BA 511 Strategic Games *Some examples are drawn from Thinking Strategically by Dixit & Nalebuff

Games in WSJ, Holman Jenkins 2

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 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 Dilemma 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 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 Information Divide the Cities Game ◦ Harvard v. Stanford MBA Students ◦ Cities Worth Points, Monopoly Worth Points ◦ Select “in the dark” 7

Bargaining Games Bargaining Games Games of Chicken ◦ Don’t Expect Quick Resolution (12 th 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 Decision LowHigh CokeDecision Low 10,10 10,10 1,20 1,20 High 20,1 20,1 3,3 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 10,10 High 20,1 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 Pepsi High Coke Low 1,20 1,20 High 3,3 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 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 17

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 respond If enter: Current Firm better off if accepts; so trim “fight” branch from tree 20 F fight acc (-10,-20) (20,75)

… And Reasoning Back Now consider entrant’s move with tree trimmed Solution = (In, Accept Passively ) 21 E out in F (0, 100) (20,75) acc