On the cheating problem in Stackelberg games†

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Abstract
This paper deals with the problem of cheating in two-person games. First we discuss different ways of cheating and give examples of practical economic game problems where cheating is a realistic policy alternative. We consider the Stackelberg setting where the leader makes his decision first and announces this to the follower. When the follower does not know the performance criterion of the leader then the leader can cheat by making a false announcement to the follower. Three different alternatives for cheating are described. Necessary conditions for the open-loop cheating strategies in deterministic linear-quadratic differential games are developed. One of the cheating formulations results in a three stage dynamic optimization problem. The solution of the TPBVP obtained in this case is considered in detail. The feasibility of obtaining the cheating solutions is demonstrated by solving a simple pursuit-evasion game.

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