Prove that every trembling-hand perfect equilibrium (for the agent normal form) is sequential. Show by example that the converse is false. The remaining problems in this chapter concern game-theoretic variations on the classic models of oligopoly. They are primarily about those models and so relate more to material in other chapters, but they could not have been posed until we had covered Nash equilibria and sub game perfection.
Prove that every trembling-hand perfect equilibrium (for the agent normal form) is sequential. Show by example that the converse is false. The remaining problems in this chapter concern game-theoretic variations on the classic models of oligopoly. They are primarily about those models and so relate more to material in other chapters, but they could not have been posed until we had covered Nash equilibria and sub game perfection.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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1. Prove that every trembling-hand perfect equilibrium (for the agent normal form) is sequential. Show by example that the converse is false.
The remaining problems in this chapter concern game-theoretic variations on the classic models of oligopoly. They are primarily about those models and so relate more to material in other chapters, but they could not have been posed until we had covered Nash equilibria and sub game perfection.
2. Prove that in the Bertrand game, if prices must be charged in integer multiples of a penny, then there is always at least one Nash equilibrium in which players do not use weakly dominated strategies.
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