A Bound Computed

The Prompt

Compute or verify the Price of Anarchy for a specific game instance — a routing game, a congestion game, a resource-allocation game, or another setting of your choice. Define the game formally, identify the worst-case Nash equilibrium, compute the social optimum, and calculate the ratio. Compare your result with the known theoretical bounds for the game class. If you find a gap between the known bound and your instance, explain what it reveals.

Completion Criteria

A formal game definition, the Nash equilibrium identified, the social optimum computed, the Price of Anarchy ratio, and a comparison with known bounds. At least one citation to the relevant theoretical result.

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