Question

or 5. 1. Consider the following game tree. In this tree, a player, say Player 3, has an information set with three nodes, I, II, and III in it. Explain whether each of the following is true or false. (a) Node I is Player 3's decision node, but node II is Player 2's decision node. (b) Player 3 has three actions at node III and two at node I (c) Player 3 has exactly two actions at node III, labeled as a, b, and two actions at node I, labeled as b, c. (d) The game is one of imperfect information (e) When she is called upon to move, Player 3 cannot distinguish node I from node IIl or node II from node III

Answer 1

given data

x:y:z = a:b:c

(a) Assume that the payoff of the best option is 3, the second best 2 and the worst is 1. Playerl's actions are which alternative to remove and player 2's which of the remaining two to choose 3 (b) Player 1 has three pure strategies while player 2 has eight (2 actions in each of three information sets.) (c) Let ryz be a strategy for player 2 where r is what he does following the removal of a, y for b and z for c so that we can use the following matrix PLAYER 2 baa bab bca bcb caa cab cca ccb 2,2 2,2 2,2 2,2 1,3 1,3 1,3 1,3 PLAYER 1 b 3,3,1 1,3 1,3 3,1 3,1,31,3 c 3,1 2,2 3,1 2,2 3,1 2,23,1 2,2 and we see that b is the only outcome that can be supported as an equilibrium via two Nash equilibria, (c, bcb) and (c, ceb

a) true

b) false

c) true