavior is a good strategy
• Most managers dont know how long they will be
  competing with their rivals
• In a repeated game, prisoners dilemma can have
  cooperative outcome

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Repeated Games

• Conclusion
• Cooperation is difficult at best since these
  factors may change in the long run
• Need a small number of firms
• Need stable demand and cost conditions
• This could lead to price wars if dont have them

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Oligopolistic Cooperationin the Water Meter
Industry

• Characteristics of the Market
• Four producers of water meters
• Rockwell International
• Badger Meter
• Neptune Water Meter Company
• Hersey Products
• Rockwell has about 35 of market share
• Badger, Neptune, and Hersey combined have about a
  50 to 55 share

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Oligopolistic Cooperationin the Water Meter
Industry

• Most buyers are municipal water utilities
• Very inelastic demand
• Not a significant part of the budget for
  providing water
• Demand is stable
• Demand grows steadily with population
• Utilities have long-standing relationships with
  suppliers
• Reluctant to switch

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Oligopolistic Cooperationin the Water Meter
Industry

• Significant economies of scale
• Both long term relationship and economies of
  scale represent barriers to entry
• Hard for new firms to enter market
• If firms were to cooperate, could earn
  significant monopoly profits
• If compete aggressively to gain market share,
  profits will fall to competitive levels

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Oligopolistic Cooperationin the Water Meter
Industry

• This is a Prisoners Dilemma what should the
  firms do?
• Lower price to a competitive level
• Cooperate
• Companies have been playing repeated game for
  decades
• Cooperation has prevailed given market
  characteristics

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Sequential Games

• Players move in turn, responding to each others
  actions and reactions
• Ex Stackelberg model (ch. 12)
• Responding to a competitors ad campaign
• Entry decisions
• Responding to regulatory policy

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Sequential Games

• Going back to the product choice problem
• Two new (sweet, crispy) cereals
• Successful only if each firm produces one cereal
• Sweet will sell better
• Both still profitable with only one producer

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Modified Product Choice Problem

• If firms both announce their decisions
  independently and simultaneously, they will both
  pick sweet cereal and both will lose money
• What if Firm 1 sped up production and introduced
  new cereal first?
• Now there is a sequential game
• Firm 1 will think about what Firm 2 will do

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Modified Product Choice Problem
Firm 2
Crispy
Sweet
Crispy
Firm 1
Sweet
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Extensive Form of a Game

• Extensive Form of a Game
• Representation of possible moves in a game in the
  form of a decision tree
• Allows one to work backward from the best outcome
  for Firm 1

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Product Choice Game in Extensive Form
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Sequential Games

• The Advantage of Moving First
• In this product-choice game, there is a clear
  advantage to moving first
• The first firm can choose a large level of
  output, thereby forcing second firm to choose a
  small level
• Can show the firms mover advantage by revising
  the Stackelberg model and comparing to Cournot

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First Mover Advantage

• Assume Duopoly

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First Mover Advantage

• Duopoly

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Choosing Output
Firm 2
7.5
10
15
7.5
10
Firm 1
15
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Choosing Output

• This payoff matrix illustrates various outcomes
• Move together, both produce 10
• If Firm 1 moves first (Q15), best Firm 2 can do
  is 7.5

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Threats, Commitments, and Credibility

• Strategic Moves
• What actions can a firm take to gain advantage in
  the marketplace?
• Deter entry
• Induce competitors to reduce output, leave, raise
  price
• Implicit agreements that benefit one firm

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Threats, Commitments, and Credibility

• Strategic Move
• Action that gives a player an advantage by
  constraining his behavior
• Firm 1 must constrain his behavior to the extent
  Firm 2 is convinced that he is committed

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Threats, Commitments, and Credibility

• How to Make the First Move
• Demonstrate Commitment
• Firm 1 must do more than announce they will
  produce sweet cereal
• Invest in expensive advertising campaign
• Buy large order of sugar and send invoice to Firm
  2
• Commitment must be enough to induce Firm 2 to
  make the decision Firm 1 wants it to make

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Threats, Commitments, and Credibility

• Empty Threats
• If a firm will be worse off if it charges a low
  price, the threat of a low price is not credible
  in the eyes of the competitors
• When firms know the payoffs of each others
  actions, firms cannot make threats the other firm
  knows they will not follow
• In our example, Firm 1 will always charge high
  price and Firm 2 knows it

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Pricing of Computers and Word Processors
Firm 2
High Price
Low Price
High Price
Firm 1
Low Price
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Threats, Commitments, and Credibility

• Sometimes firms can make credible threats
• Scenario
• Race Car Motors, Inc. (RCM) produces cars
• Far Out Engines (FOE) produces specialty car
  engines and sells most of them to RCM
• Sequential game with RCM as the leader
• FOE has no power to threaten to build big engines
  since RCM controls output

73
Production Choice Problem
Race Car Motors
Small cars
Big cars
Small engines
Far Out Engines
Big engines
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Threats, Commitments, and Credibility

• RCM does best by producing small cars
• Knows that Far Out will then produce small
  engines
• Far Out prefers to make big engines
• Can Far Out induce Race Car to produce big cars
  instead?

75
Threats, Commitments, and Credibility

• Suppose Far Out threatens to produce big engines
  no matter what RCM does?
• Not credible since once RCM announces they are
  producing small cars, FOE will not have incentive
  to carry out threat
• Can make threat credible by altering pay off
  matrix by constraining its own choices
• Shutting down or destroying some small engine
  production capacity

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Modified Production Choice Problem
Race Car Motors
Small cars
Big cars
Small engines
Far Out Engines
Big engines
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Modified Production Choice Problem

• Strategic commitments can be effective but not
  without risk
• Rely heavily on accurate knowledge of payoff
  matrix and industry
• May have competitors out there that they dont
  know about and lose sales

78
Role of Reputation

• If Far Out gets the reputation of being
  irrational
• They threaten to produce large engines no matter
  what Race Car does
• Threat might be credible because irrational
  people dont always make profit maximizing
  decisions
• A party thought to be crazy can lead to a
  significant advantage

79
Bargaining Strategy

• Bargaining situation can depend on ability to
  affect relative bargaining position
• Consider two firms introducing one of two
  complementary goods
• Firm 1 has cost advantage in Good A
• Firm 2 has cost advantage in Good B

80
Bargaining Strategy
Firm 2
Produce A
Produce B
Produce A
Firm 1
Produce B
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Bargaining Strategy

• With collusion
• Firm 1 Produces A and Firm 2 produces B (50,50)
• Without collusion
• Firm 1 produces A and Firm 2 produces B (50,50)
• Nash equilibrium

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Bargaining Strategy

• Suppose each firm is also bargaining on the
  decision to join in a research consortium with a
  third firm
• Dominant strategy is for both firms to enter
  consortium

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Bargaining Strategy
Firm 2
Work alone
Enter consortium
Work alone
Firm 1
Enter consortium
84
Bargaining Strategy

• Linking the Bargaining Problem
• Firm 1 announces it will join the consortium only
  if Firm 2 agrees to produce A and Firm 1 will
  produce B
• Firm 2s best interest is to produce A with Firm
  1 producing B
• Firm 1s profit increases from 50 to 60

85
Bargaining Strategy

• Strategic moves can be used in bargaining
• Combining issues in bargaining can benefit one
  side at others expense

86
Wal-Mart Stores Preemptive Investment Strategy

• How did Wal-Mart become the largest retailer in
  the U.S. when many established retail chains were
  closing their doors?
• Gained monopoly power by opening in small towns
  with no threat of other discount competition
• Preemptive game with Nash equilibrium

87
The Discount Store Preemption Game
Company X
Enter
Dont enter
Enter
Wal-Mart
Dont enter
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The Discount Store Preemption Game

• Two Nash equilibrium
• Low left
• Upper right
• Must be preemptive to win

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Entry Deterrence

• Barriers to entry important for monopoly power
• Economies of scale, patents and licenses, access
  to critical inputs
• Firms can also deter entry
• To deter entry, the incumbent firm must convince
  any potential competitor that entry will be
  unprofitable

90
Entry Possibilities
Potential Entrant (X) (80 fixed costs)
Enter
Stay out
High price (accommodation)
Incumbent (I)
Low Price (warfare)
91
Entry Deterrence

• Scenario
• If X does not enter, I makes a profit of 200
  million
• If X enters and charges a high price, I earns a
  profit of 100 million and X earns 20 million
• If X enters and charges a low price, I earns a
  profit of 70 million and X earns -10 million

92
Entry Deterrence

• Could threaten X with warfare if enters market
• Not credible because once X has entered, it is in
  your best interest to accommodate and maintain
  high price

93
Entry Deterrence

• What if firm I makes an investment before entry
  to increase capacity?
• Irrevocable commitment
• Gives new payoff matrix since profits will be
  reduced by investment
• Threat is completely credible
• Rational for Firm X to stay out of market

94
Entry Deterrence
Potential Entrant (X)
Enter
Stay out
High price (accommodation)
Incumbent (I)
Low price (warfare)
95
Entry Deterrence

• If incumbent has reputation of price cutting
  competitors even at loss, then threat will be
  credible
• Short run losses may be offset by long run gains
  as monopolist

96
Entry Deterrence

• Production of commercial airlines exhibit
  significant economies of scale
• Airbus and Boeing considering new aircraft
• Suppose it is not economical for both firms to
  produce the new aircraft

97
Development of a New Aircraft
Airbus
Produce
Dont produce
Produce
Boeing
Dont produce
98
Development of a New Aircraft

• Boeing has head start
• Boeing will produce
• Airbus will not produce

99
Development of a New Aircraft

• Governments can change outcome of game
• European government agrees to subsidize Airbus
  before Boeing decides to produce
• With Airbus being subsidized, the payoff matrix
  for the two firms would differ significantly

100
Development of an AircraftAfter European Subsidy
Airbus
Produce
Dont produce
Produce
Boeing
Dont produce
101
Development of an AircraftAfter European Subsidy

• Airbus will produce
• Boeing will not produce

Airbus
Produce
Dont produce
Produce
Boeing
Dont produce
102
Diaper Wars

• Even though there are only two major firms,
  competition is intense
• The competition occurs mostly in the form of
  cost-reducing innovation
• Small cost savings can lead to capturing of
  market share
• Both firms spend significantly on RD

103
Competing Through R D
Kimberly-Clark
RD
No RD
RD
PG
No RD
104
Competing Through R D

• Both spend on RD
• Dominant strategy
• Why not cooperate?
• Strengthening Bargaining Power
• Credibility
• Reducing flexibility

105
Auctions

• Markets in which products are bought and sold
  through formal bidding processes
• Encourages competition that increases sellers
  revenue
• Low cost of transactions
• Useful for unique items or those with fluctuating
  value
• Tokyo fish market

106
Auction Formats

• Traditional English (oral)
• Seller actively solicits progressively higher
  bids from a group of potential buyers
• Buyers are always aware of highest bid
• Stops when no one passes highest bid

107
Auction Formats

• Dutch auction
• Seller begins by offering item at relatively high
  price, then reduces it by fixed amounts until
  item is sold
• First buyer accepting offered price can buy item
  at that price

108
Auction Formats

• Sealed-bid
• All bids are made simultaneously in sealed
  envelopes, where winning bid is the one who
  submitted highest bid
• First price
• Sales price equals highest bid
• Second price
• Sales price equals second highest bid

109
Valuation and Information

• How to choose an auction format
• Private-value auction bidder knows individual
  valuations of object, but valuations differ from
  bidder to bidder
• Signed baseball
• Common-value auction bidders uncertain what the
  value is
• Offshore oil reserve

110
Price-Value Auctions

• Each bidder must choose bidding strategy
• Payoff for winning is reservation price minus
  price paid
• Payoff for losing is zero

111
Private Value Auction

• English oral auction and secondprice sealed bid
  auctions
• Bidding truthfully is dominant strategy
• Pay based on value of second highest bidder so no
  incentive not to bid reservation price
• Risk to bidding higher than reservation price

112
Private Value Auctions

• English auction
• Continue bidding until second person is unwilling
  to make bid
• Sealed-bid auction
• Winning bid approximately equal to the second
  highest bidders reservation price
• Both yield the same revenue

113
Common Value Auctions

• Winners Curse
• The winner is worse off because they
  overestimated the value of the item and thereby
  overbid
• Must reduce bid by amount equal to the expected
  error of the winning bidder
• If a lot of variation in other bidders, then
  estimates are fairly imprecise

114
Maximizing Auction Revenue

• Private Value Auction
• Encourages many bidders to increase expected bid
  of winner
• Common Value Auction
• Uses open rather than sealed bid
• Generates greater revenue
• Reveals information about true value, reducing
  concern of winners curse

115
Maximizing Auction Revenue

• Private value auction
• Sets min bid equal to or higher than value to you
  of keeping good for future sale
• Protects against loss if bidders are unaware of
  value
• Increases size of bids by letting bidders think
  item is valuable
• No sale could make bidders think item is low
  quality

116
Bidding and Collusion

• Buyers can allow benefit from collusion
• Can be done legally through buying groups
• Can be done illegally through collusive
  agreements that violate antitrust laws
• Collusion is not easy because of large incentive
  to cheat
• Repeated auctions allow for penalizing
  participants that break agreement

117
Bidding and Collusion

• Examples
• Collusion among baseball owners to limit their
  bidding for free agent players in the 1980s
• Two of the worlds most successful auction houses
  were found guilty of agreeing to fix prices of
  commissions
• Sothebys and Christies

118
Internet Auctions

• Popularity of auctions has skyrocketed with
  growth of internet
• Most popular site is eBay
• Dominates online person-person auction industry
• Subject to large network externalities
• Choose auction site with largest number of
  potential bidders

119
Internet Auctions

• eBay auctions are somewhat different from types
  discussed
• A few caveats
• No quality control function
• Poor seller feedback
• Bid manipulation may occur