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
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Bidding-Negotiation; Auctions
Employment: Job Market; BoardManagement; ManagementLabor;
Politics/Group Dynamics
Pricing, Ad, … Competition
Dating, Marriage
Families: Parent-Child, Spouses,
Siblings
Games: Poker, Chess, Risk, …
Behavior
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Signaling & Filtering Info
Altering Perceptions-Beliefs
Promises/Threats
Changing “Rules”
Mixing Actions
Incentives for Cooperation
Cooperation-Compete Dilemmas
Free-Riding
• Interdependent Actions & Outcomes
• Not Just Playing Against “Market” or “Nature”
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Looking Ahead, Reasoning Back
 Apollo
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 NASA, North American & Congress
 From the Earth to the Moon, HBO
 Business
 Unit/Office Politics
 Entry
 Products
 Markets
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Prisoner’s Dilemma
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2 suspects interrogated/no contact
Confess-Don’t Confess
1 Confess: low/high sentences
2 Confess: moderate sentences
No Confess: low/low sentences
Hostage’s Dilemma
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Business:
◦ Price Wars
◦ Ad Wars
◦ Entry Wars
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The Location Games
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Battle of the Beach
◦ If beachgoers evenly distributed along beach,
where to locate hot dog stand?
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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
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Location Game with Limited
Information
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Divide the Cities Game
◦ Harvard v. Stanford MBA Students
◦ Cities Worth Points, Monopoly Worth Points
◦ Select “in the dark”
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Bargaining Games
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Games of Chicken
◦ Don’t Expect Quick Resolution (12th Hour Agreements)
◦ “Crazy” Offers Advantages
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“Ultimatum Game” Experiments
◦ Split pot if 2 parties agree on split; First makes offerSecond 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
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◦ Cortez Burning His Ships
◦ Large Sunk Costs (e.g. ads)
Change Size/Order of Payoffs/Choices
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“Salami Tactics”
Crimea, My Daughter
Retailers agents as response
Agenda Control,Voting Rules
Change Beliefs
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◦ Bargaining
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First Mover Advantage?
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Last Better if info
from observing
◦ Sailing
◦ NCAA Overtime
◦ Innovation
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First Better if change
beliefs/incentivespayoffs 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
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“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
Coke
Decision
Low
High
Pepsi Decision
Low
High
10,10
1,20
20,1
3,3
Example Solution to a Simultaneous
Game
• First Iteration: Coke considers best choice if Pepsi sets low price (column 1)
Best choice for Coke,
if Pepsi Sets Low Price
Pepsi
Coke
Low
High
Low
10,10
20,1
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
Best outcome for Coke,
If Pepsi Sets High Price
Pepsi
Coke
Low
High
High
1,20
3,3
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 game
 Determine the best course(s) of action for the
player with the last move
 Trim the tree -- Eliminate the dominated
strategies
 Repeat the procedure at the prior decision
node(s) with the trimmed tree
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An Example: Market Entry
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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)
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Market Entry in Game Tree
Payoffs = (E, F) expressed as profits (mil $)
(0, 100)
E
(-10,-20)
F
(20,75)
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Looking Forward…
Entrant makes the first move:
 Must consider how F will respond
 If enter:
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(-10,-20)
F
(20,75)
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Current Firm better off if accepts; so trim “fight”
branch from tree
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… And Reasoning Back
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Now consider entrant’s move with tree
trimmed
(0, 100)
E
F
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acc
(20,75)
Solution = (In, Accept Passively )
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