University of Arizona Department of Economics Professor Dufwenberg Fall 2019 2. (15) Consider Dufwenberg, Sundaram & Butler's "game of 21" (reminder: There are two players, call them A and B, who take turns. Player A begins, choosing number I or number 2. Then it is player B's turn to choose, by incrementing A's choice by 1 or by 2. That is, if A chose 1, then B can choose 2 or 3. If, instead, A chose 2, then B can choose 3 or 4. The game continues with each player incrementing the other's choice by 1 or by 2, until a player reaches 21. That player wins.) (i) Does player A have exactly two strategies? Explain why or why not? (ii) Does either player have a dominant strategy? If yes, say what player, and describe such a strategy. If no, explain why this is the case. Player Boo have dominant strategy, what ever playerA choose player B just make it become 3, player B win 5 (iii) Find a strategy for player B which is not dominant, and explain why this is the case. one turn when player H choose 2, player Balso choose 2. or playAchoose 1 . player is also choose / 5 theit will make player B become not dominant . A will become dominant 11