game theory
DESCRIPTION
GAME THEORYAbhishek Shukla MBA(IT) IIITASurvivor Immunity Challenge There are 21 flags Players alternate removing 1, 2, or 3 flags The player to take the last flag winsWhat is Game Theory? Game theory is the branch of decision theory concerned with interdependent decisions.Strategic interaction: When actions of a player influence payoffs to other playersWhere can we use GT? Any situation that requires us to anticipate our rival¶s response to our action is a potential contexTRANSCRIPT
GAME THEORY
Abhishek Shukla
MBA(IT)
IIITA
Survivor Immunity Challenge
There are 21 flags Players alternate removing 1, 2, or 3 flags The player to take the last flag wins
What is Game Theory?
Game theory is the branch of decision theory concerned with interdependent decisions.
Strategic interaction: When actions of a player influence payoffs to other players
Where can we use GT?
Any situation that requires us to anticipate our rival’s response to our action is a potential context for GT.– Games: Checkers, poker, chess, tennis, soccer etc.– Economics: Industrial Organization, Micro/Macro/
International/Labor/Natural resource Economics, and Public Finance
– Political science: war/peace – Law: Designing laws that work– Biology: animal behavior, evolution– Information systems: System competition/evolution
Where can we use GT? (cont.)
Business:– Games against rival firms:
• Pricing, advertising, marketing, auctions, R&D, joint ventures, investment, location, quality, take over etc.
– Games against other players• Employee/employer, managers/stockholders• Supplier/buyer, producer/distributor,
firm/government
Why Do Economists Study Games?
Games are a convenient way in which to model strategic interactions among economic agents.
Many economic issues involve strategic interaction.
Behaviour in imperfectly competitive markets,
e.g. Coca-Cola versus Pepsi. Behaviour in auctions, e.g. when to bid in
dynamic internet auctions. Behaviour in economic negotiations, e.g. trade.
How to use GT
Explanation: What is the game to be played?
Prediction: What outcome will prevail? Advice or prescription: Which strategies
are likely to yield good results in which situations?
Rules, Strategies, Payoffs, and Equilibrium
Economic situations are treated as games.The rules of the game state who can do
what, and when they can do it.
A player's strategy is a plan for actions in each possible situation in the game.
Rules, Strategies, Payoffs, and Equilibrium
A player's payoff is the amount that the player wins or loses in a particular situation in a game.
A players has a dominant strategy if that player's best strategy does not depend on what other players do.
Prisoners’ Dilemma
Two suspects are caught and put in different rooms (no communication). They are offered the following deal:– If both of you confess, you will both get 5 years in
prison (-5 payoff)– If one of you confesses whereas the other does not
confess, you will get 0 (0 payoff) and 10 (-10 payoff) years in prison respectively.
– If neither of you confess, you both will get 2 years in prison (-2 payoff)
Easy to Read Format of Prisoner’s Dilemma
Prisoner 2P
riso
ner
1
Confess Don’t Confess
Confess -5, -5 0, -10
Don’t Confess
-10, 0 -2, -2
Solution of Prisoners’ DilemmaDominant Strategy Equilibrium
Confess Don’t Confess
Confess -5, -5 0, -10
Don’t Confess -10, 0 -2, -2
Prisoner 2P
riso
ner
1
Nash Equilibrium
– In equilibrium neither player has an incentive to deviate from his/her strategy, given the equilibrium strategies of rival players.
– Neither player can unilaterally change his/her strategy and increase his/her payoff, given the strategies of other players.
NE of Prisoners’ Dilemma
The strategy profile {confess, confess} is the unique pure strategy NE of the game.
In equilibrium both players get a payoff of –5.
Inefficient equilibrium; (don’t confess, don’t confess) yields higher payoffs for both.
An Example: Advertising
The prisoner's dilemma applies to advertising.
All firms advertising tends to equalize the effects.
Everyone would gain if no one advertised.
Simultaneous v. Sequential Move Games
Games where players choose actions simultaneously are simultaneous move games.
Examples: Prisoners' Dilemma, Sealed-Bid Auctions. Must anticipate what your opponent will do right now,
recognizing that your opponent is doing the same. Games where players choose actions in a particular
sequence are sequential move games.
Examples: Chess, Bargaining/Negotiations. Must look ahead in order to know what action to choose
now. Many sequential move games have deadlines/ time limits
on moves.
A Sequential GameNew Firm Chooses
New Firm Enters New Firm Does Not Enter
Monopoly gets $3, New firm
gets $2
High Price Low Price
Monopoly Chooses
Monopoly gets $5, New firm
gets $0
Monopoly gets $2, New firm
gets $0
Monopoly Chooses
Monopoly gets $0, New firm
gets –$1
High Price Low Price
($ millions)
Payoffs in a Sequential Game of Entry
New Firm
Enter Do Not Enter
Monopoly HighPrice
Monopoly gets $3New firm gets $2
Monopoly gets $5New firm gets $0
LowPrice
Monopoly gets $0New firm gets –$1
Monopoly gets $2New firm gets $0
Decision Tree for the Coca Cola Company
If Pepsi Charges theMonopoly Price
If Pepsi Charges theLow Price
Coke
$3 million
$2 million
$8 million
$6 million
Coke
Monopoly Price
Low Price Low Price
Monopoly Price
BestStrategy Best
Strategy
Decision Tree for the United States
If Japan Does NotImpose a Tariff
If JapanImposes a Tariff
UnitedStates
$5 million
$4 million
$9 million
$8 million
UnitedStates
Free Trade
Tariff Tariff
Free Trade