Tony | ||||
X | Y | Z | ||
Bill | A | (10,30) | (0,20) | (20,30) |
B | (15,35) | (10,40) | (10,40) | |
C | (25,25) | (5,25) | (5,25) |
Tony
X Y Z
Bill A (10,30)
(0,20) (20,30)
B (15,35) (10,40)
(10,40)
C (25,25) (5,25) (5,25)
Now we have two player (Bill, Tony) where strategy set for each player is as follows
Bill={A,B,C}
Tony={X,Y,Z}
When Bill choose to play A then best response of Tony would be either X or Z because in this scenario Tony will have higher payoff of 30
When Tony chooses to play X then best response of Bill is C as in this case Bill have higher payoff from strategy C payoff of 25
When Tony chooses to play Z then best response of Bill is A as in this case Bill have higher payoff from strategy A payoff of 20
Hence combination of (A,Z) is Pure strategy Nash Equilibrium because it completes the cycle such as if Bill chooses A then Tony responds with Z and if Tony chooses Z then Bill responds with A.
When Bill choose to play B then best response of Tony would be Y or Z because in this scenario Tony will have higher payoff of 40
When Tony chooses to play Y then best response of Bill is B as in this case Bill have higher payoff from strategy B payoff of 10
Hence combination of (B,Y) is Pure strategy Nash Equilibrium because it completes the cycle such as if Bill chooses B then Tony responds with Y and if Tony chooses Y then Bill responds with B.
When Bill choose to play C then best response of Tony would be
either X or Y or Z because in this scenario Tony will have higher
payoff of 25
When Tony chooses to play X then best response of Bill is C as in this case Bill have higher payoff from strategy C payoff of 25
When Tony chooses to play Y then best response of Bill is B as in this case Bill have higher payoff from strategy A payoff of 10
When Tony chooses to play Z then best response of Bill is A as in
this case Bill have higher payoff from strategy A payoff of 20
Hence combination of (C,X) is Pure strategy Nash
Equilibrium because it completes the cycle such as if Bill
chooses C then Tony responds with X and if Tony chooses X then Bill
responds with C.
Therefore in total we have 3 Pure strategy Nash Equilibrium and they are as follows
(C,X); (B,Y); (A,Z)
2 Consider the following normal form game. Bill's payoffs are given first. Find all pure strategy Nash equilibrium....
#1. (30 points) Consider the following normal-form game. (a) (10 points) Find all pure strategy Nash equilibria. (b) (20 points) Find all mixed strategy Nash equilibria. EFG | A 0,0 3, 4, 1 B5,5 0,01,-1 C 2.0 1,0 2,6 D 1,0 1,4 6,3
Consider the following extensive-form game with two players, 1 and 2. a). Find the pure-strategy Nash equilibria of the game. [8 Marks] b). Find the pure-strategy subgame-perfect equilibria of the game. [6 Marks] c). Derive the mixed strategy Nash equilibrium of the subgame. If players play this mixed Nash equilibrium in the subgame, would 1 player In or Out at the initial mode? [6 Marks] [Hint: Write down the normal-form of the subgame and derive the mixed Nash equilibrium of...
PLZ TYPE THE ANSWER NOT HAND WRITEING CUZ CANT READ IT Q3 Consider the game below between Tony and Bil Each has two strategies. Tony's payoffs are given first. The game has a unique Nash equilibrium. Bill Drink Pass Safe-3, 3 3, -3 Risky 3, -33, 3 (1). What is the mixed strategy Nash equilibrium? What is Tony's expected payoff? What is Bill's expected payoff? (20 points) (2). Recently, the rules of the game have changed. If Tony selects Safe...
PLZ TYPE THE ANSWER NOT HAND WRITEING CUZ CANT READ IT Q3 Consider the game below between Tony and Bil Each has two strategies. Tony's payoffs are given first. The game has a unique Nash equilibrium. Bill Drink Pass Safe-3, 3 3, -3 Risky 3, -33, 3 (1). What is the mixed strategy Nash equilibrium? What is Tony's expected payoff? What is Bill's expected payoff? (20 points) (2). Recently, the rules of the game have changed. If Tony selects Safe...
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