Description
Problem
Rock, Paper, Scissors is a popular game among kids. It is also a good game to study Game Theory, Nash Equilibrium, Mixed Strategies, and Linear Programming.
Procedure
For this assignment, you are asked to compute the Nash equilibrium for the given zero sum games. You will be give the reward matrix for Player A. Player B’s reward matrix will be the opposite of Player A’s matrix. You need to find the ideal mixed strategy for the game. While there are different ways to calculate this we will use Linear Programming in hopes of preparing you for your final project. Use a Linear Programming solver — such as CVXOPT — to create a program that can solve arbitrary Rock, Paper, Scissor games.
You will submit the objective, constraints and strategy for your Linear Program. Much like the previous assignments answers will be graded to a 0.001 precision.
Examples
Given
| Rock | Paper | Scissor | |
| Rock | 0 | 1 | -1 |
| Paper | -1 | 0 | 1 |
| Scissor | 1 | -1 | 0 |
Calculate
Objective function = ?
Linear constraints = ?
Strategy: πRock = 0.333, πPaper = 0.333, πScissor = 0.333
Given
| Rock | Paper | Scissor | |
| Rock | 0 | 2 | -1 |
| Paper | -2 | 0 | 1 |
| Scissor | 1 | -1 | 0 |
Calculate
Objective function = ?
Linear constraints = ?
Strategy: πRock = 0.25, πPaper = 0.25, πScissor = 0.5
Resources
The concepts explored in this homework are covered by:
- Lectures
- Lesson 11A: Game Theory
○ Lesson 11B: Game Theory Reloaded
- Readings
- Littman (1994)
○ Littman and Stone (2003)
