[a] Let Game 1 (left) and Game 2 (right) - which is different from Game 1...

  

 

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[a] Let Game 1 (left) and Game 2 (right) - which is different from Game 1 - be the games given by Player 2 R L Player 1 Ta, bc,d Be,fg,h Consider Game 3 defined by Player 1 T B L Player 2 Player 2 L R Player 1 Ta+a²₂b+bc+c²₁d+d Be+ef+fg+g',h+h' R e.d g.h that is, the players' payoffs are the sum of their payoffs in Games 1 and 2. Suppose that (T. L) is the unique pure-strategy Nash equilibrium of Game 1 and that (T, L) is also the unique pure-strategy Nash equilibrium of Game 2. Is (T. L) also an equilibrium of Game 3? Is it unique? Explain your work! [b] Let Game 4 (left) and Game 5 (right) - which is different from Game 4 - be the games given by Player 2 R L Player 1 Ti, j||k₂l| Bm, no,r Consider Game 6 defined by Player 1 T B Player 2 L R k, l' Bm, no,r Player 1 T Player 2 L m', n' R O,T that is, player l's payoffs are from Game 4 and player 2's payoffs from Game 5. Now suppose that (p, q) is the unique mixed strategy Nash equi- librium of Game 4, where 0 < p < 1 is the probability that player 1 plays T, and 0 <q <1 is the probability that player 2 plays L. Similarly, suppose that (p', q') is the unique mixed strategy Nash equilibrium of Game 5, where 0 < p < 1 is the probability that player 1 plays T, and 0< d < 1 is the probability that player 2 plays L. Finally, suppose also that p is different from p' and q is different from q. Only one of the following statements about the unique mixed strategy Nash equilibrium of Game 6 is correct: 1. player 1 assigns probability p' to T and player 2 assigns prob- ability q to L. 2. player 1 assigns probability p to T and player 2 assigns prob- ability q' to L. 3. player 1 assigns probability p to T and player 2 assigns prob- ability q to L. 4. player 1 assigns probability p' to T and player 2 assigns prob- ability q' to L. Choose the statement [1]-[4] that you think is the correct one and explain why. [a] Let Game 1 (left) and Game 2 (right) - which is different from Game 1 - be the games given by Player 2 R L Player 1 Ta, bc,d Be,fg,h Consider Game 3 defined by Player 1 T B L Player 2 Player 2 L R Player 1 Ta+a²₂b+bc+c²₁d+d Be+ef+fg+g',h+h' R e.d g.h that is, the players' payoffs are the sum of their payoffs in Games 1 and 2. Suppose that (T. L) is the unique pure-strategy Nash equilibrium of Game 1 and that (T, L) is also the unique pure-strategy Nash equilibrium of Game 2. Is (T. L) also an equilibrium of Game 3? Is it unique? Explain your work! [b] Let Game 4 (left) and Game 5 (right) - which is different from Game 4 - be the games given by Player 2 R L Player 1 Ti, j||k₂l| Bm, no,r Consider Game 6 defined by Player 1 T B Player 2 L R k, l' Bm, no,r Player 1 T Player 2 L m', n' R O,T that is, player l's payoffs are from Game 4 and player 2's payoffs from Game 5. Now suppose that (p, q) is the unique mixed strategy Nash equi- librium of Game 4, where 0 < p < 1 is the probability that player 1 plays T, and 0 <q <1 is the probability that player 2 plays L. Similarly, suppose that (p', q') is the unique mixed strategy Nash equilibrium of Game 5, where 0 < p < 1 is the probability that player 1 plays T, and 0< d < 1 is the probability that player 2 plays L. Finally, suppose also that p is different from p' and q is different from q. Only one of the following statements about the unique mixed strategy Nash equilibrium of Game 6 is correct: 1. player 1 assigns probability p' to T and player 2 assigns prob- ability q to L. 2. player 1 assigns probability p to T and player 2 assigns prob- ability q' to L. 3. player 1 assigns probability p to T and player 2 assigns prob- ability q to L. 4. player 1 assigns probability p' to T and player 2 assigns prob- ability q' to L. Choose the statement [1]-[4] that you think is the correct one and explain why.

Answer rating: 100% (QA)

Answer 3 player 1 assigns probability p to T and player 2 assigns probability q to L The unique mixed strategy Nash equilibrium of Game 6 is determined by the probabilities assigned to each action by ... View the full answer