Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Slide 51Slide 52Slide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59ECON 410Continuous Games“’Over’? Did you say ‘over’? Nothing is over until we decide it is!” – Bluto Blutarsky2What’s Left?HW3 Due Thursday, Feb. 14Game Theory, Classes of GamesTuesday’s lecture available onlineHW7Game Theory, Mixed NE & BR GraphseRecitationHW7GameTheoryPractice.xlsmGame Theory, Continuous GamesLDOC lecture & available onlineFinal Practice/LDOC Practice Problems.pdfCournot Practice.xlsmGame Theory, Classes of GamesTuesday’s lecture available onlineHW7Game Theory, Mixed NE & BR GraphseRecitationHW7GameTheoryPractice.xlsmGame Theory, Continuous GamesLDOC lecture & available onlineFinal Practice/LDOC Practice Problems.pdfCournot Practice.xlsm3Class 26 - Continuous GamesExtended Final Exam EIM Sessions:Sunday (4/27): 10am-1pm (somewhere in GA)Monday (4/28): 1:00pm-4:00pm (somewhere in GA)Friday (5/2): 1:00pm-4:00pm (somewhere in GA)Sunday (5/4): 3:00pm-6:00pm (somewhere in GA)Extended Final Exam EIM Sessions:Sunday (4/27): 10am-1pm (somewhere in GA)Monday (4/28): 1:00pm-4:00pm (somewhere in GA)Friday (5/2): 1:00pm-4:00pm (somewhere in GA)Sunday (5/4): 3:00pm-6:00pm (somewhere in GA)44 sides of 8.5 x 11” paper as your Cheat Sheet. 28 MC (~1 Question per class/HW section)4 sides of 8.5 x 11” paper as your Cheat Sheet. 28 MC (~1 Question per class/HW section)Class 26 - Continuous Games5If you were on the overflow list before, you’re still on it....If you were on the overflow list before, you’re still on it....Class 26 - Continuous Games…but the rooms might have changed.4/29/2014 (3:30 class) 4-7pm Overflow room: GA0085/5/2014 (2:00 class) 12-3pm Overflow room: CP201 (Chapman)…but the rooms might have changed.4/29/2014 (3:30 class) 4-7pm Overflow room: GA0085/5/2014 (2:00 class) 12-3pm Overflow room: CP201 (Chapman)Group-Clicker Question (P): Unless you’ve given me a pink Exam Excuse slip (or plan on giving me one), you must take the final exam with your section:2:00 Section: Monday May 5, 12pm-3pm3:30 Section: Tuesday, April 29, 4pm-7pmWhen will you take your final?1. Tuesday, April 29, 4pm-7pm2. Monday May 5, 12pm-3pm7Continuous Normal Form GamesCournot ModelBertrand ModelExtensive Form GamesClass 26 - Continuous Games8Class 26 - Continuous GamesNormal-Form Game:1. A set of players2. Moves each player can make3. Payoffs the players might receive under each combination of moves Cardinality of action space if infiniteIf there are an infinite number of actions, then there must be a corresponding infinite number of payoffs.9Class 26 - Continuous GamesProblem:1. Cardinality of action space is infinite: Define the action space as an interval (or nicely defined set) instead of listing every possibility.Example: “Player 1 has actions {1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11…} Player 2 has actions {1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11…} Player 3 has actions {1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11…}”can be written}3,2,1{,  iNai10Class 26 - Continuous GamesProblem:2. If there are an infinite number of actions, then there must be a corresponding infinite number of payoffs: Use a payoff function, which maps every possible strategy set to a payoff.Example: “If P1 plays 1 and P2 plays 1P1’s payoff=2P2’s payoff=1If P1 plays 1 and P2 plays 2P1’s payoff=5P2’s payoff=1If P1 plays 2 and P2 plays 2P1’s payoff=6P2’s payoff=2”can be written12221;1aaa 11Class 26 - Continuous GamesSteps to Solve for the NE of a 2-Player Discrete Game1. For Player 1, find Player 1’s Best Response (BR) for each possible strategy of Player 2.2. For Player 2, find Player 2’s BR for each possible strategy of Player 1.3. To find the Nash, find the set of strategies that is a simultaneous BR.12Class 26 - Continuous GamesSteps to Solve for the NE of a 2-Player Continuous Game1. For Player 1, derive the BR Function by finding Player 1’s BR for each possible strategy of Player 2.2. For Player 2, derive the BR Function by finding Player 2’s BR for each possible strategy of Player 1.3. To find the Nash, find the set of strategies that simultaneously solves the BR functions.13Class 26 - Continuous Gamesq1q2BR1BR2*1 20.5 5q q=- +*2 10.5 5q q=- +22* *00.5( ) 5.5 5qq = +- +-2 2* *0.25 2.5 5q q= - +2*0.75 2.5q =*23.33q =*1(0.5) 3.3( ) 53q =- +*13.33q =14Class 26 - Continuous GamesGroup-Clicker Question (P): A firm with market power faces an inverse demand curve of p(q)=10-q and a constant marginal cost of 2. What quantity will maximize the firm’s profit (i.e. what is it’s “best response” to this scenario)?1. q*=42. q*= 63. q*= 84. q*= 16Group-Clicker Question (P): A firm with market power faces an inverse demand curve of p(q)=10-q-a (where a is a constant) and a constant marginal cost of 2. What quantity will maximize the firm’s profit (i.e. what is it’s “best response” to this scenario)?1. q*=(8-a)/22. q*=(8+a)/23. q*= 44. q*= 8-(a/2)17Class 26 - Continuous GamesCournot GameThe baseline Cournot Game is a normal-form game widely used in theoretical models of oligopoly in which the industry structure is such that: 1. Firms produce identical goods.2. Firms commit irreversibly to a certain quantity level, allowing the market price to be dictated by demand.3. The more each firm produces, the lower the market price needs to be to sell all the good.4. Each firm is profit maximizing.18Class 26 - Continuous GamesCournot GameThe baseline Cournot Game is a normal-form game widely used in theoretical models of oligopoly in which the industry structure is such that: 1. Firms produce identical goods.2. Firms commit irreversibly to a certain quantity level, allowing the market price to be dictated by demand.3. The more each firm produces, the lower the market price needs to be to sell all the good.4. Each firm is profit maximizing.19Class 26 - Continuous GamesMarket Power ModelOur Market Power Model is a model of firm profit-maximizing behavior in which the following assumptions hold:1. Consumers purchase goods according to their demand functions.2. A firm cost-minimizes by selecting inputs