The Lemke-Howson Algorithm Applied

The Prompt

Implement or trace by hand the Lemke-Howson algorithm for a two-player game with at least three strategies per player. Record each pivot step, identify the Nash equilibrium found, and verify that neither player can profitably deviate. Reflect on the algorithm's path length: how many pivots were required, and how does this compare to the number of strategies? If you have access to a computer, compare the Lemke-Howson solution with the output of the support-enumeration method.

Completion Criteria

The game matrix, a trace of the pivot steps, the equilibrium found, a verification of no profitable deviation, and a note on the number of pivots required.

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