Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper scissors гock 0. -3 1. 0. раper scissors -1 (a) Show that xT= (,) and yT= (;,) together are not a Nash equilibrium 3 3 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.

Consider the two period Repeated Prisoner's Dilemma Game where each player is interested in the SUM of the payoffs she gets in each period. Players see the outcome after the play in each period. (The period payoffs are 10,5,1,0.) (i) Write out this game in its strategic form. (ii) Find all Nash equilibria and all Subgame Perfect Nash Equilibria.

Player 2 Left Right P1: $4 Player 1 Up P2: $1 P1: $10 Down P2:s10 Which of the Nash Equilibrium to this game are efficient? [Check all that apply] A) (up, left) B) (down, left) C None are efficient (D) (up right) E (down, right) Last saved 4:31:15 PM P1:S1 P2: $6 P1: $0 P2: $11 Grading

Consider the following sequential game: 1 O D,L U.L U,R U D,R D (0,2) 2 L What is the subgame perfect Nash equilibrium of this game? R. (-1,-1) (1,1)