with Augeas, the king and the hero make alternating offers to each other. Only one offer per day is allowed. If the offer is accepted, Heracles cleans the stables and receives the agreed payment. If the offer is rejected, the king and the hero have to wait one day before the new offer is made. Each day, both Augeas and Heracles have an option of abandoning the enterprise of cleaning the stables for good and receiving a payoff of zero. (a) Formalize this problem as an extensive-form game. (b) Find all subgame perfect Nash equilibria of this game. (c) Find a Nash equilibrium of this game that is not subgame perfect. Using this equilibrium as an example, explain why subgame perfection is a reasonable requirement for equilibria in extensive form games.

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