Games are a powerful tool to model reactive systems; especially systems that include several agents, of which one can assume that they behave rationally with regards to some objectives. But, then, several concepts of rationality are available, and while Nash equilibrium is the most classical of them, subgame-perfect equilibrium (SPE) may be preferred in many situations. Therefore, we propose some algorithmic tools to decide the existence of SPEs satisfying some constraints on the payoffs, in perfect-information sequential games played on graphs, with various classes of objectives.
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