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In integer programming games, players' feasible strategies are described by lattice points inside polyhedra. This game representation is natural when players' decisions have integrality restrictions. In this talk, we will start by presenting practical examples of integer programming games. Then, we will focus on a particular "dynamic" integer programming game played over a graph, the Multilevel Critical Node problem. Besides a discussion on the problem difficulty, we will describe an exact cutting plane algorithm to determine the game equilibrium and a reinforcement learning based heuristic to approximate it.