Strategic Thinking What is Strategic Thinking Game Theory Applications to Business Applications to Life This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

Survivor: Picking Sticks Rules: 12 Sticks During a player’s turn each person can pick 1-3 sticks. Last person to move wins Question: Is there a winning strategy? Solution Strategy: Look ahead and reason back 12 11 10 9 8 7 6 5 4 3 2 1 This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

Modified Picking Sticks Game Rules: 14 Sticks During a player’s turn each person can pick 1-3 sticks. Last person to move wins 14 13 12 11 10 9 8 7 6 5 4 3 2 1 This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

The Cambridge May Ball Casino Night Roulette Play Money Winner gets ticket to the ball In the final round Barry has $700, and Eva $300 This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

The Cambridge May Ball Roulette What should each person do? Numbers 0-36 0 is green 1-36 odd numbers are Red, even are black Betting $1 on Red wins with prob 18/37 and pays $2 Betting $1 on a multiple of 3 wins with probability 12/37 and pays $3. What should each person do? This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

Forecasting Stock Performance Bob is a veteran predictor of stocks. His predictions appear on a popular Web-Site Each Monday Morning. Jim is unknown If his stocks perform better than Bob’s he may attract attention If his stocks perform the same or worse than Bob’s he remains unknown. When should Bob post his picks on his web-site? How should he make his choices? This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

America’s Cup A two boat sailing race The Australian boat starts out behind This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

It’s your move Charlie Brown Lucy: “I’ll hold the ball, you come running up and kick it Charlie Brown” Charlie Brown “This year I’m gonna kick the ball out of the universe.” This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

New Cleaners & Fast Cleaners Vacuum Cleaners Existing company Fast Cleaner’s Vacuums Potential Entrant: New Cleaners Post Entry choices for Fast Cleaners Accommodate entry Fight a price war This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

New Cleaners & Fast Cleaners Accommodate $100,000 to New Cleaners Fast Cleaners Enter Price War $-200,000 to New Cleaners Newcleaners $0 to New Cleaners Keep Out This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

New Cleaners & Fast Cleaners Accommodate $100,000 to New Cleaners $100,000 to Fast Cleaners Fast Cleaners Enter Price War $-200,000 to New Cleaners -$100,000 to Fast Cleaners Newcleaners $0 to New Cleaners Keep Out This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

Bargaining: Ice-Cream Pie Take-it-or-leave-it offers The pie is melting This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

Politics and the High Road Obama Wins McCain Low Road McCain has a chance High Road Obama McCain has a chance High Road Obama has incentive to keep the decision a secret. The general principle is that for the look ahead and reason back solution to work, the second player must be able to observe the first. Low Road McCain Low Road Obama Wins This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

Dominant Strategies Professor Jones choosing the right grail Baseball: 2-outs, 2-strikes, runner on first Terminology Dominant Strategy Dominated Strategy This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

Time and Newsweek Newsweek’s Choices AIDS Budget Time’s Choices 35* / 35** 70* / 30** 30* / 70** 15* / 15** Illustrates a dominant strategy equilibrium *Magazine sales for Time; ** Magazine sales for Newseek This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

A different situation Newsweek’s Choices AIDS Budget Time’s Choices 42* / 28** 70* / 30** 30* / 70** 18* / 12** If your opponent has a dominant strategy…assume they will use it This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

Football 3* 7* 15* 9* 8* 10* Defense’s Strategies Counter Run Counter Pass Blitz Offense’s Strategies Run 3* 7* 15* Pass 9* 8* 10* Eliminate any dominated strategies from consideration, the re-examine and see if there are more. * Offense’s expected yardage gain This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

Missile warfare C Iraqi Ship F B E A I H D American Ship G Iraqi ship is about to fire a missile at the American ship The American ship has missile defense. The anti-missile has only fuel for one minute Missile goes in straight line or turns every 20 seconds H D American Ship G This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

Table of Hits and Misses Iraqi Strategy A M E R I C N 1-IFCB 2-IFEB 3-IFED 4-IFEH 5-IHGD 6-IHED 7-IHEB 8-IHEF 1-ABCF H O 2-ABEF 3-ABEH 4-ABED 5-ADGH 6-ADEH 7-ADEF 8-ADEB For American’s ….A2 is dominated by A4; A4 also dominates A3, A6 and A7 A1 is dominated by A8 This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

Dominated Strategies Iraqi Strategy A M E R I C N H O 1-ABCF 2-ABEF 1-IFCB 2-IFEB 3-IFED 4-IFEH 5-IHGD 6-IHED 7-IHEB 8-IHEF 1-ABCF H O 2-ABEF 3-ABEH 4-ABED 5-ADGH 6-ADEH 7-ADEF 8-ADEB This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

Reduced Table of Hits and Misses Iraqi Strategies American Strategies IFCB IHGD ABED O H ADEB No dominated strategies left…no dominant strategies. But there may be an equilibrium. This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

Nash Equilibrium Definition Feast: Too many equilibria Famine Standards: Driving on the right side of the road. Phone connection breaks off: Who calls back Famine Re-examine the Missile game Mixed Strategies This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

Summary of Concepts Sequential Games Simultaneous Move Games First Mover Advantage Second Mover Advantage Solve the game backwards Simultaneous Move Games Look for Dominant Strategies If there are no Dominant Strategies, eliminate Dominated Strategies, and check for dominant strategies in the simplified game. This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

Summary Continued… More on Simultaneous move games If all else fails use Nash Equilibrium Each player selects a strategy that maximizes his payoff given the strategy selected by the other player. Characteristics of Nash Equilibrium Sometimes there is more than one Sometimes there is no Nash Equilibrium in pure strategies. There is always a Nash Equilibrium in mixed strategies This slideshow was written by Ken Chapman, but is substantially based on concepts from Thinking Strategically by Avinash K. Dixit and Barry J. Nalebuff, W.W. Norton 1991.

Mary and Bob are playing the game described in the table below Mary and Bob are playing the game described in the table below. Bob picks the columns (either A, B, C, D or E while Mary picks the rows (either 1, or 2). Use concepts from class to pick the likely outcome of this game if their choices are made non-cooperatively and simultaneously.

Statement 1: Non-cooperative Nash equilibrium is the economists favorite solution to use in games because you can always find a single predicted outcome to any situation. Statement 2: When we say that a player has a “Dominant” strategy, we mean that no matter what his/her opponent does, that player will always make the same choice. a. Statement 1 is true, but 2 is false b. Statement 2 is true, but 1 is false Both are true Both are false

Alice and Bob are playing the game described in the table below Alice and Bob are playing the game described in the table below. Bob picks the rows (either A, B, or C, while Alice picks the columns (either D, E, or F). Use concepts from class to pick the likely outcome of this game if their choices are made non-cooperatively and simultaneously. a. Bob will pick B and Alice D b. Bob will pick C, and Alice F. c. Bob will pick C and Alice E. d. Bob will pick A and Alice D. e. None of the above are the solution to this problem

Bob and Alice are going to play the non-cooperative sequential game described below. Bob picks first choosing A or B. Alice picks second, picking C or D. After Alice picks, Bob gets to pick once again, choosing either E or F. Payoffs marked with * are for Bob and ** for Alice. What is the likely outcome of this game according to concepts discussed in class?

Statement 1: “In a two-player, simultaneous-choice game if strategy A is better for every possible choice of your opponent than strategy B, then we say that you have a dominant strategy.” Statement 2: “If there are no dominant strategies, and no dominated strategies in a game, then there will always be a single Nash equilibrium outcome to help predict what will happen.” a. Statement 1 is true, but 2 is false b. Statement 2 is true, but 1 is false c. Both statements are correct. d. Neither statement is correct

Statement 1: “In the ‘casino night’ story from Dixit and Nalebuff by the last spin of the roulette wheel in the evening Barry had $700 and Eva had $300. Sine the money amounts were significant only if you had the most at the end of the evening, Barry’s best strategy was to wait for Eva to place her bet, and bet the same amount on the same event.” Statement 2: “In the ‘casino night’ story mentioned above, Eva’s best choice was to put her $300 on a multiple of 3 so that she would receive $900 if she won. Realizing this she should place her bet immediately and hope Barry didn’t know how to respond.” a. Statement 1 is true, but 2 is false. b. Statement 2 is true, but 1 is false.. c. Both statements are correct. d. Both statements are false.

Which of the following statements best describe the situation in the simultaneous choice game depicted above? a. Strategy F is a dominated strategy for Edna, while strategy A is a dominated strategy for Bob. b. Strategy E is a dominated strategy for Edna, while strategy A is dominated strategy for Bob. c. There are no dominated strategies in this game. d. Strategy F is a dominated strategy for Edna, while strategy c is a dominated strategy for Bob.