BA 511 Strategic Games

*Some examples are drawn from Thinking Strategically by

Dixit & Nalebuff

Games in WSJ, Holman Jenkins

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Strategic Games All Around

Situations Bidding-Negotiation;

Auctions Employment: Job Market;

Board-Management; Management-Labor;

Politics/Group Dynamics Pricing, Ad, …

Competition Dating, Marriage Families: Parent-Child,

Spouses, Siblings Games: Poker, Chess,

Risk, …

Behavior Signaling & Filtering Info Altering Perceptions-Beliefs Promises/Threats Changing “Rules” Mixing Actions Incentives for Cooperation Cooperation-Compete

Dilemmas Free-Riding

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• Interdependent Actions & Outcomes • Not Just Playing Against “Market” or “Nature”

Looking Ahead, Reasoning Back

Apollo 1 NASA, North American & Congress From the Earth to the Moon, HBO

Business Unit/Office Politics Entry

Products Markets

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Prisoner’s Dilemma2 suspects interrogated/no contactConfess-Don’t Confess 1 Confess: low/high sentences2 Confess: moderate sentencesNo Confess: low/low sentences Hostage’s Dilemma

Business:◦Price Wars ◦Ad Wars◦Entry Wars

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The Location Games

Battle of the Beach◦ If beachgoers evenly distributed

along beach, where to locate hot dog stand?

Business Examples◦ Fast Food/Restaurants◦ Retail◦ TV Reality Shows◦ Politics

Examples: McDonalds & Burger King; Many retail stores; primary & general election races;Harvard-Stanford MBA “Divide the Cities” and focal points 6

Location Game with Limited InformationDivide the Cities Game

◦Harvard v. Stanford MBA Students◦Cities Worth Points, Monopoly Worth

Points◦Select “in the dark”

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Bargaining GamesGames of Chicken

◦ Don’t Expect Quick Resolution (12th Hour Agreements)◦ “Crazy” Offers Advantages

“Ultimatum Game” Experiments◦ Split pot if 2 parties agree on split; First makes

offer- Second accepts or declines offer ◦ Variations: size of pot; depreciation of pot;

anonymity; repetition; wealth of participants … Money matters but not all that matters Typical outcomes: bigger than 99:1, less

than 50:50 Patience is a virtue Patience is the best signal of patience

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“Strategic Moves”: Game Changers

Credible Threats/Promises/Commitments◦ Cortez Burning His Ships◦ Large Sunk Costs (e.g. ads)

Change Size/Order of Payoffs/Choices◦ “Salami Tactics”◦ Crimea, My Daughter◦ Retailers agents as response◦ Agenda Control, Voting Rules

Change Beliefs◦ Bargaining

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First Mover Advantage?Last Better if info

from observing◦ Sailing◦ NCAA Overtime◦ Innovation

First Better if change beliefs/incentives-payoffs or loyalty◦ Innovation◦ Poker

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Don’t Outsmart Yourself

Dixit & Nalebuff: Jerusalem TaxiJerusalem Taxi Ride

Colts v. Saints 2010 Super Bowl olts-Saints Super Bowl

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Essentials of Strategic Games

Who are Key Decision makers (units)?

What is the Timing of Decisions?

What Information is Available?

What Actions are Possible?

Payoffs to decisions?

Manipulation Possibilities?

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Insight on Solutions “Nash Equilibrium”

Choosing the best when opponent choosing best

◦Sequential Games “Rollback”: Look ahead to last period and

work back

◦Simultaneous Games Iterative: step-by-step analysis of best choice

given a decision by other

◦Repeated-Simultaneous Games Rollback + Iterative

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“Nash”Iterative Solutions to Simultaneous Game (PD Example)

• Payoffs = (Coke profits , Pepsi profits)

• Decisions: Price Low or Price High

Pepsi DecisionLow High

CokeDecision

Low 10,10 1,20

High 20,1 3,3

Example Solution to a Simultaneous Game

• First Iteration: Coke considers best choice if Pepsi sets low price (column 1)

Pepsi Low

Coke Low 10,10

High 20,1

Best choice for Coke, if Pepsi Sets Low Price

Solutions to Simultaneous

• Second Iteration: Coke considers best choice if Pepsi sets high price;

• Low is dominant strategy for Coke; Low better than high in both iterations

PepsiHigh

CokeLow 1,20

High 3,3

Best outcome for Coke, If Pepsi Sets High Price

Solving Sequential Games

“Life must be understood backward, but … it must be lived forward.” - Soren Kierkegaard

Diagram a game tree – simplify if needed

Start with the last move in the gameDetermine the best course(s) of action

for the player with the last move Trim the tree -- Eliminate the

dominated strategiesRepeat the procedure at the prior

decision node(s) with the trimmed tree

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An Example: Market Entry

Game Essentials:◦Players: Current firm (F) with large

market share faces a potential entrant (E)

◦Timing: Potential entrant moves first◦Moves: Potential entrant (enter-stay

out) Current firm (accept passively-fight)

◦Information: full information◦Payoffs: (see game tree)◦Rules: Fixed (to simplify game for

now)18

Market Entry in Game Tree

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E out

inF fight

acc

(0, 100)

(-10,-20)

(20,75)

Payoffs = (E, F) expressed as profits (mil $)

Looking Forward…

Entrant makes the first move: Must consider how F will respond

If enter:

Current Firm better off if accepts; so trim “fight” branch from tree

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F fight

acc

(-10,-20)

(20,75)

… And Reasoning Back

Now consider entrant’s move with tree trimmed

Solution = (In, Accept Passively )

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E out

in F

(0, 100)

(20,75)acc