Game theory

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Game theory

  1. 1. GAME THEORY AN APPLICATION
  2. 2. Game Theory <ul><li>A theory that attempts to mathematically capture behavior in strategic situations or games, in which an individual's success in making choices depends on the choices of others . </li></ul>
  3. 3. Game Theory – An Introduction <ul><li>Firstly presented by the legendary mathematician “John Von Neumann”. </li></ul><ul><li>Attempt to analyze competitions in which one individual does better at another ’ s expense ( zero sum games). </li></ul><ul><li>Later developed by “John Nash”, the Nobel Prize winner and a professor at Princeton University. </li></ul>
  4. 4. DOMINANT FIRM GAME
  5. 5. Dominant Firm Game <ul><li>Two firms, one large and one small. </li></ul><ul><li>Either firm can announce an output level (lead) or else wait to see what the rival does and then produce an amount that does not saturate the market. </li></ul>
  6. 6. Dominant Firm Game Lead Follow Dominant Subordinate Lead Follow (0.5, 4) (1, 8) (3, 2) (0.5, 1)
  7. 7. Dominant Firm Game Lead Follow Dominant Subordinate Lead Follow (0.5, 4 ) (1, 8) (3, 2 ) (0.5, 1)
  8. 8. Dominant Firm Game Lead Follow Dominant Subordinate Lead Follow (0.5, 4) (1, 8 ) (3, 2) (0.5, 1 )
  9. 9. <ul><li>Conclusion: </li></ul><ul><li>Dominant Firm will always lead. </li></ul><ul><li>But what about the Subordinate firm? </li></ul>Dominant Firm Game
  10. 10. Dominant Firm Game Lead Follow Dominant Subordinate Lead Follow (0.5, 4) (1, 8) ( 3 , 2) ( 0.5 , 1)
  11. 11. Dominant Firm Game Lead Follow Dominant Subordinate Lead Follow ( 0.5 , 4) ( 1 , 8) (3, 2) (0.5, 1)
  12. 12. <ul><li>Conclusion: </li></ul><ul><li>No dominant strategy for the Subordinate firm. </li></ul><ul><li>Does this mean we cannot predict what they will do? </li></ul>Dominant Firm Game
  13. 13. Dominant Firm Game Lead Follow Dominant Subordinate Lead Follow (0.5, 4) ( 1 , 8 ) (3, 2) (0.5, 1)
  14. 14. <ul><li>Conclusion: </li></ul><ul><li>Subordinate firm will always follow, because dominant firm will always lead. </li></ul>Dominant Firm Game
  15. 15. NASH EQUILIBRIUM
  16. 16. Nash Equilibrium <ul><li>A solution concept of a game involving two or more players . </li></ul><ul><li>If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices constitute a Nash equilibrium . </li></ul>
  17. 17. CASE I: APPLICATION OF GAME THEORY IN TWO ADVERTISING AGENCIES
  18. 18. Advertising Agencies <ul><li>Two firms, Mudra Communication Pvt. Ltd and </li></ul><ul><li>Waltz Entertainment Pvt. Ltd must decide how </li></ul><ul><li>much to spend on advertising. </li></ul><ul><li>Each firm may adopt either a high (H) budget or </li></ul><ul><li>a low (L) budget. </li></ul>
  19. 19. An Advertising Game <ul><li>Mudra makes the first move by choosing either H or L at the first decision “node.” </li></ul><ul><li>Next, Waltz chooses either H or L, but the large oval surrounding Waltz’s two decision nodes indicates that Waltz does not know what choice Mudra made. </li></ul>
  20. 20. The Advertising Game in Decision Tree Form The numbers at the end of each branch, measured in thousand or millions of dollars, are the payoffs. 7,5 L L H L H H B B A 5,4 6,4 6,3
  21. 21. <ul><li>The numbers at the end of each branch, measured in thousand or millions of dollars, are the payoffs. </li></ul><ul><ul><li>For example, if Mudra chooses H and Waltz chooses L, profits will be 6 for firm Mudra and 4 for firm Waltz. </li></ul></ul>The Advertising Game in Decision Tree Form
  22. 22. The Advertising Game in Decision Tree Form <ul><li>The game in normal (tabular) form is where Mudra’s </li></ul><ul><li>strategies are the rows and Waltz’s strategies </li></ul><ul><li>are the columns. </li></ul><ul><li>For example, if Mudra chooses H and Waltz chooses </li></ul><ul><li>L, profits will be 6 for firm Mudra and 4 for firm Waltz. </li></ul>
  23. 23. Dominant Strategies and Nash Equilibria <ul><li>A dominant strategy is optimal regardless of the strategy adopted by an opponent. </li></ul><ul><li>The dominant strategy for Waltz is L since this yields a larger payoff regardless of Mudra’s Choice. </li></ul>
  24. 24. <ul><ul><ul><li>If Mudra chooses H, Waltz’s choice of L yields 5, one better than if the choice of H was made. </li></ul></ul></ul><ul><ul><ul><li>If Mudra chooses L, Waltz’s choice of L yields 4 which is also one better than the choice of H. </li></ul></ul></ul>Dominant Strategies and Nash Equilibria
  25. 25. Dominant Strategies and Nash Equilibria <ul><li>Mudra will recognize that Waltz has a dominant </li></ul><ul><li>strategy and choose the strategy which will </li></ul><ul><li>yield the highest payoff, given Waltz’s choice of L. </li></ul><ul><li>- Mudra will also choose L since the payoff of </li></ul><ul><li> 7 is one better than the payoff from </li></ul><ul><li> choosing H. </li></ul><ul><li>The strategy choice will be (Mudra: L, Waltz: L) with </li></ul><ul><li>payoffs of 7 to A and 5 to B. </li></ul>
  26. 26. <ul><li>Since Mudra knows Waltz will play L, Mudra’s best play is also L. </li></ul><ul><li>If Waltz knows Mudra will play L, Waltz’s best play is also L. </li></ul><ul><li>Thus, the (Mudra: L, Waltz: L) strategy is a Nash equilibrium: it meets the symmetry required of the Nash criterion. </li></ul><ul><li>No other strategy is a Nash equilibrium. </li></ul>Dominant Strategies and Nash Equilibria
  27. 27. CASE II: APPLICATION OF GAME THEORY IN TWO TELEVISION CHANNELS
  28. 28. Business Example: Rating War 35, 65 10, 90 60, 40 45, 55 55, 45 65, 35 75, 25 10, 90 40, 60 MTV Channel V Game Show TV Drama Music Program Game Show TV Drama Music Program
  29. 29. Business Example: Rating War 35, 65 10, 90 60, 40 45, 55 55, 45 65, 35 75, 25 10, 90 40, 60 MTV Channel V Game Show TV Drama Music Program Game Show TV Drama Music Program
  30. 30. PRISONER ’S DILEMMA
  31. 31. Prisoner’s Dilemma <ul><li>The prisoner's dilemma is a fundamental problem in game theory that demonstrates why two people or groups might not cooperate even if it is in both their best interests to do so. </li></ul>
  32. 32. CASE III: TERRORISM
  33. 33. Case : Terrorism <ul><li>There is terrorism in Thailand. Two hotel buildings were set on fire. One in Chiang Mai and the other one in Phuket. </li></ul><ul><li>There are 500 guests stuck in Chiang Mai hotel and 300 guests in Phuket hotel. </li></ul><ul><li>It is the responsibility of the chief of the Rescue Team stationed in Bangkok to send staff on the site(s) to save lives. </li></ul>
  34. 34. <ul><li>Unfortunately, the team has only one helicopter. </li></ul><ul><li>Since the 2 hotels are too far apart, we have to select only one mission: to rescue people in Chiang Mai OR in Phuket. </li></ul><ul><li>However, there is the other Rescue Team who is our arch rival. It also owns only one helicopter as well. </li></ul>Case : Terrorism
  35. 35. Case : Terrorism <ul><li>Now the leader of the other team has to make the same decision as we do. </li></ul><ul><li>We want to save as many lives as possible and they want to do the same. </li></ul><ul><li>Since both the parties hate each other so they two cannot communicate. </li></ul>
  36. 36. <ul><li>PROBLEM: </li></ul><ul><li>Should we send our team to Chiang Mai </li></ul><ul><li>or Phuket? </li></ul>Case : Terrorism
  37. 37. Case : Terrorism 500 guests in Chiang Mai hotel / 300 guests in Phuket hotel Go Chiang Mai Go Phuket The Rival Team Our Team Go Chiang Mai Go Phuket (250, 250) (300, 500) (500, 300) (150, 150)
  38. 38. <ul><li>Scenario I: Both teams go to Chiang Mai. Each team rescues 250 people. </li></ul><ul><li>Scenario II: Our team goes to Chiang Mai, our rival goes to Phuket. We rescue 500, they rescue 300. </li></ul>Case : Terrorism
  39. 39. <ul><li>Scenario III: Our team goes to Phuket, our rival goes to Chiang Mai. We rescue 300, they rescue 500. </li></ul><ul><li>Scenario IV: Both the teams go to Phuket and rescue 150 per team. </li></ul>Case : Terrorism
  40. 40. Case : Terrorism <ul><li>The answer is… </li></ul>
  41. 41. <ul><li>Wherever our rival goes, we should go to the other place to save most lives possible. </li></ul><ul><li>However, we cannot know their decision and they cannot know ours either. </li></ul><ul><li>There is NO best strategy for both sides because each team can never know where the other team is going. </li></ul>Case : Terrorism
  42. 42. Case : Terrorism <ul><li>Knowing what they know, both teams must go to Chiang Mai. </li></ul><ul><li>To go to Chiang Mai is Dominant strategy , though not the best strategy. </li></ul>
  43. 43. <ul><li>QUES: What if there are only 200 people in </li></ul><ul><li> Phuket hotel? </li></ul>Case : Terrorism ANS: We should always go to Chiang Mai since we will save more lives no matter where the other team is going.
  44. 44. Case : Terrorism 500 guests in Chiang Mai hotel / 200 guests in Phuket hotel Go Chiang Mai Go Phuket The Rival Team Our Team Go Chiang Mai Go Phuket (250, 250) (200, 500) (500, 200) (100, 100)
  45. 45. <ul><li>If there are only 200 people in Phuket Hotel. Then, to go to Chiang Mai is our “Dominant Strategy” . It is also the best strategy possible. </li></ul><ul><li>“ Dominant Strategy” only exists in some situations. </li></ul>Case : Terrorism
  46. 46. Case : Terrorism <ul><li>Dominant Strategy is the rational move that a </li></ul><ul><li>player will make no matter what the other </li></ul><ul><li>side’s decision is . </li></ul><ul><li>Sometimes Dominant Strategy is the best strategy </li></ul><ul><li>in a situation, sometimes it is not. </li></ul><ul><li>Anyway, a player will always use Dominant </li></ul><ul><li>Strategy as his choice. </li></ul>
  47. 47. CONCLUSION <ul><li>Mimics most real-life situations well. </li></ul><ul><li>Solving may not be efficient. </li></ul><ul><li>Applications are in almost all fields. </li></ul><ul><li>Big assumption: players being rational. </li></ul><ul><ul><li>Can you think of “irrational” game theory? </li></ul></ul>
  48. 48. A PRESENTATION BY: Amritanshu Mehra (11DCP008) Kush Aggarwal (11DCP024) Ravi Gupta (11DCP038 )

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