Computation of Incentive Stackelberg Solution

This work introduces a new method for computing the incentive Stackelberg solution. Stackelberg games are models for decision making situations, where the parties, called players, act in predetermined order. The first is called the leader and the others are followers. In an incentive game the leader can commit to a decision that depends on the followers' moves. This kind of a strategy is called an incentive. The leader aims to announce an incentive that leads to the most decired outcome for him. The method for computing the incentive solution is based on solving a system of nonlinear equations using standard iterative schemes. Fixed point iteration is the simplest method for finding a solution for a system of equations. In this work we prove that fixed point iteration converges when the system of equations has properties that are similar to those that arise in price coordination equations in economics. We show the use of the method in two examples. In the first example we consider a two-player incentive Stackelberg game with a follower having a quadratic cost function. The second example introduces a duopoly model with government acting as the leader and the two firms as the followers playing Nash equilibrium strategies against each other. The numerical computations can be considered as simulations of simple learning processes. Another method studied in this work in solving the incentive Stackelberg game is the genetic algorithm that imitates biological evolution. The calculations show that the algorithm finds the incentive solution fast but it requires more computational effort than fixed point iteration. Systems Analysis Laboratory, for creating optimal working conditions. I thank Mr. Otso Ojanen for his assistance with the genetic algorithm. I would also like to thank the floorball team of the Systems Analysis Laboratory and the people who have shared several lunch, coffee and quiz breaks with me. Finally, I thank my parents and my brother for their support.