First steps towards finding a solution of a dynamic investor-bank game

The subject of this paper is a one-leader-one-follower dynamic inverse Stackelberg game with a fixed duration between a bank acting as the leader and an investor acting as the follower. The investor makes her transaction decisions with the bank as intermediary and the bank charges her transaction costs that are dependent on the investor's transactions. The goal of both players is to maximize their profits. The problem is to find a closed-form ε-optimal strategy for the bank. This problem belongs to the realm of composed functions and therefore is very difficult to solve. In this paper we first propose general guidelines for finding such an ε-optimal strategy for the bank and then apply these guidelines on specific academic examples. First we present an example in which we are able to find a closed-form ε-optimal solution, but we also introduce an example in which it is impossible to find such a solution and one has to proceed in a numerical way.