BA 511 Examples and Ideas on Strategic Games

1. *Some examples are drawn from Dixit & Nalebuff, Thinking Strategically BA 511 Examples and Ideas onStrategic Games

2. Strategic Decisions All Around Strategic Situations • Bidding-Negotiation; Auctions; (homes, cars, yard sales, …) • Employment: Job Market; Board-Management; Management-Labor; • Politics/Group Dynamics • Pricing, Ad, … Competition • Dating, Marriage • Families: Parent-Child, Spouses, Siblings • Games: Poker, Chess, Risk, … Strategic Behavior • Signaling & Filtering Info • Altering Perceptions-Beliefs • Promises/Threats • Changing “Rules” • Mixing Actions • Incentives for Cooperation • Cooperation-Compete Dilemmas • Free-Riding • Situations with active responses by participants; • Not merely playing against “the market” or “nature”

3. Stuck In Jail “Prisoner’s Dilemma” • 2 criminals arrested/Interrogated no contact • Confess-Don’t Confess • 1 Confess: low/high sentences • 2 Confess: moderate sentences • No Confess: low/low sentences Price Wars (ad, entry, … Competition) • Confess = competitive outcome • No Confess = “cooperative” outcome (positive sum for participants) “Hostage’s Dilemma”

4. Political Chess:Losing the Battle, Winning the War • Tom Hanks’ HBO series-- From the Earth to the Moon – dramatizes the aftermath of the Apollo 1 deaths of 3 astronauts during a routine launch pad test. • A capsule fire broke out from a spark in wiring • North American (the capsule contractor) had sent repeated warnings to NASA about pressurized, oxygen-only tests • NA “eats” their memos, accepts big part of blame. Why? • Looking ahead and reasoning back: • Chance Congress will cancel program, especially of primary blame on NASA • If program retained, NASA doesn’t have time to employ new contractor • Accept/share blame, retain program, retain contract

5. Beach Battles: “Location Games • Where to setup shop if consumers positioned uniformly along a beach that competitor is trying to setup shop in best location also? • Move to the middle (median), otherwise, competitor can locate just to the “busier” side and capture everyone on that side Business Examples: McDonalds & Burger King; Many retail stores; primary & general election races; • Basic outcome holds with extensive information and single choice dimension • Harvard-Stanford MBA “Divide the Cities” and focal points

6. First Shall Be Last? Sailboat Races/NCAA Football Overtime • Second Mover Advantage: gain information … • Business: innovation, e.g. MS Windows Princess Bride “game of wits” • First Mover Advantage: manipulate rival’s information or choices • Business: make rival’s entry/exit costly, build up reputation Hold’em Poker Tradeoff: • Info manipulation v. info gathering … first or last best seat

7. Too Clever by One-Half? • Jerusalem Taxi Ride • Colts-Saints Super Bowl

8. Game Changers: Strategic Moves • Cortez Burning His Ships • Threats/Promises/Commitments • My Daughter’s “Salami Tactics” • Inflexible Personalities: DeGaulle • Retail Stores • Changing set/range of choices • Office Politics • Order of decisions • Set of choices/proposals/matchups • Voting rules

9. Bargaining Basics • “Ultimatum Game” Experiments • Split of pot if 2 parties agree on split; 1 makes offer-1 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 • Homebuilding Bargaining • Tradeoff of Incentives: • Flex-price: sub info problem; easy changes • Fixed-price: no sub problem; changes hard

10. Six Essentials Questions 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?

11. 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

12. “Nash”Iterative Solutions to Simultaneous Game (PD Example) • Payoffs = (Coke profits , Pepsi profits) • Decisions: Price Low or Price High

13. 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

14. 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

15. Solving Sequential Games “Life must be understood backward, but … it must be lived forward.” - Soren Kierkegaard (Consider Chess as Example) • 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

16. 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)

17. out (0, 100) E in (-10,-20) fight F acc (20,75) Market Entry in Game Tree Payoffs = (E, F) expressed as profits (mil $)

18. (-10,-20) fight F acc (20,75) 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

19. (0, 100) out E in F acc (20,75) … And Reasoning Back • Now consider entrant’s move with tree trimmed • Solution = (In, Accept Passively )