In the following symmetric general sum game (2, 2) (0,0) (0,0) (0,0) (0,0) (2, 2) (0,0) (2,2) (0, 0) (i) Find all pure Nash equilibria. (ii) Find all mixed Nash equilibria in which all probabilities are positive. (vi) Which of these are evolutionary stable strategies?
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- 5,3 4,4 3,6 7,6 Find the pure strategy nash equilibriaAsap(ii) A mixed strategy profile (p, q) is one in which p = (p,P2.... P) is the mixed strategy of player 1, and q- (g1, q2,..q4) is the mixed strategy of player 2. Show that if p, >0 in a Nash equilibrium profile (p*, q*), the player 2 must also play i with strictly positive probability q'; > 0. (State clearly any theorem you use to show this. You are not required to justify the theorem.) %3D
- In this game, (80, 50) 52% a) (R, N) b) (R, R) c) (S, N) d) (R, P) S is a Nash equilibrium First Player (20,68) 12% R P Second Player N (90,70) 36%Q2 Consider the following game. (a) Find all pure-strategy Nash equilibria. (b) Find all mixed-strategy Nash equilibria. 2, 4 6, 0 5,1 1,9 A ВWith what probability does player 1 play Down in the mixed strategy Nash equilibrium? (Input your answer as a decimal to the nearest hundredth, for example: 0.14, 0.56, or 0.87). PLAYER 1 Up Down PLAYER 2 Left 97,95 47, 33 Right 8,43 68,91
- Suppose there are two players playing a game with east or west and south and nerth ways. Find the expected Nash equilibrium by using the concept of probabilities. Player X Left[L) Right|R) Player Y Up(U) (5,6) (0,8) (4,6) Down[D) (0,9)Question 1 Consider the following game. Find all Nash equilibria, subgame perfect Nash equilibria, and weak perfect Bayesian equilibria in pure and mixed strategies. a P2 (12, 12) b (12,-8) (7.-3) P1 m d (-3,2) r P2 C (2,7) d (22,17)8) Find the mixed strategy Nash equilibrium of the following normal form game. Player 2 T1 T2 T3 2, 3 3, 5 1, 1 Player 1 S2 1, 4 4, 3 0, 5 Player 1 attaches probability (S1, S2) = () and Player 2 attaches probability (T1, T2, T3) = ( ) Player 1 attaches probability (S1, S2) = (.) and Player 2 attaches probability (T1, T2, T3) = (qi, 42, 1 – q1 – 92) where q1 , and 0 < q2 S %3D Player 1 attaches probability (S1, S2) = (G,;) and Player 2 attaches probability (T1, T2, T1) = (qı.42, 1 – q1 – 42) where 0 < qi <, and q2 = 3. Player 1 attaches probability (S1, S) = (;, -) and player 2 attaches probability (T1, T2, T3) = (1.42, 1- q1- 42) where 0 s qı s and q2 =
- Which is the correct mixed strategy Nash equilibrium for the below game? A B Confess Confess (3,2) Doesn't (0,0) confess a. (2/5); (3/5) b. (1/4); (3/4) c. (1/2); (1/2) d. (1/3); (2/3) Doesn't confess (0,0) (2,3)which is the nash equilibrium? small pig does press large pig does press (20, 130), small pig doesn't press large pig does press (140, 10), small pig does press large pig doesn't press (-5, 150), small pig does not press large pig doesn't press (0,0).Two network TV channels compete in the same market. They can broadcast a sitcom or a game show in prime time. Their objective is to maximize viewership in their local market. The outcomes corresponding to each of their strategies is shown below. Use your mouse to point and click on the Nash equilibrium outcome(s). [There may be more than one so make sure you work out all the best response strategies]. Network 1 Sitcom O Game show O Sitcom Network 2 55%,45% 50%,50% Game show 52%,48% O 45%,55% O