Section-8-Game-Theory-Mixed-Strategy-NE-slides

Section-8-Game-Theory-Mixed-Strategy-NE-slides - Game...

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Unformatted text preview: Game Theory: Mixed-Strategy Nash Equilibrium Todd Sarver Northwestern University Econ 310-2 Fall 2011 Todd Sarver (Northwestern University) Game Theory Econ 310-2 Fall 2011 1 / 31 Outline 1 Games without Pure-Strategy NE 2 Mixed Strategies Definition Expected Utility Mixed-Strategy Nash Equilibrium 3 Tricks for Finding MSNE 4 Combining IESDS with MSNE 5 Existence of MSNE Todd Sarver (Northwestern University) Game Theory Econ 310-2 Fall 2011 2 / 31 Not All Games Have a Pure-Strategy Nash Equilibrium Example (Penalty Kick) Suppose the match comes down to a penalty kick. . . Kicker L R Goalkeeper L 1 ,- 1- 1 , 1 R- 1 , 1 1 ,- 1 Todd Sarver (Northwestern University) Game Theory Econ 310-2 Fall 2011 3 / 31 Not All Games Have a Pure-Strategy Nash Equilibrium Example (Penalty Kick) Suppose the match comes down to a penalty kick. . . Kicker L R Goalkeeper L 1 ,- 1- 1 , 1 R- 1 , 1 1 ,- 1 There is no Pure-Strategy Nash Equilibrium in this game. (Notice this game is strategically equivalent to Matching Pennies.) Todd Sarver (Northwestern University) Game Theory Econ 310-2 Fall 2011 3 / 31 Not All Games Have a Pure-Strategy Nash Equilibrium Example (Penalty Kick) Suppose the match comes down to a penalty kick. . . Kicker L R Goalkeeper L 1 ,- 1- 1 , 1 R- 1 , 1 1 ,- 1 There is no Pure-Strategy Nash Equilibrium in this game. (Notice this game is strategically equivalent to Matching Pennies.) What predictions can we make in games like this one? Should we consider a different solution concept than NE? Todd Sarver (Northwestern University) Game Theory Econ 310-2 Fall 2011 3 / 31 Not All Games Have a Pure-Strategy Nash Equilibrium Example (Penalty Kick) Suppose the match comes down to a penalty kick. . . Kicker L R Goalkeeper L 1 ,- 1- 1 , 1 R- 1 , 1 1 ,- 1 There is no Pure-Strategy Nash Equilibrium in this game. (Notice this game is strategically equivalent to Matching Pennies.) What predictions can we make in games like this one? Should we consider a different solution concept than NE? Or, instead, should we consider allowing for more strategies? Todd Sarver (Northwestern University) Game Theory Econ 310-2 Fall 2011 3 / 31 Example (Penalty Kick) Kicker L R Goalkeeper L 1 ,- 1- 1 , 1 R- 1 , 1 1 ,- 1 Lets think about what really happens in this game to get an idea of how to proceed. Todd Sarver (Northwestern University) Game Theory Econ 310-2 Fall 2011 4 / 31 Example (Penalty Kick) Kicker L R Goalkeeper L 1 ,- 1- 1 , 1 R- 1 , 1 1 ,- 1 Lets think about what really happens in this game to get an idea of how to proceed. If a kicker always kicks in one direction, he becomes predictable and the goalkeeper will be able to block his kick. Todd Sarver (Northwestern University) Game Theory Econ 310-2 Fall 2011 4 / 31 Example (Penalty Kick) Kicker L R Goalkeeper L 1 ,- 1- 1 , 1 R- 1 , 1 1 ,- 1 Lets think about what really happens in this game to get an idea of how to proceed....
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Section-8-Game-Theory-Mixed-Strategy-NE-slides - Game...

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