Chapter 13 Game Theory and Competitive Strategy

Topics to be Discussed Gaming and Strategic Decisions Dominant Strategies The Nash Equilibrium Revisited Repeated Games

Gaming and Strategic Decisions

Dominant Strategies

The Nash Equilibrium Revisited

Repeated Games

Topics to be Discussed Sequential Games Threats, Commitments, and Credibility Entry Deterrence Bargaining Strategy Auctions

Sequential Games

Threats, Commitments, and Credibility

Entry Deterrence

Bargaining Strategy

Auctions

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

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

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

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

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)

“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)

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

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

Noncooperative vs. Cooperative Games Noncooperative Game Negotiation and enforcement of binding contracts between players is not possible Example: Two competing firms, assuming the other’s behavior, independently determine pricing and advertising strategy to gain market share Binding contracts are not possible

Noncooperative Game

Negotiation and enforcement of binding contracts between players is not possible

Example: Two competing firms, assuming the other’s behavior, independently determine pricing and advertising strategy to gain market share

Binding contracts are not possible

Noncooperative vs. Cooperative Games “The strategy design is based on understanding your opponent’s point of view, and (assuming your opponent is rational) deducing how he or she is likely to respond to your actions.” (Text, p. 475)

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

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

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

Acquiring a Company Scenario Company A: The Acquirer Company T: The Target A will offer cash for all of T’s shares The value and viability of T depends on the outcome of a current oil exploration project

Scenario

Company A: The Acquirer

Company T: The Target

A will offer cash for all of T’s shares

The value and viability of T depends on the outcome of a current oil exploration project

Acquiring a Company Project failure: T’s value = $0 Project success: T’s value = $100/share All outcomes in between equally likely T’s value will be 50% greater with A’s management

Project failure: T’s value = $0

Project success: T’s value = $100/share

All outcomes in between equally likely

T’s value will be 50% greater with A’s management

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?

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?

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

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

Payoff Matrix for Advertising Game Firm A Advertise Don’t Advertise Advertise Don’t Advertise Firm B 10, 5 15, 0 10, 2 6, 8

Payoff Matrix for Advertising Game Observations A: regardless of B, advertising is the best B: regardless of A, advertising is best Firm A Advertise Don’t Advertise Advertise Don’t Advertise Firm B 10, 5 15, 0 10, 2 6, 8

Observations

A: regardless of B, advertising is the best

B: regardless of A, advertising is best

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 Firm A Advertise Don’t Advertise Advertise Don’t Advertise Firm B 10, 5 15, 0 10, 2 6, 8

Observations

Dominant strategy for A and B is to advertise

Do not worry about the other player

Equilibrium in dominant strategy

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

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

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

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

Modified Advertising Game Firm A Advertise Don’t Advertise Advertise Don’t Advertise Firm B 10, 5 15, 0 20, 2 6, 8

Modified Advertising Game Observations A: No dominant strategy; depends on B’s actions B: Dominant strategy is to advertise Firm A determines B’s dominant strategy and makes its decision accordingly 10, 5 15, 0 20, 2 6, 8 Firm A Advertise Don’t Advertise Advertise Don’t Advertise Firm B

Observations

A: No dominant strategy; depends on B’s actions

B: Dominant strategy is to advertise

Firm A determines B’s dominant strategy and makes its decision accordingly

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

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

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 firm’s outputs are fixed. Cournot equilibrium is a Nash Equilibrium.

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 firm’s outputs are fixed. Cournot equilibrium is a Nash Equilibrium.

The Nash Equilibrium Revisited Dominant Strategy “I’m doing the best I can no matter what you do. You’re doing the best you can no matter what I do.” Nash Equilibrium “I’m doing the best I can given what you are doing. You’re doing the best you can given what I am doing.” Dominant strategy is a special case of Nash equilibrium

Dominant Strategy

“I’m doing the best I can no matter what you do. You’re doing the best you can no matter what I do.”

Nash Equilibrium

“I’m doing the best I can given what you are doing. You’re doing the best you can given what I am doing.”

Dominant strategy is a special case of Nash equilibrium

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

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

Product Choice Problem Firm 1 Crispy Sweet Crispy Sweet Firm 2 -5, -5 10, 10 -5, -5 10, 10

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? Firm 1 Crispy Sweet Crispy Sweet Firm 2 -5, -5 10, 10 -5, -5 10, 10

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?

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

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

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. Ocean 0 B Beach A 200 yards C

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.

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

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

Maximin Strategy Firm 1 Don’t invest Invest Firm 2 Don’t invest Invest 0, 0 -10, 10 20, 10 -100, 0

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 Firm 1 Don’t invest Invest Firm 2 0, 0 -10, 10 20, 10 -100, 0 Don’t invest Invest

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

Maximin Strategy Observations If Firm 2 does not invest, Firm 1 incurs significant losses Firm 1 might play don’t invest Minimize losses to 10 – maximin strategy Firm 1 Don’t invest Invest Firm 2 0, 0 -10, 10 20, 10 -100, 0 Don’t invest Invest

Observations

If Firm 2 does not invest, Firm 1 incurs significant losses

Firm 1 might play don’t invest

Minimize losses to 10 – maximin strategy

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

If both are rational and informed

Both firms invest

Nash equilibrium

If Player 2 is not rational or completely informed

Firm 1’s maximin strategy is to not invest

Firm 2’s maximin strategy is to invest

If 1 knows 2 is using a maximin strategy, 1 would invest

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 1’s strategy depends critically on its assessment of probabilities for Firm 2

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 1’s strategy depends critically on its assessment of probabilities for Firm 2

Prisoners’ Dilemma Prisoner A Confess Don’t Confess Confess Don’t Confess Prisoner B -5, -5 -1, -10 -2, -2 -10, -1

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 Prisoner A Confess Don’t Confess Confess Don’t Confess Prisoner B -5, -5 -1, -10 -2, -2 -10, -1

What is the:

Dominant strategy

Nash equilibrium

Maximin solution

Dominant strategies are also maximin strategies

Both confess is both Nash equilibrium and maximin solution

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

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

Matching Pennies Player A Heads Tails Heads Tails Player B 1, -1 -1, 1 1, -1 -1, 1

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 Player A Heads Tails Heads Tails Player B 1, -1 -1, 1 1, -1 -1, 1

Pure strategy: No Nash equilibrium

No combination of head and tails leaves both players better off

Mixed strategy: Random choice is a Nash equilibrium

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

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

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

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

The Battle of the Sexes Jim Wrestling Opera Wrestling Opera Joan 2,1 0,0 1,2 0,0

The Battle of the Sexes Pure Strategy Both watch wrestling Both watch opera Mixed Strategy Jim chooses wrestling Joan chooses wrestling Jim Wrestling Opera Wrestling Opera Joan 2,1 0,0 1,2 0,0

Pure Strategy

Both watch wrestling

Both watch opera

Mixed Strategy

Jim chooses wrestling

Joan chooses wrestling

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

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

Pricing Problem Firm 1 Low Price High Price Low Price High Price Firm 2 10, 10 100, -50 50, 50 -50, 100

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 opponent’s previous play, cooperating with cooperative opponents and retaliating against uncooperative ones

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 opponent’s previous play, cooperating with cooperative opponents and retaliating against uncooperative ones

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

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

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

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

Tit-for-Tat Strategy If firms don’t believe their competitors are rational or think perhaps they aren’t, cooperative behavior is a good strategy Most managers don’t know how long they will be competing with their rivals In a repeated game, prisoner’s dilemma can have cooperative outcome

If firms don’t believe their competitors are rational or think perhaps they aren’t, cooperative behavior is a good strategy

Most managers don’t know how long they will be competing with their rivals

In a repeated game, prisoner’s dilemma can have cooperative outcome

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 don’t have them

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 don’t have them

Oligopolistic Cooperation in 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

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

Oligopolistic Cooperation in 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

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

Oligopolistic Cooperation in 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

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

Oligopolistic Cooperation in 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

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

Sequential Games Players move in turn, responding to each other’s actions and reactions Ex: Stackelberg model (ch. 12) Responding to a competitor’s ad campaign Entry decisions Responding to regulatory policy

Players move in turn, responding to each other’s actions and reactions

Ex: Stackelberg model (ch. 12)

Responding to a competitor’s ad campaign

Entry decisions

Responding to regulatory policy

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

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

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

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

Modified Product Choice Problem Firm 1 Crispy Sweet Crispy Sweet Firm 2 -5, -5 10, 20 -5, -5 20, 10

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

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

Product Choice Game in Extensive Form Crispy Sweet Crispy Sweet -5, -5 10, 20 20, 10 -5, -5 Firm 1 Crispy Sweet Firm 2 Firm 2

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 firm’s mover advantage by revising the Stackelberg model and comparing to Cournot

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 firm’s mover advantage by revising the Stackelberg model and comparing to Cournot

First Mover Advantage Assume: Duopoly

Assume: Duopoly

First Mover Advantage Duopoly

Duopoly

Choosing Output Firm 1 7.5 Firm 2 10 15 7.5 10 15 112.50, 112.50 56.25, 112.50 0, 0 112.50, 56.25 125, 93.75 50, 75 93.75, 125 75, 50 100, 100

Choosing Output This payoff matrix illustrates various outcomes Move together, both produce 10 If Firm 1 moves first (Q=15), best Firm 2 can do is 7.5 Firm 1 7.5 Firm 2 112.50, 112.50 56.25, 112.50 0, 0 112.50, 56.25 125, 93.75 50, 75 93.75, 125 75, 50 100, 100 10 15 7.5 10 15

This payoff matrix illustrates various outcomes

Move together, both produce 10

If Firm 1 moves first (Q=15), best Firm 2 can do is 7.5

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

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

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

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

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

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

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 other’s 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

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 other’s 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

Pricing of Computers and Word Processors Firm 1 High Price Low Price High Price Low Price Firm 2 100, 80 80, 100 10, 20 20, 0

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

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

Production Choice Problem Far Out Engines Small cars Big cars Small engines Big engines Race Car Motors 3, 6 3, 0 8, 3 1, 1

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?

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?

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

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

Modified Production Choice Problem Far Out Engines Small cars Big cars Small engines Big engines Race Car Motors 0, 6 0, 0 8, 3 1, 1

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 don’t know about and lose sales

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 don’t know about and lose sales

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 don’t always make profit maximizing decisions A party thought to be crazy can lead to a significant advantage

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 don’t always make profit maximizing decisions

A party thought to be crazy can lead to a significant advantage

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

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

Bargaining Strategy Firm 1 Produce A Produce B Produce A Produce B Firm 2 40, 5 50, 50 5, 45 60, 40

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 Firm 1 Produce A Produce B Produce A Produce B Firm 2 40, 5 50, 50 5, 45 60, 40

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

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

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

Bargaining Strategy Firm 1 Work alone Enter consortium Work alone Enter consortium Firm 2 10, 10 10, 20 40, 40 20, 10

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 2’s best interest is to produce A with Firm 1 producing B Firm 1’s profit increases from 50 to 60

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 2’s best interest is to produce A with Firm 1 producing B

Firm 1’s profit increases from 50 to 60

Bargaining Strategy Strategic moves can be used in bargaining Combining issues in bargaining can benefit one side at other’s expense

Strategic moves can be used in bargaining

Combining issues in bargaining can benefit one side at other’s expense

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

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

The Discount Store Preemption Game Wal-Mart Enter Don’t enter Enter Don’t enter Company X -10, -10 20, 0 0, 0 0, 20

The Discount Store Preemption Game Two Nash equilibrium Low left Upper right Must be preemptive to win Wal-Mart Enter Don’t enter Enter Don’t enter Company X -10, -10 20, 0 0, 0 0, 20

Two Nash equilibrium

Low left

Upper right

Must be preemptive to win

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

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

Entry Possibilities Incumbent (I) Enter Stay out High price (accommodation) Low Price (warfare) Potential Entrant (X) ($80 fixed costs) 100, 20 200, 0 130, 0 70, -10

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

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

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

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

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

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

Entry Deterrence Incumbent (I) Enter Stay out High price (accommodation) Low price (warfare) Potential Entrant (X) 50, 20 150, 0 130, 0 70, -10

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

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

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

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

Development of a New Aircraft Boeing Produce Don’t produce Airbus Produce Don’t produce -10, -10 100, 0 0, 0 0, 120

Development of a New Aircraft Boeing has head start Boeing will produce Airbus will not produce Boeing Produce Don’t produce Airbus -10, -10 100, 0 0, 0 0, 120 Produce Don’t produce

Boeing has head start

Boeing will produce

Airbus will not produce

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

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

Development of an Aircraft After European Subsidy Boeing Produce Don’t produce Airbus Produce Don’t produce -10, 10 100, 0 0, 0 0, 120

Development of an Aircraft After European Subsidy Airbus will produce Boeing will not produce Boeing Produce Don’t produce Airbus Produce Don’t produce -10, 10 100, 0 0, 0 0, 120

Airbus will produce

Boeing will not produce

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 R&D

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 R&D

Competing Through R & D P&G R&D No R&D R&D No R&D Kimberly-Clark 40, 20 80, -20 60, 40 -20, 60

Competing Through R & D Both spend on R&D Dominant strategy Why not cooperate? Strengthening Bargaining Power Credibility Reducing flexibility P&G R&D No R&D R&D No R&D Kimberly-Clark 40, 20 80, -20 60, 40 -20, 60

Both spend on R&D

Dominant strategy

Why not cooperate?

Strengthening Bargaining Power

Credibility

Reducing flexibility

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

Markets in which products are bought and sold through formal bidding processes

Encourages competition that increases seller’s revenue

Low cost of transactions

Useful for unique items or those with fluctuating value

Tokyo fish market

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

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

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

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

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

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

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

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

Price-Value Auctions Each bidder must choose bidding strategy Payoff for winning is reservation price minus price paid Payoff for losing is zero

Each bidder must choose bidding strategy

Payoff for winning is reservation price minus price paid

Payoff for losing is zero

Private Value Auction English oral auction and second–price 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

English oral auction and second–price 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

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 bidder’s reservation price Both yield the same revenue

English auction

Continue bidding until second person is unwilling to make bid

Sealed-bid auction

Winning bid approximately equal to the second highest bidder’s reservation price

Both yield the same revenue

Common Value Auctions Winner’s 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

Winner’s 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

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 winner’s curse

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 winner’s curse

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

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

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

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

Bidding and Collusion Examples Collusion among baseball owners to limit their bidding for free agent players in the 1980’s Two of the world’s most successful auction houses were found guilty of agreeing to fix prices of commissions Sotheby’s and Christie’s

Examples

Collusion among baseball owners to limit their bidding for free agent players in the 1980’s

Two of the world’s most successful auction houses were found guilty of agreeing to fix prices of commissions

Sotheby’s and Christie’s

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

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

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

eBay auctions are somewhat different from types discussed

A few caveats:

No quality control function

Poor seller feedback

Bid manipulation may occur