Download - BA 511 Strategic Games
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BA 511 Strategic Games
*Some examples are drawn from Thinking Strategically byDixit & Nalebuff
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Games in WSJ, Holman Jenkins
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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
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• Interdependent Actions & Outcomes • Not Just Playing Against “Market” or “Nature”
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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 5
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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
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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 13
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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 1,20High 20,1 3,3
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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
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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
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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
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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
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Market Entry in Game Tree
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E out
in F fight
acc
(0, 100)
(-10,-20)
(20,75)
Payoffs = (E, F) expressed as profits (mil $)
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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
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F fight
acc
(-10,-20)
(20,75)
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… And Reasoning BackNow consider entrant’s move with tree
trimmed
Solution = (In, Accept Passively )
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E out
in F
(0, 100)
(20,75)acc