Economic
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LectureNotesTopic6-StrategicGames.pptxLecture Notes
Strategic Games
Objectives
You should understand when game theory is used
You should understand dominant strategy and Nash equilibrium
You should understand the Prisoner’s Dilemma situation
You should be able to determine the payoff matrix and the optimal strategy for a firm given the payout matrix
From Abstraction to Reality, Sort of
So far, we have assumed that firms (and people) make decisions in isolation
Solitary firms calmly choosing a price and output that maximizes profits
We did not consider the reactions of rival firms when making such decisions regarding price, output and advertising
Depending on how competitors react, a firm’s sales and profitability might be more negatively affected
But, you do not know with certainty how competitors will react
However, many firms make predictions or conjectures about their competitor’s reactions.
Competitive Analysis
As an entrepreneur, as a manager in a firm:
You must learn how to anticipate the actions and reactions of other firms in your industry
Strategic Behavior: actions taken by firms (or threaten to take) in order to plan for and react to the actions of competitor
Interdependence of Firms and Strategic Behavior
PRINCIPLE: Interdependence of firms’ profits, arises when the number of firms is small enough so that every firm’s pricing and output decision affects the demand and marginal revenues of every other firm
Number of firms are small (oligopoly)
Impact of decisions by 1 firm significantly affect the profits of the other firms
Each firm makes a decision on price, output and advertising in order to maximize profit – after considering all of the possible reactions of its competitors
This makes decision making much more complicated and uncertain
You need to anticipate the decision of every other firm in your industry
You need to think “strategically”
How do you go about making strategic decisions?
No set of rules to follow
Art of making strategic decisions is learned from experience
Tool for thinking about strategic decision making: Game Theory
Useful guideline on how to make strategic decisions involving interdependence
Can only provide you with general principles or guidelines to follow in strategic situations
Game Theory will not help you “win” or make greater profits than competitors
Game Theory: Introduction
Each firm is like a player in a game, such as chess – trying to decide the best move given what you expect your opponent’s next moves are.
In a game, such as tic-tac-toe, checkers, chess, or Wheel of Fortune
the players are individuals who make decisions
Each player may have a planned moves: strategy in order to win the game
Each player needs to make a move considering the reaction of the other player(s)
At the end of the game, there is some sort of payoff
In a game involving firms:
The firm (or the firm’s managers) are the PLAYERS of the game
The planned decisions or STRATEGIES are how much to produce, how to price, how to differentiate the product, how much to advertise, etc.
The PAYOFF to the firms are usually the profits or losses that result from the strategies
The payoffs not only depend upon the firm’s strategy, but also on the strategies used by the other firms in the industry
PAYOFF MATRIX: usually the profits or losses of the firm as a result of the firm’s strategies and the rivals’ response to that strategy
Different Types of Games
Simultaneous-Move vs. Sequential Move Games
Simultaneous Move: each firm makes a move without knowledge of the other firm’s decisions
Ex. Dueling, rock-scissors-paper
Sequential Move: One firm makes a move after observing the other firm’s move
Ex: chess, checkers, tic-tac-toe, Wheel of Fortune
One-Shot vs. Repeated Games
One shot: game is only played once
Repeated game: game is played more than once
Simultaneous Move Game: An Example
Object of the firm is to maximize its PAYOFF (profits) by making the best decision (choosing the best STRATEGY)
Simple General Example:
There are 2 firms A and B
Each firm has 2 possible strategies (representing virtually any decision)
Firm A can choose UP or DOWN
Firm B can choose LEFT or Right
Payoffs to these strategies is given by the payoff table:
First entry refers to Firm A (always the player on the left)
Second entry refers to Firm B (always the player on the top)
If A chooses UP and B chooses LEFT, A’s profits are 10 and B’s profits are 20
If A chooses UP and B chooses RIGHT, A’s profits are 15 and B’s profits are 8
Prisoner’s Dilemma
Suppose that a serious crime, auto theft, is committed by 2 suspects, Bill and Jane
They are apprehended and questioned by police.
Suspects know that police do not have enough evidence to make the charges stick unless one of them confesses.
If neither suspect confesses, the police can only convict the suspects on much less serious charges, say vandalism.
Police offer: (1) if one suspect confesses to the crime and testifies in court against the other, one who confesses will receive a 1 year sentence. The one who does not confess will get 12 years
(2) if both confess, each gets a 6 year sentence
(3) if neither confess, both receive 2 year sentences
Prisoner’s Dilemma (continued)
Payoff table:
Both prisoners know the payoff table and know that the other prisoner knows the payoff table
Since decisions are made simultaneously, each prisoner does not know what the other has decided to do.
Both Jane and Bill will be induced to confess
Confessing is always better than not confessing for Bill, no matter what Jane does
Confessing is always better than not confessing for Jane, no matter what Bill does
Simultaneous Move One-Shot Games: Optimal Strategy
Optimal Strategy in a Simultaneous Move One-Shot Game: Part 1
Choose the DOMINANT STRATEGY (if one exists): produces the best outcome no matter what the other player (firm) does
DOMINANT STRATEGY: a strategy that results in the highest payoff no matter what the action of the opponent
And assume that your competitor will play its dominant strategy
In the prisoner’s dilemma situation, the dominant strategy is to confess for each prisoner
For Bill, the dominant strategy is to confess
If Jane does not confess, than Bill will get a lighter sentence if he does confess
If Jane does confess, than Bill will get a lighter sentence if he does confess
For Jane, the dominant strategy is to confess
If Bill does not confess, than Jane will get a lighter sentence if he does confess
If Bill does confess, than Jane will get a lighter sentence if he does confess
When both players have dominant strategies, it is relatively easy to predict competitors actions
Note that when both players have dominant strategies, this is an equilibrium: there is no reason for players to change their strategies
Why is this a Prisoner’s Dilemma?
Both prisoners played their dominant strategy: the strategy that is best for them no matter what the other prisoner does
Both prisoners end up with 6 years in prison by confessing
But they are worse off than if they had cooperated by not confessing
If both of them had agreed to not confess both of them could have gotten lighter sentences (2 year sentences)
Prisoner’s Dilemma arises when the players can earn a higher payoff than they can when they choose to follow their dominant strategies.
Cooperation is possible but is not stable in a one-shot game.
Since there are no future consequences from cheating, both players are expected to cheat, which makes cheating the best response for both players
Decisions with One Dominant Strategy
Optimal Strategy in a Simultaneous Move One-Shot Game: Part 2
If you do not have a dominant strategy, look at the game from your rivals’ perspective. If your rival has a dominant strategy, anticipate that he or she will play it and choose the your own best alternative.
2 gasoline stations are located side by side. Their products are somewhat differentiated but competition is primarily by price.
For illustrative purposes, suppose each gasoline station can charge only two prices: High Price and Low Price
Profits depend upon which price each of them choose
Decisions with One Dominant Strategy
Payoff Table:
Gasoline Station B does have a dominant strategy:
If Station “A” chooses high price, Station “B” should choose a Low Price
If Station “A” chooses low price, Station “B” should choose a Low Price
Gasoline Station A does NOT have a dominant strategy
If “B” chooses high price, Station “A” should choose a Low Price
If “B” chooses low price, Station “A” should choose a High Price
However, Station A knows that Station B will choose its dominant strategy, “Low Price”
Knowing that Station B will choose Low Price, Station A should choose its best strategy, which is a High Price.
Simultaneous Move One-Shot Games: Nash Equilibrium
Nash Equilibrium: Given the strategy chosen by the other player, each player chooses his or her optimal strategy
Given the strategies of other players, no player can improve his or her payoff by changes his or her own strategy
Every player is doing the best he or she can given what the other players are doing
Note that we call it an “Equilibrium” because there is no incentive for either player to change strategies
Dominant Strategy Equilibrium: both firms are making the best decision no matter what the competitor does
In a Nash Equilibrium, both firms are making the best decision given the decision they BELIEVE their rivals will make.
Firms believe that their rivals will choose their dominant strategy.
All dominant strategy equilibria are Nash Equilibria
But Nash equilibrium can occur without dominant strategies
Application of One Shot Games
Pricing Decisions
Consider the gasoline station example provided earlier with a different payoff
If both charge the same price, both stations get some customers
If each charges different prices, the firm with the lower price gets most if not all of the customers
Higher prices mean higher profits, lower prices mean lower profits
The payoff matrix, in terms of profits, might look like this:
Application of One Shot Games: Pricing
Nash Equilibrium strategies are for each firm to charge the Low Price!
If Station B charges a High Price, Station A ‘s best strategy is to charge a Low Price
Is Station B charges a Low Price, Station A’s best strategy is to charge a Low Price
Similar Arguments hold from Station B’s perspective
Charging a Low Price is the Dominant Strategy for both Stations
Station A is always better off charging Low Price
Station B is always better off charging Low Price
However, profits are clearly higher if both Stations adopted a High Price strategy
Example of Prisoner’s Dilemma: Nash equilibrium outcome is inferior (from the firm’s perspective)
to the situation when both firms could “agree” to charge High Price
Agreeing on a high price or Collusion is illegal in the US
Suppose the game could be repeated – it was not just one move:
If firms colluded an agreed upon a high price, there is an incentive for each firm to lower the price
Need for constant monitoring of rivals to make sure that they live up to the agreement
Application of One Shot Games: Advertising
2. Advertising and Product Quality
Firms frequently use advertising and/or changes in product quality to increase the demand for their products
In most cases, advertising increases the demand for a firm’s products by taking customers away from other firms in the industry.
Example: breakfast cereal industry
Each firm is not trying to induce consumers to eat cereal for lunch or dinner
Each firm is inducing customers to switch to its brand from another brand
This can lead to each firm trying to “cancel out” the effects of the other firm’s advertising
Result: high levels of advertising, no change in industry or firm demand and low profits
Application of One Shot Games: Advertising Example
Suppose you and your main rival know that your products will be obsolete at the end of the year and must simultaneously determine how much to advertise. Advertising does not increase total industry demand but instead induce customers to switch among the products of different firms.
If both you and your rival advertise, each firm will earn $4M in profits
If neither of you advertise, each firm will earn $10M in profits
If one of you advertises and the other one does not advertise, the firm that advertises will earn $20M and the firm that does not advertise will earn $1M in profits.
Should you advertise or not advertise?
How much do you expect to earn?
Application of One Shot Games: Advertising Example
Dominant strategy for each firm is to advertise
Nash equilibrium is for each firm to advertise
Prisoner’s Dilemma situation: firms will be better off if they collude and agree not to advertise
You can expect to earn $4M
Application of One Shot Games: Coordinating Decisions
3. Coordinating Decisions
Analysis so far has looked at competing objectives: one firm can gain only at the expense of another
Not all games have this structure………
Imagine a world with 2 competing standards: 90 Volt four prong outlets or 120 volt 2 prong outlets for appliances
If 2 different standards, consumers would need to spend considerable sums on wiring their house – reducing the demand for appliances
So, coordinating among appliance manufacturers to produce one standard will increase the demand for appliances and increase all manufacturers’ profits
Application of One Shot Games: Coordinating Decisions
Coordination Game:
Consider 2 firms in the appliance industry
If each firm produces appliances requiring 120 volts, each firm earns profits of $100
If each firm produces appliances requiring 90 volts, each firm earns profits of $100
If the 2 firms produce appliances with different voltages, each firm earns $0 profits due to the lower demand for appliances
What would you do if you were the manager of Firm A?
Application of One Shot Games: Coordinating Decisions
This game has 2 Nash equilibria:
One to produce 90 volt appliances
One to produce 120 volt appliances
The problem is how the firms will get to one of these equilibria
Both you and Firm B will do better by “coordinating” your decisions
Or the government could set a standard for electrical outlets
Once an agreement is in place to produce 120 volt outlets, there is no incentive to “cheat”
Similar to game of “Battle of Sexes” where husband wants to go to ball game and wife wants to go to ballet (or vice-versa)
Both will be better off by being together than attending the event alone
The 2 equilibria will be if the husband and wife go to the same event. But which one?
Matter of bargaining and staying power
Application of One-Shot Games: Market Entry
4. Market Entry
Suppose Staples and Office Depot are considering a new superstore in a midsize city
Each chain recognizes that demand is sufficient to support only 1 store
If both chains create superstores, both will suffer losses
Application of One-Shot Games: Market Entry (continued)
Neither firm has a dominant strategy
Both firms entering is not an equilibrium
Each firm would be better off by staying out given the strategy of the other firm (entering)
Both firms staying out is not an equilibrium
Each firm would be better off by entering given the strategy of the other firm (staying out)
There are 2 equilibrium:
Office Max entering and Staples staying out
Staples entering and Office Max staying out
Application of One-Shot Games: Market Entry (continued)
But which firm will be the one which enters and which one stays out
The first firm to enter the market will “win”: First Mover Advantage
Once one firm enters, the other firm’s best strategy is to stay out
One firm can claim a first mover advantage not by acting but by making a CREDIBLE commitment to enter the market
Staples must convince its rival of it entry commitment (not just a threat)
Example: a campaign announcing and promoting the new store
: entering into a binding real estate lease
Of course, sometimes both firms enter (sometimes with disastrous results)
Similar to a game of “chicken”
Application of One Shot Games: Employee Monitoring
5. Employee Monitoring
Consider a game between a worker and a manager
The manager has 2 possible actions:
Monitor the worker
Don’t monitor
The worker has 2 possible actions:
Work
Shirk
If the manager monitors while the employee works, the employee “wins” with a payoff of 1 and the manager “loses” with a payoff of -1
If the manger monitors while the employee shirks, the employee loses with a payoff of -1 and the manager wins with a payoff of 1
If the manager does not monitor and the employee works, the employee loses with a payoff of -1 and the manager wins with a payoff of 1
If the manager does not monitor while the employee shirks, the employee wins with a payoff of 1 and the manager loses with a payoff of -1
Application of One Shot Games: Employee Monitoring
There is no Nash Equilibrium:
If manager monitors, the workers best strategy is to work
Given that workers is working, the manager’s best strategy is not to monitor
The manager can improve upon his payoff by changing his/her strategy
If manager doesn’t monitor, the workers best strategy is to shirk
Given that the worker is shirking, the manager’s best strategy is to monitor
Both workers and managers want to keep their actions “secret”
If manager knows that workers are shirking…….
If workers know what the manager is doing…..
In such situations, players find it in their best interests to engage in a mixed or randomized strategy: randomly work sometimes and shirk at other times; randomly monitor sometimes and don’t monitor at other times
Repeated Games
Cooperation is more likely to occur in repeated games, games involving many consecutive moves and countermoves by players.
In a repeated game, firm must weigh the benefits of current actions against the future cost of those actions (think present values)
A decision which brings high profits today may cause extremely low profits in the future
If the interest rate is low, firms may find it in their best interest to collude and charge high prices (unlike the one shot game)
If a player deviates from this strategy and chooses to price low, all other firms will price low in the future in order to wipe out the gains from having deviated from the collusive agreement
Threat of punishment makes cooperation work in repeated games
Prisoner’s Dilemma Repeated Game
Both firms dominant strategy is to price low.
But, they can both be better off by cooperating (colluding) and pricing high – and there is an incentive for each firm to cheat
Firms agree to collude, charge High Price and earn $10 a profit in 1st year.
Firm A decides to cheat, charge Low Price, in 2nd year and earns $50 in profit – an increase of $40
Firm B retaliates by charging Low Price too
Instead of Firm A earning $10 in profit for Years 3 onward, firm A will earn $0 from Years 3 onward
At some point in time, the PV of the loss of $10 from Year 3 onward will be greater than the increase in profits from cheating ($50 - $10)
The lower the interest rate, the greater the number of years it will take for the PV of the loss in profits to overtake the increase in profits from cheating
Cheating is more likely if interest rates are low
Threat of retaliation in the future makes cheating less likely and allows cooperation to work in repeated games
In one shot games, there is no tomorrow and no future negative consequences from cheating once.
Threat of Punishment as a Strategy in Repeated Games
In repeated games, punishment or the threat of punishment itself becomes a strategy
Tit-for-tat strategy: do what your competitor does
cheating triggers punishment in the next decision period
Punishment continues until the cheating stops
Which hopefully triggers a return to cooperation
Tit-for-tat strategies are best way to play a game in a repeated Prisoner’s dilemma situation
Pricing Practices that Facilitate Cooperation (and Discourage “Cheating”)
Price Matching: benefit of cutting prices to steal rival’s customers largely vanishes
Sales Price Guarantees: promising customers who buy an item today that they are entitled to receive any sales prices your firm might offer after, say, 30 days of purchase
Discourage price-cutting by making the price cuts apply to more customers (not only customers today but customers who made purchases within last 30 days)
Public Pricing: give everyone access to your prices, not just potential buyers, including rival sellers.
Makes detection of cheating easier and quicker
Price Leadership: one firm sets its price at a level it believes will maximize total industry profit and all of the other firms follow
Not an explicit agreement among firms
Repeated Games: Application to Product Quality
Desirability of Warranties and Guarantees
Game between consumers and firms:
Consumers want durable, high quality products at low prices
Firms want to maximize profits
Consider the following game:
Repeated Games: Application to Product Quality
In a one shot game, with no prospect for repeat business, firm may have an incentive to sell shoddy products.
If consumer decides to buy, the optimal strategy for the firm is to produce a low quality product
But if firm produces low quality product, the optimal strategy for consumer is not to buy
But if consumer chooses not to buy, it doesn’t pay for firm to produce high quality product
Nash Equilibrium is for firm to produce low quality product and consumer not to buy
The consumer knows not to buy the product because the firm’s optimal strategy is to produce a low quality product (the firm will “take the money and run”)
Repeated Games: Application to Product Quality
Story is different for an infinitely REPEATED game
Consumer has 2 scenarios:
Buy a high quality product and will continue to buy the product in future
Buy a low quality product and will tell all his friends that it is low quality and never buy the product again
Assuming that the interest rate is not too high, the optimal strategy for the firm is to produce a high quality product
By selling low quality product, firm earns $10 instead of $1
Gain from “cheating” is $9
The cost of selling a low quality product is to earn $0 instead of $1 on future sales
If interest rate is low, the one time gain will be more than offset by lost future sales
Repeated Games: Application to Product Quality
Lesson for the Firm with Repeat Purchases
It does not pay to “cheat” customers if the one-time gain is more than offset by lost future sales
If the firm may produce shoddy products inadvertently, this could prove to be disastrous to the firm
Firm may offer guarantees/warranties to assure that product is of high quality
No incentive for consumers to “punish” the firm by spreading news that it sells shoddy merchandise
Lesson for the Customer with Purchases made Infrequently:
The firm has an incentive to provide a shoddy product or shoddy service
Make sure that the firm is reputable, offers warranties/guarantees or your money back
Sequential Games
Players take turns and each player observes what the rival does before having to move
Example:
Potential entrant into a market will make a decision to enter the market (or not)
Incumbent firms will respond to the entry decision by adjusting prices and output to maximize profits
Even though decisions are made at different times, sequential decisions do involve interdependence
Sequential decisions are linked by time:
Best decision firms make today depends upon on how rivals will respond tomorrow
How to Think with Sequential Decisions (Backward Induction)
You must think ahead to anticipate rival’s future reactions
You must jump ahead in time to anticipate your rival’s reaction and then think backwards to the present
Summary: Look ahead to future decisions to reason back to the best current decision
Sequential Decisions: Trees
Instead of using payoff tables to analyze decisions, we will use game trees
A tree is a diagram showing the firm’s decisions as “decision nodes” or branch
Single point “A” depicts the beginning of the game (the first decision)
Numbers at the end of the branches represent the payoffs
A
B
B
Up
Down
10, 15
5, 5
0 ,0
6, 20
Up
Up
Down
Down
Sequential Decisions: Simple Example
A
B
B
Up
Down
10, 15
5, 5
0 ,0
6, 20
Up
Up
Down
Down
Suppose Player B’s strategy is: “Choose down if Player A chooses up, and down if Player A chooses down”
The best strategy for Player A:
If Player A chooses up, she will earn $5 since Player B chooses down
If Player A chooses down, she will earn $6 since Player B chooses down – Player A chooses down
Given that Player A has chosen down, should Player B change his strategy?
No, because by choosing down Player B earns 20 (instead of 0 if choosing up)
Neither player has an incentive to change their strategy: Nash equilibrium with Player A earning $6 and
B earning $20
Sequential Decisions: Simple Example continued
We have found 1 Nash Equilibrium strategy
Player A: down
Player B: down if Player A chooses up and down if Player A chooses down
Is this a reasonable outcome for the game?
Note that the highest payoff for Player A is to choose up when B chooses up
Why didn’t Player A choose Up when Player B chose Up?
Because Player B has “threatened” or made it known that he will choose Down if Player A chooses Up
Does Player A believe that threat? Is it credible?
There is another Nash Equilibrium for this game:
Player B: Choose Up if Player A chooses up and down if Player A chooses down
Player A: best response to this strategy is Up
Player A earns $10 and Player B earns $15
Note that Player A earns more and Player B earns less
But the threat of Player B to Play Down if Player A plays up is not credible:
Player B can earn more ($15) by playing Up than Playing Down ($5)
Since it is not likely that Player B will play down when Player A chooses Up, the more likely Nash Equilibrium is the 2nd one
In order for threats to work, they have to be credible
Sequential Decisions: The Entry Game
Entrant
Incumbent
In
Out
5, 5
0, 10
Fight
Accommodate
A potential entrant is deciding to enter a new market
If he decides not to enter the market, the incumbent continues its existing behavior earning $10M in profits
If the entrant decides to enter the market:
Incumbent fights it by lowering prices, lowering its profits to $1M
Incumbent could accommodate and do nothing, lowering its profits to $5M
-1,1
Sequential Games: The Entry Game
There are 2 Nash Equilibria:
Incumbent threatens to choose “Fight” if Entrant enters
Entrant stays out of the market
Comments: Given that Incumbent Fights, best strategy for Entrant is to stay out of the market (earns $0 instead of -$1M). There is no incentive for either firm to change its strategy
But the threat of the Incumbent is not credible. Incumbent would do better if it accommodates instead of fights (if the potential entrant decides to enter ($5M profit vs. $1M profit)
Incumbent chooses “Accommodate” if Entrant enters
Entrant chooses “Enter”
Comments on Entry Game
Emphasize the importance of a credible commitment
Convincing the entrant of a low price (now and in the future) would stop his/her entry
Ways to Convince:
Lower prices before the firm enters
Making long-term price agreements with customers
Staking the firm’s reputation on low prices
Lowering prices to forestall entry is called “limit pricing”
Other ways to stop entry:
Maintaining excess capacity
High levels of advertising
Saturating the product space by proliferating the number of brands
Making product improvements requiring high levels of R&D
Welcoming government regulation
Sequential Decisions: The Innovation Game
Developer
Rival
Introduce
Don’t Introduce
100, 0
1,1
Clone
Don’t Clone
You are deciding whether to introduce a new product
Your rival has to decide whether to clone the new product
Should you introduce the new product?
Should you introduce the new product if your rival “promised” not to clone?
What would you do if patent law prevented your rival from cloning the product?
-5, 20
Sequential Games: The Innovation Game
If you introduce the product, Rival’s best choice is to clone. Your firm will lose $5M. If you don’t introduce the product, you earn $1M. Your profit maximizing decision is to not introduce the product.
If you believe your rival’s promise, you will earn $100M. But, your rival’s promise is not incredible: your rival would love you to spend money developing the product so he/she could clone it and earn $20M. Since the promise is not credible, think twice!
In this case (assuming patent law is enforceable), you should introduce the new product and earn $100M. This illustrates that the ability to patent a new product often induces firms to introduce products that they would not introduce in the absence of a patent system.
Implications of Game Theory
Try to reduce interdependence of your firms with other firms in the industry
Product Differentiate/Lower Costs
Use Pricing Practices that Encourage Cooperation
In a Prisoner’s Dilemma Situation:
Use Tit-for-Tat strategies
Make sure that rivals can easily understand and interpret your actions
Game Theory: Summary
Managers/Entrepreneurs must make decisions knowing that their actions will affect the profitability of other firms and that these firms will react to that decision
Depending upon how rivals react, this will affect the profitability of your firm
Successful managers must learn how to anticipate the actions and reactions of the firm’s rivals
Making strategic decisions involve “getting into the heads” of rivals to predict their decisions – so you can make better decisions for yourself
Game Theory: Summary
There is no set of rules for a manager to follow in making decisions in such an environment
There is an indispensable tool, game theory, for the way to think about making such decisions
Game theory can only provide you with general principles and guidelines to follow when facing the kinds of strategic decisions that involve interdependence among firms
Always follow your dominant strategy
When your firm does not have a dominant strategy, and other firms do have one, assume that the other firms will choose dominant strategy. Then your firm can choose its own best strategy, knowing that the other firms will choose their dominant strategy.
Make sure that the threats of rival firms are credible.
Make sure that any threats you make to rival firms are credible
Game Theory: Summary
Game Theory cannot teach you how to make such decisions……
These types of decisions are best learned by experience
The foundation of game theory will make it easier for you to learn from experience
Firm B
LeftRight
Firm A
Up
10, 2015, 8
Down
-10, 710, 10
Bill
Don't ConfessConfess
Jane
Don't Confess
2 years, 2 years12 years, 1 year
Confess
1 year, 12 years6 years, 6 years
Gasoline Station B
High PriceLow Price
Gasoline
High Price
$1,000, $1,000$500, $1,200
Station A
Low Price
$1, 200, $300$400, $400
Gasoline Station B
High PriceLow Price
Gasoline
High Price
$1,000, $1,000$200, $1,200
Station A
Low Price
$1, 200, $200$400, $400
FIRM B
AdvertiseDon't Advertise
Advertise(4, 4)(20, 1)
FIRM A
Don't Advertise(1, 20)(10, 10)
FIRM B
120 Volt Outlets90 Volt Outlets
120 Volt Outlets(100, 100)(0, 0)
FIRM A
90 Volt Outlets(0, 0)(100, 100)
Office Depot
Stay OutEnter
Staples
Stay Out(0,0)(0,4)
Enter(4,0)(-4,-4)
Worker
WorkShirk
Manager
Monitor
-1, 11, -1
Don't Monitor
1, -1-1, 1
WORKER
WorkShirk
Monitor(-1, 1)(1, -1)
EMPLOYEE
Don't Monitor(1, -1)(-1, 1)
FIRM B
LowHigh
Low(0, 0)(50, -40)
FIRM A
High(-40, 50)(10, 10)
FIRM
Low Quality ProductHigh Quality Product
Don't Buy(0, 0)(0, -10)
CONSUMER
Buy(-10, 10)(1, 1)
