An interesting possibility in the citizen-candidate model is that there is a Nash equilibrium in which...

  

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An interesting possibility in the citizen-candidate model is that there is a Nash equilibrium in which a candidate loses. To make the argument simple, consider a very special distri- bution of preferences that is very different from the ones considered in class. The range of possible positions is from 0 to 1. Forty percent of citizens have favorite position 0, 5% have favorite position 0.25, 15% have favorite position 0.6, and 40 % have favorite position 1. Figure 1: The 40% 5% 2 0.25 15% 0.6 40% 1 in Problem 6. See Figure 1. The Positions of the three candidates are indicated in red color. No citizen has a favorite position different from 0, 0.25, 0.6, and 1. Suppose that three citizens enter as 2 candidates: one ("candidate 1") with favorite position 0, one ("candidate 2") with favorite position 0.25, and one ("candidate 3") with favorite position 1. What is the outcome? Are there values of b and c for which the action profile is a Nash equilibrium? An interesting possibility in the citizen-candidate model is that there is a Nash equilibrium in which a candidate loses. To make the argument simple, consider a very special distri- bution of preferences that is very different from the ones considered in class. The range of possible positions is from 0 to 1. Forty percent of citizens have favorite position 0, 5% have favorite position 0.25, 15% have favorite position 0.6, and 40 % have favorite position 1. Figure 1: The 40% 5% 2 0.25 15% 0.6 40% 1 in Problem 6. See Figure 1. The Positions of the three candidates are indicated in red color. No citizen has a favorite position different from 0, 0.25, 0.6, and 1. Suppose that three citizens enter as 2 candidates: one ("candidate 1") with favorite position 0, one ("candidate 2") with favorite position 0.25, and one ("candidate 3") with favorite position 1. What is the outcome? Are there values of b and c for which the action profile is a Nash equilibrium?

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ANSWER To determine the outcome and potential Nash equilibria in this scenario we need to consider the preferences of the citizens and how they align with the positions of the candidates Lets analyze ... View the full answer