When Nash Meets Stackelberg
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We analyze Nash games played among leaders of Stackelberg games (), and prove it is both Σ^p_2-hard to decide if the game has a pure-strategy () or mixed-strategy Nash equilibrium (). We then provide a finite algorithm that computes exact for when there is at least one, or returns a certificate if no exists. We introduce an inner approximation hierarchy that increasingly grows the description of each Stackelberg leader feasible region. Furthermore, we extend the algorithmic framework to specifically retrieve a pure-strategy Nash Equilibrium if one exists. Finally, we provide computational tests on a range of instances inspired by international energy trades.
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