BA 511 Strategic Games

*Some examples are drawn from Thinking Strategically byDixit & Nalebuff

Games in WSJ, Holman Jenkins

2

Strategic Games All AroundSituations 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

3

• 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

4

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 5

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”

7

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

8

“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

9

First Mover Advantage?Last Better if info

from observing◦ Sailing◦ NCAA Overtime◦ Innovation

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

10

Don’t Outsmart Yourself Dixit & Nalebuff: Jerusalem

TaxiJerusalem Taxi Ride

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

11

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?

12

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 13

“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 1,20High 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 1,20High 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 tree17

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

19

E out

in F 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 respondIf enter:

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

20

F fight

acc

(-10,-20)

(20,75)

… And Reasoning BackNow consider entrant’s move with tree

trimmed

Solution = (In, Accept Passively )

21

E out

in F

(0, 100)

(20,75)acc