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# Game Theory

Consider the following conflict among tenant and landlord about a deposit: When the rental agreement starts, the tenant leaves a deposit x with landlord. On termination of the rental agreement, the landlord returns y. The returned amount y is either the full deposit or a fraction: y ∈ [0, x]. The tenant can accept or refuse the landlord’s offer of y. If the tenant refuses, then the tenant goes to court. In this case the tenant bears a non-refundable cost of c (litigation fees). The court settles the case, i.e. decides that the landlord must return the amount of y* to the tenant. y* is a fixed number. Both parties, the landlord and the tenant, know y*, i.e. both know how the court will settle the case.

1. a) Draw this situation (handwritten) as an extensive form game. In a first move the landlord decides about y. In a second move the tenant decides whether to accept y or whether to go to court. Since the court has no choice, there is no third move.
2. b) Find all Nash equilibria sand ubgame perfect equilibria of this game.