Market Structures

Oligopoly Market & Game Theory

Game Theory• Optimization has two shortcomings when applied to actual

business situations– Assumes factors such as reaction of competitors or

tastes and preferences of consumers remain constant.– Managers sometimes make decisions when other

parties have more information about market conditions.• Game theory is concerned with “how individuals make

decisions when they are aware that their actions affect each other and when each individual takes this into account.”

• Types of games– Zero-Sum or Non-Zero-Sum– Cooperative or Non-Cooperative– Two-Person or N-Person

• All solutions involve an equilibrium condition.

Strategic Behavior• Game Theory includes:

– Players(decision makers/managers)– Strategies(choices to change price, develop new

product,undertake new advt. campaign,build new capacity etc which affect the sales and profit of rivals)

– Payoff matrix(outcome or consequence in terms of profit/loss)

• Nash Equilibrium– Each player chooses a strategy that is optimal

given the strategy of the other player– A strategy is dominant if it is always optimal

Prisoners’ DilemmaTwo suspects are arrested for armed robbery. They are immediately separated. If convicted, they will get a term of 10 years in prison. However, the evidence is not sufficient to convict them of more than the crime of possessing stolen goods, which carries a sentence of only 1 year.

The suspects are told the following: If you confess and your accomplice does not, you will go free. If you do not confess and your accomplice does, you will get 10 years in prison. If you both confess, you will both get 5 years in prison.

Prisoners’ Dilemma

Confess Don't ConfessConfess (5, 5) (0, 10)

Don't Confess (10, 0) (1, 1)

Individual B

Individual A

Payoff Matrix (negative values)

Prisoners’ Dilemma

Confess Don't ConfessConfess (5, 5) (0, 10)

Don't Confess (10, 0) (1, 1)

Individual B

Individual A

Dominant StrategyBoth Individuals Confess

(Nash Equilibrium)

Game Theory

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (3, 2)

Firm B

Firm A

Advertising Example

Game Theory

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (3, 2)

Firm B

Firm A

Firm B chooses to advertise – options for Firm A?

Game Theory

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (3, 2)

Firm B

Firm A

What is the optimal strategy for Firm A if Firm B chooses to advertise?

If Firm A chooses to advertise, the payoff is 4. Otherwise, the payoff is 2. The optimal strategy is to advertise.

Game Theory

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (3, 2)

Firm B

Firm A

Firm B chooses not to advertise – options for Firm A?

Game Theory

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (3, 2)

Firm B

Firm A

What is the optimal strategy for Firm A if Firm B chooses not to advertise?

If Firm A chooses to advertise, the payoff is 5. Otherwise, the payoff is 3. Again, the optimal strategy is to advertise.

Game Theory

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (3, 2)

Firm B

Firm A

Regardless of what Firm B decides to do, the optimal strategy for Firm A is to advertise. The dominant strategy for Firm A is to advertise.

Game Theory

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (3, 2)

Firm B

Firm A

Firm A chooses to advertise – options for Firm B?

Game Theory

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (3, 2)

Firm B

Firm A

What is the optimal strategy for Firm B if Firm A chooses to advertise?

If Firm B chooses to advertise, the payoff is 3. Otherwise, the payoff is 1. The optimal strategy is to advertise.

Game Theory

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (3, 2)

Firm B

Firm A

Firm A chooses not to advertise – options for firm B?

Game Theory

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (3, 2)

Firm B

Firm A

What is the optimal strategy for Firm B if Firm A chooses not to advertise?

If Firm B chooses to advertise, the payoff is 5. Otherwise, the payoff is 2. Again, the optimal strategy is to advertise.

Game Theory

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (3, 2)

Firm B

Firm A

Regardless of what Firm A decides to do, the optimal strategy for Firm B is to advertise. The dominant strategy for Firm B is to advertise.

Game Theory

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (3, 2)

Firm B

Firm A

The dominant strategy for Firm A is to advertise and the dominant strategy for Firm B is to advertise. The Nash equilibrium is for both firms to advertise.

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (6, 2)

Firm B

Firm A

Game Theory

A Second Advertising Example

Game Theory

What is the optimal strategy for Firm A if Firm B chooses to advertise?

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (6, 2)

Firm B

Firm A

Game Theory

What is the optimal strategy for Firm A if Firm B chooses to advertise?

If Firm A chooses to advertise, the payoff is 4. Otherwise, the payoff is 2. The optimal strategy is to advertise.

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (6, 2)

Firm B

Firm A

Game Theory

What is the optimal strategy for Firm A if Firm B chooses not to advertise?

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (6, 2)

Firm B

Firm A

Game Theory

What is the optimal strategy for Firm A if Firm B chooses not to advertise?

If Firm A chooses to advertise, the payoff is 5. Otherwise, the payoff is 6. In this case, the optimal strategy is not to advertise.

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (6, 2)

Firm B

Firm A

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (6, 2)

Firm B

Firm A

Game Theory

The optimal strategy for Firm A depends on which strategy is chosen by Firms B. Firm A does not have a dominant strategy.

Game Theory

What is the optimal strategy for Firm B if Firm A chooses to advertise?

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (6, 2)

Firm B

Firm A

Game Theory

What is the optimal strategy for Firm B if Firm A chooses to advertise?

If Firm B chooses to advertise, the payoff is 3. Otherwise, the payoff is 1. The optimal strategy is to advertise.

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (6, 2)

Firm B

Firm A

Game Theory

What is the optimal strategy for Firm B if Firm A chooses not to advertise?

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (6, 2)

Firm B

Firm A

Game Theory

What is the optimal strategy for Firm B if Firm A chooses not to advertise?

If Firm B chooses to advertise, the payoff is 5. Otherwise, the payoff is 2. Again, the optimal strategy is to advertise.

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (6, 2)

Firm B

Firm A

Game Theory

Regardless of what Firm A decides to do, the optimal strategy for Firm B is to advertise. The dominant strategy for Firm B is to advertise.

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (6, 2)

Firm B

Firm A

Game Theory

Advertise Don't AdvertiseAdvertise (4, 3) (5, 1)

Don't Advertise (2, 5) (3, 2)

Firm B

Firm A

The dominant strategy for Firm B is to advertise. If Firm B chooses to advertise, then the optimal strategy for Firm A is to advertise. The Nash equilibrium is for both firms to advertise.

Low Price High PriceLow Price (2, 2) (5, 1)High Price (1, 5) (3, 3)

Firm B

Firm A

Prisoners’ Dilemma

Application: Price Competition

Low Price High PriceLow Price (2, 2) (5, 1)High Price (1, 5) (3, 3)

Firm B

Firm A

Prisoners’ Dilemma

Application: Price Competition

Dominant Strategy: Low Price

Advertise Don't AdvertiseAdvertise (2, 2) (5, 1)

Don't Advertise (1, 5) (3, 3)

Firm B

Firm A

Prisoners’ Dilemma

Application: Nonprice Competition

Prisoners’ Dilemma

Application: Nonprice Competition

Dominant Strategy: Advertise

Advertise Don't AdvertiseAdvertise (2, 2) (5, 1)

Don't Advertise (1, 5) (3, 3)

Firm B

Firm A

Cheat Don't CheatCheat (2, 2) (5, 1)

Don't Cheat (1, 5) (3, 3)

Firm B

Firm A

Prisoners’ Dilemma

Application: Cartel Cheating

Cheat Don't CheatCheat (2, 2) (5, 1)

Don't Cheat (1, 5) (3, 3)

Firm B

Firm A

Prisoners’ Dilemma

Application: Cartel Cheating

Dominant Strategy: Cheat

Games of ParticularRelevance in Economics

• Beach Kiosk Game– Two-Person, Zero-Sum, Non-cooperative– Example: two companies provide snacks and

sunscreen on a beach.• Beachgoers spread themselves out evenly along

the beach.• Both companies ultimately locate at the midpoint of

the beach, otherwise the other company has an advantage (closer to more beachgoers)

• Real life example: location of gas stations

Games of ParticularRelevance in Economics

• Repeated Game: game is played repeatedly over a period of time.

• In a repeated game, equilibria that are not stable may become stable due to the threat of retaliation.

Games of ParticularRelevance in Economics

• Repeated Game: game is played many times, and equilibria that are not stable may become stable due to the threat of retaliation.

• Assume (High, High) equilibrium reached and both firms start off charging the high price.

• In the next period, if one firm cheats (charges low price), it receives 600 in that period.

• Other firm will change to low prices in the next period to “retaliate” and both will end up at (Low, Low) equilibrium.

• Thus, incentive exists not to “cheat” in a repeated game and (High, High) is a viable equilibrium, though it is not in a single-period game.

• If number of periods are fixed, both firms will have incentive to cheat (charge low price) in the last period due to lack of threat of retaliation, which will then allow them to cheat in all periods.

Games of ParticularRelevance in Economics

• Simultaneous games are games in which players make their strategy choices at the same time.

• Sequential games are games in which players make their decisions sequentially.

• In sequential games, the first mover may have an advantage.

Games of ParticularRelevance in Economics

• Consider the following payoff matrix in which firms choose their capacity, either high or low.

• Suppose firm C has the ability to move first.– C would choose Low, then D would choose High.

Game Theory and Auctions

• Non-cooperative, non-zero-sum game• Seller wants to sell at highest price, buyer wants to

buy at lowest price.• Dutch Auction

– All product sold at the highest price that clears the market– Each buyer describes the quantity demanded and price

to pay– Starting at highest price, sum quantity demanded up to

the quantity available. The associated price for the last quantity added is the price for all products.

• In an auction with a time limit, every player has a dominant strategy to bid as late as possible.

Extensions of Game Theory

• Tit-For-Tat Strategy– Stable set of players– Small number of players– Easy detection of cheating– Stable demand and cost conditions– Game repeated a large and uncertain

number of times

Strategy and Game Theory

• Fundamental aspects of game theory– Players are interdependent– Uncertainty: other players’ actions are not entirely predictable

• PARTS: paradigm for studying a situation, predicting players’ actions, making strategic decisions– Players: Who are players and what are their goals?– Added Value: What do the different players contribute to the pie?– Rules: What is the form of competition? Time structure of the

game?– Tactics: What options are open to the players? Commitments?

Incentives?– Scope: What are the boundaries of the game?