Most people say that Shakespeare rocked merely because most people say that Shakespeare rocked Mokokoma Mokhonoana Group Clicker Question 1 pt Are you here today 1 2 ECON 410 Yes No Game Theory Classes of Games 0 0 What s Left 2 Game Theory Classes of Games today s lecture available online HW7 Game Theory Mixed NE BR Graphs eRecitation HW7 GameTheoryPractice xlsm Game Theory Continuous Games LDOCHW3 lecture availableFeb online Due Thursday 14 Final Practice LDOC Practice Problems pdf Cournot Practice xlsm Class 25 Classes of Games 3 Normal Form Game 1 Set of players Who is playing 2 Strategy space of each player How they can play 3 Payoff each player receives given any strategy profile What they will win given each combination of their strategy and their opponents strategies Class 25 Classes of Games 4 Nash Equilibrium NE Solution Concept One prediction on how a game will resolve itself is the Nash Equilibrium Solution Concept Specifically a Nash Equilibrium is a set of strategies such that no player has an incentive to unilaterally deviate Class 25 Classes of Games 5 Steps to Solve for the NE of a 2 Player Discrete Game 1 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 Class 25 Classes of Games 6 Finding the Pure Strategy NE in a Game Matrix To solve for the Nash Equilibria of a normal form game represented by a game matrix 1 2 3 4 5 Assume Player 2 plays one of her strategies Underline the highest possible Player 1 payoff s given that Player 2 is playing this strategy The strategy that corresponds to this payoff is called Player 1 s best response to Player 2 s action Repeat this process until you have assumed Player 2 has played all her strategies Now assume Player 1 plays one of his strategies Underline the highest possible Player 2 payoff s given that Player 1 is playing this strategy The strategy that corresponds to this payoff is called Player 2 s best response to Player 1 s action Repeat this process until you have assumed Player 1 has played all his strategies The cell s that has both payoffs underlined corresponds to a pure strategy Nash equilibrium Note there can be multiple pure strategy Nash equilibria There can also be no pure strategy Nash equilibrium Class 25 Classes of Games 7 Example Player 2 Player 1 a b A 6 6 0 9 B 9 0 1 1 Class 25 Classes of Games 8 Example Player 2 Player 1 a b A 6 6 0 9 B 9 0 1 1 Class 25 Classes of Games 9 Example Player 2 Player 1 a b A 6 6 0 9 B 9 0 1 1 Class 25 Classes of Games 10 Example Player 2 Player 1 a b A 6 6 0 9 B 9 0 1 1 Class 25 Classes of Games 11 Example Player 2 Player 1 a b A 6 6 0 9 B 9 0 1 1 Class 25 Classes of Games 12 Example Player 2 Player 1 a b A 6 6 0 9 B 9 0 1 1 Class 25 Classes of Games 13 Example Player 2 Player 1 a b A 6 6 0 9 B 9 0 1 1 Class 25 Classes of Games 14 Class 25 Classes of Games 15 Prisoner s Dilemma The category of games in which players have a dominant strategy to cheat preventing beneficial cooperation from occurring Class 25 Classes of Games 16 http www youtube com watch v p3Uos2fzIJ0 stop at 2 50 Class 25 Classes of Games 17 Prisoner s Dilemma The category of games in which players have a dominant strategy to cheat preventing beneficial cooperation from occurring Girl Steal Split 50 50 0 100 Steal 100 0 0 0 Guy Split Class 25 Classes of Games 18 Prisoner s Dilemma The category of games in which players have a dominant strategy to cheat preventing beneficial cooperation from occurring Girl Steal Split 50 50 10 100 Steal 100 10 0 0 Guy Split Class 25 Classes of Games 19 Prisoner s Dilemma The category of games in which players have a dominant strategy to cheat preventing beneficial cooperation from occurring Girl Steal Split 50 50 10 100 Steal 100 10 0 0 Guy Split Class 25 Classes of Games 20 Prisoner s Dilemma The category of games in which players have a dominant strategy to cheat preventing beneficial cooperation from occurring Girl Steal Split 50 50 10 100 Steal 100 10 0 0 Guy Split Class 25 Classes of Games 21 Prisoner s Dilemma The category of games in which players have a dominant strategy to cheat preventing beneficial cooperation from occurring Girl Steal Split 50 50 10 100 Steal 100 10 0 0 Guy Split Class 25 Classes of Games 22 Prisoner s Dilemma The category of games in which players have a dominant strategy to cheat preventing beneficial cooperation from occurring Girl Steal Split 50 50 10 100 Steal 100 10 0 0 Guy Split Class 25 Classes of Games 23 Prisoner s Dilemma The category of games in which players have a dominant strategy to cheat preventing beneficial cooperation from occurring Girl Steal Split 50 50 10 100 Steal 100 10 0 0 Domina nt Strateg y Guy Split Dominant Strategy Class 25 Classes of Games 24 Prisoner s Dilemma The category of games in which players have a dominant strategy to cheat preventing beneficial cooperation from occurring Girl Steal Split 50 50 10 100 Steal 100 10 0 0 Domina nt Strateg y Guy Split Dominant Strategy Class 25 Classes of Games 25 Prisoner s Dilemma The category of games in which players have a dominant strategy to cheat preventing beneficial cooperation from occurring Class 25 Classes of Games 26 Prisoner s Dilemma The category of games in which players have a dominant strategy to cheat preventing beneficial cooperation from occurring Class 25 Classes of Games 27 Prisoner s Dilemma The category of games in which players have a dominant strategy to cheat preventing beneficial cooperation from occurring Class 25 Classes of Games 28 Prisoner s Dilemma The category of games in which players have a dominant strategy to cheat preventing beneficial cooperation from occurring Class 25 Classes of Games 29 Prisoner s Dilemma The category of games in which players have a dominant strategy to cheat preventing beneficial cooperation from occurring Girl Steal Split 50 50 10 100 Steal 100 10 0 0 Guy Split Class 25 Classes of Games 30 Prisoner s Dilemma The category of games in which players have a dominant strategy to cheat preventing beneficial cooperation from occurring Girl Steal Split 50 50 10 100 Steal 45 10 20 0 Guy Split Class 25 Classes of Games 31 SELF Clicker Question P Everyone in the class must decide whether to gamble 10 clicker points from their Clicker Total If less than 90 decide …