Game Theory

1. Use a generalized version (payoffs as variables - not specific numbers) of an anti- coordination game to prove that anti-coordination games have a Mixed Strategy Nash Equilibrium (MSNE). (Clue: The game of Chicken is an example of an anti-coordination game.)Street : O= center of street R = 14 way down street Example of on, outcome : Plat O ( left side ) P2 at O ( sight side ) p3 at R The diagram shows regions of demand given this outcome :Pl gets 50% P2 get 14 of 50% = 12.5% P3 gets $/4 of 50% = 37.5% Note : these are payoffs AFTER " nature " . Why did IV get 50% : 12 get 12.5% ? - Nature chooses , so you need to do expected vele : E( PI ) : 2 ( 50 ) + E ( 12 . 5 ) = 31.25% E ( 92 ) = E ( 50) + E ( 12.5) = 31.25% So if more than are player shows up at a location , you need to calculate expected values . Then you can draw gamefree / normal Forms : PI 2 P3 O L R R R P2 P2 O 31.25, 31.25 37.5 Simultaneous Zoom in move game 31.25, 31.25, 37.5 each outcome has 3 lexpected ) payotts.Once you have all outcares you can set up 3 equations wl 3 unknowns make players indifferent between O and R