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Game Theory

Game Theory. Mike Shor Lecture 4. “It is true that life must be understood backward, but … it must be lived forward.”. - Søren Kierkegaard. Review. Understanding the outcomes of games Sometimes easy Dominant strategies Sometimes more challenging “I know that you know …”

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Game Theory

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  1. Game Theory Mike ShorLecture 4 “It is true that life must be understood backward, but … it must be lived forward.” - Søren Kierkegaard

  2. Review • Understanding the outcomes of games • Sometimes easy • Dominant strategies • Sometimes more challenging • “I know that you know …” • What if a game is sequential? • Market entry

  3. Very Large Airplanes:Airbus vs. Boeing • Airbus lacked a jumbo jet: • “ The problem is the monopoly of the 747 … They have a product. We have none. ” - Airbus Executive • Initiated plans to build a super-jumbo jet • Industry feasibility studies: • Room for at most one megaseater • Boeing preemption: • “Boeing, the world’s top aircraft maker, announced it was building a plane with 600 to 800 seats, the biggest and most expensive airliner ever.” - BusinessWeek, 1993

  4. out out in in Sequential Games The Game $0, $0 out – $1 billion, – $1billion Airbus $0.3 billion, – $3 billion in Boeing – $4 billion, – $4billion

  5. out in Looking Forward … • Airbus makes the first move: • Must consider how Boeing will respond • If stay out: • Boeing stays out $0billion Boeing – $1 billion

  6. out in Looking Forward … • Airbus makes the first move: • Must consider how Boeing will respond • If enter: • Boeing accommodates, stays out – $3billion Boeing – $4 billion

  7. out in … And Reasoning Back • Now consider the first move: • Only ( In, Out ) is sequentially rational • In is not credible (for Boeing) $0, $0 out Airbus $0.3 billion, – $3 billion out Boeing

  8. Airbus vs. BoeingWhat a Difference Seven Years Make • “Boeing, the world’s top aircraft maker, announced it was building a plane with 600 to 800 seats, the biggest and most expensive airliner ever.” - BusinessWeek, 1993

  9. Solving Sequential Games • Thinking backwards is easy in game trees • Start at the end and trim the tree to the present • Thinking backwards is challenging in practice • Outline: • Strategic moves in early rounds • The rule of three (again) • Seeing the end of the game

  10. Voting Revisited Gore v. Bush before the U.S. Supreme Court • Recall member preferences: 4 (B>G>R) 3 (G>R>B) 2 (R>B>G) • Majority rule results: • B beats G ; G beats R ; R beats B • Voting results (example): • R beats G then winner versus BB

  11. Voting as a Sequential Game B B B vs. R R R R R vs. G G B B G B vs. G G

  12. Looking Forward … B B B vs. R A majority prefers R to B R R B B A majority prefers B to G G B vs. G G

  13. … And Reasoning Back Three judges prefer G to R to B. How should they vote in the first round? B vs. R R R R R vs. G G B B B vs. G

  14. What Happened? • Gore supporters have preferences • Gore > Remand > Bush • First round vote between Remand and Gore • Gore supporters prefer Gore • But a vote for Gore is in effect a vote for Bush! • So Gore supporters vote for remand. • Guarantee themselves second best choice • Thinking forward misses chance for strategic voting • Thinking forward leads us to pick the wrong game

  15. Sequential Rationality COMMANDMENT Look forward and reason back. Anticipate what your rivals will do tomorrow in response to your actions today

  16. Examples of Strategic Voting Not necessarily good to vote your true preferences • Amendments to make bad bills worse • Crossing over in open primaries • “Centrist” voting in primaries • Outcome is still predetermined: • B beats G then winner versus R • B beats R then winner versus G • G beats R then winner versus B

  17. Accommodating a Potential Entrant • Do you enter? • Do you accommodate entry? • What if there are fifty potential entrants?

  18. Survivor Immunity Challenge • There are 21 flags • Players alternate removing 1, 2, or 3 flags • The player to take the last flag wins

  19. Sequential Games • You have a monopoly market in every state • There is one potential entrant in each state • They make their entry decisions sequentially • Florida may enter today • New York may enter tomorrow • etc. • Each time, you can accommodate or fight • What do you do the first year?

  20. E3 E2 out out E1 fight fight M in in M acc acc The Game

  21. out $0, $100 + previous E in 50, 50 + previous acc M fight –50, –50 + previous Looking Forward … • In the last period: • No reason to fight final entrant, thus ( In, Accommodate )

  22. … And Reasoning Back • The Incumbent will not fight the last entrant • But then, no reason to fight the previous entrant • … • But then, no reason to fight the first entrant • Only one sequential equilibrium • All entrants play In • Incumbent plays Accommodate • But for long games, this is mostly theoretical • People “see” the end two to three periods out!

  23. Game Theory Example Sequential Entry

  24. Market Opportunity Analysis “Assesses the potential of a geographic market for a specific set of products, providing a prioritization of market coverage voids and recommending market entry strategies.”

  25. “Prioritization of Market Coverage ” Break even point: 300 SBCs 700 SBCs 400 SBCs

  26. Extended Market Analysis • If enter 400 SBC market: • Next entrant, to break even, must expect market share of 300/400 • Must expect market share of 75% • If enter 700 SBC market: • Next entrant, to break even, must expect market share of 300/700 • Must expect market share of 43% • Real decision: • All of 400 or half of 700

  27. Breakfast Cereals A small sampling of the Kellogg’s portfolio

  28. Breakfast Cereals product development costs: $1.2M per product 600 500 400 sales (in thousands) 300 200 100 000 1 2 3 4 5 6 7 8 9 10 11 less sweet more sweet

  29. First Product Entry SCENARIO 1 Profit = ½ 5(600) – 1200 = 300 600 500 400 sales (in thousands) 300 200 100 000 1 2 3 4 5 6 7 8 9 10 11 less sweet more sweet

  30. Second Product Entry SCENARIO 2 Profit = 2 x 300 = 600 600 500 400 sales (in thousands) 300 200 100 000 1 2 3 4 5 6 7 8 9 10 11 less sweet more sweet

  31. Third Product Entry SCENARIO 3 Profit = 300 x 3 – 240 x 2 = 420 600 500 400 sales (in thousands) 300 200 100 000 1 2 3 4 5 6 7 8 9 10 11 less sweet more sweet

  32. Competitor Enters SCENARIO 4 Profit = 300 x 2 - 240 = 360 600 500 400 sales (in thousands) 300 200 100 000 1 2 3 4 5 6 7 8 9 10 11 less sweet more sweet

  33. Summary • Thinking forward misses chances to make money • Make sure to see the game through to the logical end • Don’t expect others to see the end until it is close • The rule of three steps

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