Game theory

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’ Dilemma
Two 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.

Confess Don't Confess
Confess (5, 5) (0, 10)
Don't Confess (10, 0) (1, 1)
Individual B
Individual A
Payoff Matrix (negative values)

Confess Don't Confess
Confess (5, 5) (0, 10)
Don't Confess (10, 0) (1, 1)
Individual B
Individual A
Dominant Strategy
Both Individuals Confess
(Nash Equilibrium)

Game Theory
Advertise Don't Advertise
Advertise (4, 3) (5, 1)
Don't Advertise (2, 5) (3, 2)
Firm B
Firm A
Advertising Example

Game Theory
Advertise (4, 3) (5, 1)
Firm B
Firm A
Firm B chooses to advertise – options for Firm A?

Game Theory
Advertise (4, 3) (5, 1)
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 (4, 3) (5, 1)
Firm B
Firm A
Firm B chooses not to advertise – options for Firm A?

Game Theory
Advertise (4, 3) (5, 1)
Firm B
Firm A
not to advertise?
the payoff is 3. Again, the optimal strategy is to advertise.

Game Theory
Advertise (4, 3) (5, 1)
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 (4, 3) (5, 1)
Firm B
Firm A
Firm A chooses to advertise – options for Firm B?

Game Theory
Advertise (4, 3) (5, 1)
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,

Game Theory
Advertise (4, 3) (5, 1)
Firm B
Firm A
Firm A chooses not to advertise – options for firm B?

Game Theory
Advertise (4, 3) (5, 1)
Firm B
Firm A
not to advertise?

Game Theory
Advertise (4, 3) (5, 1)
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 (4, 3) (5, 1)
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 (4, 3) (5, 1)
Firm B
Firm A
Game Theory
A Second Advertising Example

Game Theory
to advertise?
Advertise (4, 3) (5, 1)
Firm B
Firm A

Game Theory
not to advertise?
Advertise (4, 3) (5, 1)
Firm B
Firm A

Game Theory
not to advertise?
the payoff is 6. In this case, the optimal strategy is not to
advertise.
Advertise (4, 3) (5, 1)
Firm B
Firm A

Advertise (4, 3) (5, 1)
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
to advertise?
Advertise (4, 3) (5, 1)
Firm B
Firm A

Game Theory
not to advertise?
Advertise (4, 3) (5, 1)
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 (4, 3) (5, 1)
Firm B
Firm A

Game Theory
Advertise (4, 3) (5, 1)
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 Price
Low Price (2, 2) (5, 1)
High Price (1, 5) (3, 3)
Firm B
Firm A
Application: Price Competition

Low Price High Price
Low Price (2, 2) (5, 1)
High Price (1, 5) (3, 3)
Firm B
Firm A
Application: Price Competition
Dominant Strategy: Low Price

Advertise (2, 2) (5, 1)
Firm B
Firm A
Application: Nonprice Competition

Application: Nonprice Competition
Dominant Strategy: Advertise
Advertise (2, 2) (5, 1)
Firm B
Firm A

Cheat Don't Cheat
Cheat (2, 2) (5, 1)
Don't Cheat (1, 5) (3, 3)
Firm B
Firm A
Application: Cartel Cheating

Cheat Don't Cheat
Cheat (2, 2) (5, 1)
Don't Cheat (1, 5) (3, 3)
Firm B
Firm A
Application: Cartel Cheating
Dominant Strategy: Cheat

Games of Particular
Relevance 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 Particular
• 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 Particular
• 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

Games of Particular
• 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 Particular
• 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?

Game theory

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Game theory