**Problem 3: Car Wash Game**Consider the "car wash" game discussed in the lecture with three car wash stations. Assume the following parameters: - \( p = 1 \)- \( k = 4 \)- \( c = 1.5 \)Tasks:1. **Find the Pure Strategy Nash Equilibrium (NE).** 2. **Find the Symmetric Mixed Strategy Nash Equilibrium (NE),** meaning each station uses the same probability for upgrading.

Symmetric Mixed Strategy Nash equilibrium: A situation in game theory where all players use the same…

3. Consider the "car wash" game in lecture with three car wash stations. Assume that p = 1, k = 4 and c = 1.5. (1) Find the pure strategy NE. (2) Find the symmetric mixed strategy NE (i.e. every station uses the same probability for upgrade).

3. Consider the "car wash" game in lecture with three car wash stations. Assume that p = 1, k = 4 and c = 1.5. (1) Find the pure strategy NE. (2) Find the symmetric mixed strategy NE (i.e. every station uses the same probability for upgrade).

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

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Question

**Problem 3: Car Wash Game**

Consider the "car wash" game discussed in the lecture with three car wash stations. Assume the following parameters:

- \( p = 1 \)
- \( k = 4 \)
- \( c = 1.5 \)

Tasks:

1. **Find the Pure Strategy Nash Equilibrium (NE).**

2. **Find the Symmetric Mixed Strategy Nash Equilibrium (NE),** meaning each station uses the same probability for upgrading.

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