3. Draw the normal-form matrix of each of the following extensive-form games C0,0 E 2,2 F3,4...
QUESTION 6 Only! 4) Draw the normal-form matrix for each of the following extensive-form games 2 E 2,2 2 F3,4 2 4, 0 0 -L-I 3,2 6) Use your normal-form matrix for (4b) above. Assume that ơ,-( ). , a. Find ui(IU, ơ2) and ui(ID, ơz). b. Assume 0 (IU)-2/3 and 01(ID)-1/3 Find player l's expected payout. Then find player 2's expected payout. Which is higher?
Game Theory: I only need help with 5 (a & b). Will rate for correct and descriptive answers! 4 Draw the normal-form matrix for each of the following extensive-form games. C 0,0 E 2,2 F3,4 1 U 4,0 (b) 11 3,2 5) Use your normal-form matrix for (4a) above. Assume that ơi-( Find the following: , , ). a. ui(oi, CE
LUSE Consider the following extensive-form games. (a) 2,6 G 3.8 7,9 →1.2 21 10.4 0,5 40 N 8,3 (b) ► 2, 2,2 3,2,1 5,0,0 - 1, 2,6 Y 7,5,5 EXERCISES Exercises 15 1. Consider the following extensive-form games. (a) 2,6 12,1 K 10,4 I 0,5 M_ 4,0 (b) N8,3 1 0 2,2,2 3,2,1 5,0,0 1, 2,6 Y 7,5,5 (c) 4, 3,1 Solve the games by using backward induction.
Game Theory: I only need help with 6 (a & b)! Will rate for correct and descriptive answers! Draw the normal-form matrix for each of the following extensive-form games C 0,0 E 2,2 F3,4 4, 0 3,2 6) Use your normal-form matrix for (4b) above. Assume that ơ,-( ). , a. Find ui(IU, ơ2) and ui(ID, ơ2). b. Assume 0 (IU)-2/3 and 0(ID)-1/3 Find player l's expected payout. Then find player 2's expected payout. Which is higher?
Consider the following extensive form game P1 RP:2 L2 R2 L1 R1 (2,2) (0,3) 1. How many sub-games are there in this game? What is the Subgame Perfect Equilibrium? 2. Represent this game as a Normal form game and find all pure strategy Nash Eq. Is there a mixed Nash eq. in this game? If yes, show one. If not, argue why not 3. Now assume that P2 cannot observe P1's action before he makes his move. As such, he...
For each of the following normal-form game below, find the rationalizable strategy profiles, using IENBRS, Iterated Elimination of Never a Best Response Strategies. (1)/(2) L C R (3,2) (4,0) (1,1) (2,0) (3,3) (0,0) (1,1) (0,2) (2,3)
4. (General Extensive Form Game ID Suppose the following general extensive-form game. Player 1 Player 2 (0, 4) (4,0 (4, 0) (0, 4) (a) Represent this game in normal form by using a matrix, and find all pure strategy (Bayesian Nash equilibrium (equilibria) b) Does a pure strategy perfect Bayesian equilibrium exist? If so, show it (or them). If not, prove it.
Calculate the probability of the following events A the first number is 2 or 3 or 4 E the second digit is 3 or less F the second digit is 4 or greater PIE or F) P(E and F) P(A) P( A and E) P( A and F) P( A and E)+P( Aand F) 2 Dice Sample Space 1,1 2,1 3,1 4,1 5,1 1,6 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 1,5 2,4 3,4 4,4...
3. Consider the following two-player game in strategic form LM R A 2,2 2,2 2,2 В 3,3 0,2 0,0 С 0,0 3,2 0,3 This game will demonstrate several methods for ruling out possible mixed- strategy equilibria (a) What are the pure strategy equilibria? (b) Show that there does not exist an equilibrium in which Player 1 (the row player) assigns strictly positive probability to A, to B, and to C. (c) Show that there does not exist an equilibrium in...
1.2 Find a stable marriage matching for the instance defined by the following ranking matrix. Break a tie using the alphabetic order. Draw a matrix after each iteration, and describe what happens in the iteration, using the format of Figure 10.12. When the process is over, write the matching a B y S A 1,3 1,4 2,2 4,1 B 2,3 4,1 1,4 2,2 C 3,2 3,4 3,3 3,1 D 4,3 2,2 4,1 1,4 AN