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Game Theory Overheads

Game Theory Overheads. Games. A game is a formal representation of a situation in which a number of decision makers (players) interact in a setting of strategic interdependence. By that, we mean that the welfare of each decision maker depends not only on her own actions,

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Game Theory Overheads

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  1. Game Theory Overheads

  2. Games A game is a formal representation of a situation in which a number of decision makers (players) interact in a setting of strategic interdependence By that, we mean that the welfare of each decision maker depends not only on her own actions, but also on the actions of the other players

  3. Structure of a Game Players or decision makers firms consumers poker or chess players

  4. Structure of a Game Rules of the game Who moves when What do players know and when What actions are available at various points

  5. Structure of a Game Outcomes For each possible set of actions by the players, what is the outcome of the game?

  6. Structure of a Game Payoffs What are the payoffs with each outcome? How do the player's rank the outcomes?

  7. Structure of a Game Players or decision makers Rules of the game Outcomes Payoffs

  8. Nash Equilibrium and Game Theory A set of strategies in a game is called a Nash equilibrium if, holding the strategies of all other firms constant, no firm can obtain a higher payoff by choosing a different strategy In a Nash equilibrium, no firm wants to change its strategy

  9. The Prisoner’s Dilemma Two criminals Al “Scarface” Capone Jack “Machine Gun” McGurn Major crime Murder of 7 people on St. Valentine’s Day

  10. Minimal evidence connecting them to massacre Plenty of evidence linking them to bootlegging

  11. Police interrogate them in separate rooms Police offer them each a deal Finger the other guy, and walk if he don’t talk You both stay mum, we lock the both of you up for a year for bootlegging You both talk, its 20 years in the slammer But if he talks and you give us the silent treatment, its 40 years at hard labor for you

  12. The Game in Matrix Form Machine Gun Collaborate Stay Mum Al gets 20 Jack gets 20 Al walks Jack gets 40 Collaborate Scarface Al gets 40 Jack walks Al gets 1 Jack gets 1 Stay Mum

  13. Structure of a Game Rules of the game Who moves when -- at the same time What do players know and when -- nothing What actions are available at various points Collaborate Stay mum

  14. Machine Gun Collaborate Stay Mum Collaborate Scarface Stay Mum Structure of a Game Outcomes Al gets 20 Jack gets 20 Al walks Jack gets 40 Al gets 40 Jack walks Al gets 1 Jack gets 1

  15. Structure of a Game Payoffs What are the payoffs with each outcome? Years in the slammer for the player How do the player's rank the outcomes? Players prefer less years in the pen

  16. Best response for Al “Scarface” Capone What if Jack stays mum?

  17. Machine Gun Stay Mum Al walks Jack gets 40 Collaborate Scarface Al gets 1 Jack gets 1 Stay Mum Jack stays mum

  18. Al gets the least years by collaborating What if Jack collaborates?

  19. Machine Gun Collaborate Al gets 20 Jack gets 20 Collaborate Scarface Al gets 40 Jack walks Stay Mum Jack collaborates

  20. Al gets the least years by collaborating Al has found a dominant strategy for this game Al sells out and collaborates

  21. Best response for “Machine Gun” McGurn What if Al stays mum?

  22. Machine Gun Collaborate Stay Mum Scarface Al gets 40 Jack walks Al gets 1 Jack gets 1 Stay Mum Al stays mum

  23. Jack gets the least years by collaborating What if Al collaborates?

  24. Machine Gun Collaborate Stay Mum Al gets 20 Jack gets 20 Al walks Jack gets 40 Collaborate Scarface Al collaborates

  25. Jack gets the least years by collaborating Jack has found a dominant strategy for this game Jack sells out and collaborates

  26. In fact Both Al and Jack sell out and get 20 years

  27. Dominant strategies A strategy that is best for a player, no matter what strategy is chosen by the competing player is called a dominant strategy A dominant strategy is a strategy that is best for a player regardless of the strategy of the other player

  28. If a player has a dominant strategy in a game, we can assume that the player will play that strategy If each player in a game has a dominant strategy, it is easy to find the equilibrium of the game It is simply the outcome that occurs when each player plays the dominant strategy

  29. Equilibrium in the prisoner’s dilemma Al and Jack get 20 years If both stayed mum, each would get 1 year

  30. The Turkey Pricing game Two stores Hy-Vee Fareway Rules of the game Game played 7 days before Thanksgiving Turkeys are the same quality

  31. Stores place a weekly advertising supplement in the local paper stating a price for turkeys The stores do not know the price that will be submitted by the other store Two possible actions for each store Low Price High Price

  32. Outcome Matrix Hy-Vee Low Price High Price F  1000 H  1000 F  1500 H  500 Low Price Fareway F  500 H  1500 F  1200 H  1200 High Price

  33. Payoffs Each store gets the number in the table in dollars Store managers prefer more dollars to less

  34. Best response for Fareway What if Hy-Vee chooses a low price?

  35. Hy-Vee Low Price F  1000 H  1000 Low Price Fareway F  500 H  1500 High Price Hy-Vee chooses low

  36. Fareway gets the most dollars with a low price What if Hy-Vee chooses a high price?

  37. Hy-Vee High Price F  1500 H  500 Low Price Fareway F  1200 H  1200 High Price Hy-Vee chooses high

  38. Fareway gets the most money with a low price Fareway has a dominant strategy for this game Fareway chooses a low price

  39. Best response for Hy-Vee What if Fareway chooses a low price?

  40. Hy-Vee Low Price High Price F  1000 H  1000 F  1500 H  500 Low Price Fareway Fareway chooses low

  41. Hy-Vee gets the most dollars with a low price What if Fareway chooses a high price?

  42. Hy-Vee Low Price High Price Fareway F  500 H  1500 F  1200 H  1200 High Price Fareway chooses high

  43. Hy-Vee gets the most money with a low price Hy-Vee has a dominant strategy for this game Hy-Vee chooses a low price

  44. Equilibrium in the turkey pricing game Hy-Vee and Fareway choose low prices If both chose high prices, individual and total profits would be higher The outcome (high, high) is Pareto superior to the outcome (low, low)

  45. An outcome is said to be Pareto superior to another outcome if both both players are better off with the Pareto superior outcome

  46. Other examples of the prisoner’s dilemma Arms race Advertising tobacco eye-glasses Common resources oil field pasture

  47. Noncooperative oligopoly as a game Zucchini pricing game 2 players or firms -- Hank and Ken Actions: number of zucchini brought to market Firm doesn’t know other firm’s quantity Outcome is market price Payoff to each firm is its profit given price and costs

  48. Outcome Matrix Ken 3 boxes 4 boxes H  $36 K  $36 H  $30 K  $40 3 boxes Hank H  $40 K  $30 H  $32 K  $32 4 boxes

  49. Ken chooses 3 Ken 3 boxes H  $36 K  $36 3 boxes Hank H  $40 K  $30 4 boxes

  50. Ken chooses 4 Ken 4 boxes H  $30 K  $40 3 boxes Hank H  $32 K  $32 4 boxes

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