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