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Game Theory
So Far…• Understood environment where actions of  agents were independent of each other.• Game Theory: Analyzing environme...
What are Games?“No Man is an Island Entire of Itself”                     -John Donne, 1624
Smartphone Market• Spate of law suitsProtecting patents filed byApple• What determines the leadership of  Smartphone marke...
Lesson 1:Strategic Interaction: Scenario whereoutcomes of actions dependent on that ofothers
MoneyBall     • Billy Beane Manager     Oakland A Baseball team     •On a massive losing spree     •To win the World Serie...
Politics• Who wins presidential elections?- Voters, Policy  announcements, funds and campaign resources• Result also depen...
Princess Bride• Strategic interaction• What does his choiceDepend upon?• Choices depend upon actions of others as  well as...
Browser Wars• October 1994, Netscape released one of the  first commercial browsers- Navigator 1.0• It was priced at $39- ...
Smartphone Market• Spate of law suitsProtecting patents filed byApple• What determines the leadership of  Smartphone marke...
Sequential Interaction• Players make alternating moves• Each player must look ahead. Anticipate rival’s  future response• ...
Movie Release• Dreamworks- The Antz : 2nd Oct 1998• Pixar- A Bug’s life: 25th Nov 1998• Movie houses decide on what kind o...
Competing over Market Share• Coke and Pepsi compete for market share• Every week they decide prices• Every week Coke meets...
Strategic Moves Game• No sequence of alternating moves• Simultaneous moves• Each player acts in ignorance of the other  pl...
Lesson 2:Modeling Strategic Environment:Sequential or Simultaneous Interaction
IPL Auction• Bid on a player reveals private information• Winning a player depends upon your bid and  that of the others
Information Rules Lesson 3 :Actions and Outcome of the game dependsupon private information
Information Rules Lesson 4: Actions reveal private informationUse the fact that others use the fact that yourbids reveal p...
What is Game Theory?• Finding the right strategy in Strategic  Environments• Bad news: Knowing game theory does not  guara...
Games Business PlayExample                  GamePrice Wars               Prisoner’s DilemmaPollution Abatement      Free R...
Coke and Pepsi : Price War• Coke has to decide whether to increase its  price or to reduce it• What should it do?• What wi...
Games Business PlayExample                  GamePrice Wars               Prisoner’s DilemmaPollution Abatement      Free R...
Games that we playExample                    GameDoing the Dishes           War of AttritionGroup Projects             Fre...
Free Riding• Collective project• Ideal if you get a high grade• However would prefer not to exert effort• Should you put e...
Why Study Game Theory?            Because the press tells us to…• “Game Theory, long an intellectual pastime, came into it...
Why Study Game Theory?  Because recruiters tell us to …• “Game theory forces you to see a business situation  over many pe...
Decision Theory         vs. Game Theory• Ten of you go to a restaurant• If each of you pays for your own meal…   – What to...
Restaurant Decision-Making          May I recommend that with the Bleu            Cheese for ten dollars more?            ...
ELEMENTS OF GAMES
Rules of the Game• The strategic environment   – Players   – Strategies   – Payoffs• The assumptions   – Rationality   – C...
The Strategic Environment• Players: Who is interacting?• Strategies: What are their options?• Payoffs: What are their ince...
Cigarette Advertising on TV       • All US tobacco companies         advertised heavily on TV1964 • Surgeon General issues...
Strategic Interaction• Players:          Reynolds and Philip Morris• Strategies:       Advertise or Not Advertise• Payoffs...
The Strategic Environment• Players     • Everyone who has an effect on your PAYOFFS• Strategies     • Actions available to...
ASSUMPTIONS
Rationality• Most economic analysis assumes “rationality” of  decision-makers, i.e. that you make decisions by1. choosing ...
Common Knowledge• Players know the rules of the game• Players know the payoffs, strategies, number  of players and the seq...
And Common Knowledge of                    Rationality??    • Each player is rational    • Each player knows that each pla...
EQUILIBRIUM
Equilibrium• The likely outcome of a game when rational, strategic  agents interact   – Each player is playing his or her ...
SEQUENCE OF PLAY
Simultaneous Move Games• Scenario where agents take actions  simultaneously not the same action• Agents may take an action...
SIMULTANEOUS MOVE GAMES
REPRESENTING THE GAME
Cigarette Advertising on TV       • All US tobacco companies         advertised heavily on TV1964 • Surgeon General issues...
Strategic Interaction• Players:          Reynolds and Philip Morris• Strategies:       Advertise or Not Advertise• Payoffs...
Representing a GamePLAYERS                         Philip Morris                      No Ad          Ad             No Ad ...
What to Do?                        Philip Morris                     No Ad          Ad            No Ad   50 , 50     20 ,...
Solving the Game                                    Philip Morris                                 No Ad          Ad       ...
SOLVING THE GAME
How to solve the game?     L      C U     8, 3   0, 2 M     4, 2   1, 5
SOLVING THE GAME• What strategy would you choose if you were  player Row?• Your decision would depend upon?• Your belief a...
SOLVING THE GAME• How do you get around the beliefs?• You must put yourself in their shoes to see  what they would do.• Th...
SOLVING THE GAME• Your action depends upon your belief about  other’s actions.• Your belief about other’s actions in turn ...
Solving the game1. Dominated/Dominant Strategy2. Best Response Functions/Nash Equilibrium3. Iterated Elimination of Weakly...
1. Dominated/Dominant StrategiesDominated StrategyStrategy, say x is said to be dominated ifthere exists another strategy,...
No Ad      Ad        50 , 50   20 , 60No Ad        60 , 20   30 , 30  Ad
No Ad      Ad        50 , 50   20 , 60No Ad        60 , 20   30 , 30  Ad
L         C         RU   8, 3       0, 4      4,4M   4,2        1,5       5,3D   3,7        0,1       2,0
L         C         RU   8, 3       0, 4      4,4M   4,2        1,5       5,3D   3,7        0,1       2,0
L          C         RU   8, 3        0, 4      4,4M   4,2        1 ,5       5,3D   3,7         0,1       2,0
Dominated/Dominant StrategiesDominant StrategyStrategy, say y is said to dominates x if it giveshigher payoff than x under...
No Ad       Ad        50 , 50   20 , 60No Ad        60 , 20   30 , 30  Ad
Dominance• A strategy is dominant if it  outperforms all other choices no matter what  opposing players do     • Technical...
DominanceIf you have a dominant strategy, use it.Expect your opponent to use herdominant strategy if she has one.
Prisoner’s DilemmaOptimal                   No Ad       Ad          No Ad   50 , 50   20 , 60             Ad   60 , 20   3...
Prisoner’s Dilemma• Two prisoner’s caught on the crime scene• Interrogated behind two separate cells• If one confesses to ...
Prisoner’s Dilemma                 Confess    Not ConfessConfess          -3, -3     0, -8Not Confess      -8, 0      -1,-1
Example: SUV Price Wars“General Motors Corp. and Ford Motor Co.  slapped larger incentives on popular sport utility vehicl...
SUV Price Wars               Discount   No DiscountDiscount       3,3        8, 0No Discount    0, 8       5,5
• No Discount is a ………… strategy• Discount is a ………. strategy
• No Discount is a dominated strategy• Discount is a dominant strategy• In this case Discount strictly dominates No  Disco...
Strictly Dominant Strategy:Strategy, say x is said to strictly dominate y ifit gives strictly higher payoff than x under a...
Prisoner’s Dilemma• Both players have a dominant strategy-  Discount• Neither player would play No discount• However, each...
Strategic TensionPrisoner’s Dilemma:• Clash between individual and group interests• The players each realize that they are...
Efficiency• Strategy profile s is more efficient than s’ if all  of the players prefer s to the outcome s’.• Pareto Effici...
SUV Price Wars               Discount   No DiscountDiscount       3,3        8, 0No Discount    0, 8       5,5
SUV Price Wars               Discount   No DiscountDiscount       3,3        8, 0No Discount    0, 8       9,9
How to find dominated strategiesTo check for the dominated strategies of a player  represented by row• Scan across the row...
L         C         RU   8, 3       0, 4      4,4M   4,2        1,5       5,3D   3,7        0,1       2,0
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Game theory 1

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Game theory 1

  1. 1. Game Theory
  2. 2. So Far…• Understood environment where actions of agents were independent of each other.• Game Theory: Analyzing environment of strategic interactions• Examples: Your performance versus learning
  3. 3. What are Games?“No Man is an Island Entire of Itself” -John Donne, 1624
  4. 4. Smartphone Market• Spate of law suitsProtecting patents filed byApple• What determines the leadership of Smartphone market?• Implications of the verdict on – Apple, Samsung, Google• Android share: 64.1%, Apple – 18.8%
  5. 5. Lesson 1:Strategic Interaction: Scenario whereoutcomes of actions dependent on that ofothers
  6. 6. MoneyBall • Billy Beane Manager Oakland A Baseball team •On a massive losing spree •To win the World Series he must strategize •Hires a Yale Economist to strategize the optimal bid for each player
  7. 7. Politics• Who wins presidential elections?- Voters, Policy announcements, funds and campaign resources• Result also depends upon the sequence in which elections are held in different primaries
  8. 8. Princess Bride• Strategic interaction• What does his choiceDepend upon?• Choices depend upon actions of others as well as beliefs of actions of others (under uncertainty)
  9. 9. Browser Wars• October 1994, Netscape released one of the first commercial browsers- Navigator 1.0• It was priced at $39- 60% market share• August 1995, Microsoft introduces Internet Explorer available only with Windows 95• Netscape has to decide its next move.• Reduce price, improve the speed, reduce the size?
  10. 10. Smartphone Market• Spate of law suitsProtecting patents filed byApple• What determines the leadership of Smartphone market?• Implications of the verdict on – Apple, Samsung, Google• Android share: 64.1%, Apple – 18.8%
  11. 11. Sequential Interaction• Players make alternating moves• Each player must look ahead. Anticipate rival’s future response• Reason back and decide optimal action
  12. 12. Movie Release• Dreamworks- The Antz : 2nd Oct 1998• Pixar- A Bug’s life: 25th Nov 1998• Movie houses decide on what kind of movie to make• When to release the movie• In this case simultaneous decision
  13. 13. Competing over Market Share• Coke and Pepsi compete for market share• Every week they decide prices• Every week Coke meets behind close doors• Coke knows that Pepsi meets behind close doors.
  14. 14. Strategic Moves Game• No sequence of alternating moves• Simultaneous moves• Each player acts in ignorance of the other player’s actual choice• Can not look ahead and reason backwards
  15. 15. Lesson 2:Modeling Strategic Environment:Sequential or Simultaneous Interaction
  16. 16. IPL Auction• Bid on a player reveals private information• Winning a player depends upon your bid and that of the others
  17. 17. Information Rules Lesson 3 :Actions and Outcome of the game dependsupon private information
  18. 18. Information Rules Lesson 4: Actions reveal private informationUse the fact that others use the fact that yourbids reveal private information about the course
  19. 19. What is Game Theory?• Finding the right strategy in Strategic Environments• Bad news: Knowing game theory does not guarantee winning• Good news: Framework for thinking about strategic interaction
  20. 20. Games Business PlayExample GamePrice Wars Prisoner’s DilemmaPollution Abatement Free RidingFCC Spectrum Auctions
  21. 21. Coke and Pepsi : Price War• Coke has to decide whether to increase its price or to reduce it• What should it do?• What will happen if it increased its price?• What if it increased the price and Pepsi did not?• What if Pepsi also increased its price?
  22. 22. Games Business PlayExample GamePrice Wars Prisoner’s DilemmaPollution Abatement Free RidingFCC Spectrum Auctions
  23. 23. Games that we playExample GameDoing the Dishes War of AttritionGroup Projects Free RidingDating Hidden Information
  24. 24. Free Riding• Collective project• Ideal if you get a high grade• However would prefer not to exert effort• Should you put effort or not?
  25. 25. Why Study Game Theory? Because the press tells us to…• “Game Theory, long an intellectual pastime, came into itsown as a business tool.” Forbes, July 3, 1995, p. 62.• “Game theory is hot.” The Wall Street Journal, 13 February 1995, p. A14
  26. 26. Why Study Game Theory? Because recruiters tell us to …• “Game theory forces you to see a business situation over many periods from two perspectives: yours and your competitor’s.” – Judy Lewent – CFO, Merck 26
  27. 27. Decision Theory vs. Game Theory• Ten of you go to a restaurant• If each of you pays for your own meal… – What to order is then a decision problem• If you all agree to split the bill... – Now, this is a game 27
  28. 28. Restaurant Decision-Making May I recommend that with the Bleu Cheese for ten dollars more? Sure! It is only a dollar more for me!• Check splitting policy changes incentives. 28
  29. 29. ELEMENTS OF GAMES
  30. 30. Rules of the Game• The strategic environment – Players – Strategies – Payoffs• The assumptions – Rationality – Common knowledge• The rules – Timing of moves – Informational conditions
  31. 31. The Strategic Environment• Players: Who is interacting?• Strategies: What are their options?• Payoffs: What are their incentives?
  32. 32. Cigarette Advertising on TV • All US tobacco companies advertised heavily on TV1964 • Surgeon General issues official warning • Cigarette smoking may be hazardous • Cigarette companies fear lawsuits • Government may recover healthcare costs1970 • Companies strike agreement • Carry the warning label and cease TV advertising in exchange for immunity from federal lawsuits.
  33. 33. Strategic Interaction• Players: Reynolds and Philip Morris• Strategies: Advertise or Not Advertise• Payoffs: Companies’ Profits• Strategic Landscape: – Each firm earns $50 million from its customers – Advertising costs a firm $20 million – Advertising captures $30 million from competitor
  34. 34. The Strategic Environment• Players • Everyone who has an effect on your PAYOFFS• Strategies • Actions available to each player • Define a plan of action for every contingency• Payoffs • Well being as a result of a set of actions of each player • Different payoffs for different set of actions.
  35. 35. ASSUMPTIONS
  36. 36. Rationality• Most economic analysis assumes “rationality” of decision-makers, i.e. that you make decisions by1. choosing an action that maximizes your welfare2. forming correct belief about the world• In principle, requires enormous powers of imagination and computation.
  37. 37. Common Knowledge• Players know the rules of the game• Players know the payoffs, strategies, number of players and the sequence in which the game is played.
  38. 38. And Common Knowledge of Rationality?? • Each player is rational • Each player knows that each player is rational • Each player knows that each player knows that each player is rational • Each player knows that each player knows that each player knows that each player is rational• Each player knows that each player knows that each player knows that each player knows that each player is rational• Etc. etc. etc .
  39. 39. EQUILIBRIUM
  40. 40. Equilibrium• The likely outcome of a game when rational, strategic agents interact – Each player is playing his or her best strategy given the strategy choices of all other players – No player has incentive to change his or her action unilaterally
  41. 41. SEQUENCE OF PLAY
  42. 42. Simultaneous Move Games• Scenario where agents take actions simultaneously not the same action• Agents may take an action at different points in time• Action is taken without the knowledge of the action taken by the other agent• You can not think ahead and rational backwards
  43. 43. SIMULTANEOUS MOVE GAMES
  44. 44. REPRESENTING THE GAME
  45. 45. Cigarette Advertising on TV • All US tobacco companies advertised heavily on TV1964 • Surgeon General issues official warning • Cigarette smoking may be hazardous • Cigarette companies fear lawsuits • Government may recover healthcare costs1970 • Companies strike agreement • Carry the warning label and cease TV advertising in exchange for immunity from federal lawsuits.
  46. 46. Strategic Interaction• Players: Reynolds and Philip Morris• Strategies: Advertise or Not Advertise• Payoffs: Companies’ Profits• Strategic Landscape: – Each firm earns $50 million from its customers – Advertising costs a firm $20 million – Advertising captures $30 million from competitor• How to represent this game?
  47. 47. Representing a GamePLAYERS Philip Morris No Ad Ad No Ad 50 , 50 20 , 60Reynolds Ad 60 , 20 30 , 30STRATEGIES PAYOFFS
  48. 48. What to Do? Philip Morris No Ad Ad No Ad 50 , 50 20 , 60 Reynolds Ad 60 , 20 30 , 30If you are advising Reynolds, what strategydo you recommend?
  49. 49. Solving the Game Philip Morris No Ad Ad No Ad 50 , 50 20 , 60 Reynolds Ad 60 , 20 30 , 30• Best reply for Reynolds: • If Philip Morris advertises: • If Philip Morris does not advertise:
  50. 50. SOLVING THE GAME
  51. 51. How to solve the game? L C U 8, 3 0, 2 M 4, 2 1, 5
  52. 52. SOLVING THE GAME• What strategy would you choose if you were player Row?• Your decision would depend upon?• Your belief about Player column’s action• If you believe that Player column would play L=> U• If you believe that Player column would play M=> C
  53. 53. SOLVING THE GAME• How do you get around the beliefs?• You must put yourself in their shoes to see what they would do.• They are also trying to guess what you are doing.
  54. 54. SOLVING THE GAME• Your action depends upon your belief about other’s actions.• Your belief about other’s actions in turn depends upon their belief about your actions
  55. 55. Solving the game1. Dominated/Dominant Strategy2. Best Response Functions/Nash Equilibrium3. Iterated Elimination of Weakly Dominated Strategies (IEWDS)
  56. 56. 1. Dominated/Dominant StrategiesDominated StrategyStrategy, say x is said to be dominated ifthere exists another strategy, say y whichgives higher payoff than x under all strategyprofiles of other players
  57. 57. No Ad Ad 50 , 50 20 , 60No Ad 60 , 20 30 , 30 Ad
  58. 58. No Ad Ad 50 , 50 20 , 60No Ad 60 , 20 30 , 30 Ad
  59. 59. L C RU 8, 3 0, 4 4,4M 4,2 1,5 5,3D 3,7 0,1 2,0
  60. 60. L C RU 8, 3 0, 4 4,4M 4,2 1,5 5,3D 3,7 0,1 2,0
  61. 61. L C RU 8, 3 0, 4 4,4M 4,2 1 ,5 5,3D 3,7 0,1 2,0
  62. 62. Dominated/Dominant StrategiesDominant StrategyStrategy, say y is said to dominates x if it giveshigher payoff than x under all strategy profilesof other players.
  63. 63. No Ad Ad 50 , 50 20 , 60No Ad 60 , 20 30 , 30 Ad
  64. 64. Dominance• A strategy is dominant if it outperforms all other choices no matter what opposing players do • Technical aside: strict dominance: Profit (Ad , any) > Profit (No , any) weak dominance: some inequalities are weak ( )• Games with dominant strategies are easy to play – No need for “what if …” thinking
  65. 65. DominanceIf you have a dominant strategy, use it.Expect your opponent to use herdominant strategy if she has one.
  66. 66. Prisoner’s DilemmaOptimal No Ad Ad No Ad 50 , 50 20 , 60 Ad 60 , 20 30 , 30 Equilibrium• Both players have a dominant strategy• The equilibrium results in lower payoffs for each player
  67. 67. Prisoner’s Dilemma• Two prisoner’s caught on the crime scene• Interrogated behind two separate cells• If one confesses to crime, its proved they both were involved.
  68. 68. Prisoner’s Dilemma Confess Not ConfessConfess -3, -3 0, -8Not Confess -8, 0 -1,-1
  69. 69. Example: SUV Price Wars“General Motors Corp. and Ford Motor Co. slapped larger incentives on popular sport utility vehicles, escalating a discounting war in the light-truck category … Ford added a $500 rebate on SUVs, boosting cash discounts to $2,500.The Dearborn, Mich., auto maker followed GM, which earlier in the week began offering $2,500 rebates on many of its SUVs.” -- Wall Street Journal, January 31, 2003
  70. 70. SUV Price Wars Discount No DiscountDiscount 3,3 8, 0No Discount 0, 8 5,5
  71. 71. • No Discount is a ………… strategy• Discount is a ………. strategy
  72. 72. • No Discount is a dominated strategy• Discount is a dominant strategy• In this case Discount strictly dominates No Discount
  73. 73. Strictly Dominant Strategy:Strategy, say x is said to strictly dominate y ifit gives strictly higher payoff than x under allstrategy profiles of other players.
  74. 74. Prisoner’s Dilemma• Both players have a dominant strategy- Discount• Neither player would play No discount• However, each would be better off if they selected No Discount.
  75. 75. Strategic TensionPrisoner’s Dilemma:• Clash between individual and group interests• The players each realize that they are jointly better off if they play NO DISCOUNT- Group interest.• However, each has the individual incentive to choose Discount- Individual interest.
  76. 76. Efficiency• Strategy profile s is more efficient than s’ if all of the players prefer s to the outcome s’.• Pareto Efficient: A strategy profile s is pareto efficient if there is no other strategy profile s’ such that every player gets more from s’ than s.
  77. 77. SUV Price Wars Discount No DiscountDiscount 3,3 8, 0No Discount 0, 8 5,5
  78. 78. SUV Price Wars Discount No DiscountDiscount 3,3 8, 0No Discount 0, 8 9,9
  79. 79. How to find dominated strategiesTo check for the dominated strategies of a player represented by row• Scan across the rows, look at all columns• If the payoff in one row is greater than the payoff in another, and this is true for all columns, then the former dominates the latter.
  80. 80. L C RU 8, 3 0, 4 4,4M 4,2 1,5 5,3D 3,7 0,1 2,0

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