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When Nash Meets Stackelberg
Motivated by international energy trade between countries with
profit-maximizing domestic producers, we analyze Nash games played among
leaders of Stackelberg games (\NASP). We prove it is both -hard to
decide if the game has a pure-strategy (\PNE) or a mixed-strategy Nash
equilibrium (\MNE). We then provide a finite algorithm that computes exact
\MNEs for \NASPs when there is at least one, or returns a certificate if no
\MNE exists. To enhance computational speed, 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 \PNE if one exists. Finally, we provide
computational tests on a range of \NASPs instances inspired by international
energy trades.Comment: 40 Pages and a computational appendix. Code is available on gitHu