  We propose an algorithm for computing Nash equilibria (NE) in a class of
conflicts with multiple battlefields with uniform battlefield values and a
non-linear aggregation function. By expanding the symmetrization idea of Hart
[9], proposed for the Colonel Blotto game, to the wider class of symmetric
conflicts with multiple battlefields, we reduce the number of strategies of the
players by an exponential factor. We propose a clash matrix algorithm which
allows for computing the payoffs in the symmetrized model in polynomial time.
Combining symmetrization and clash matrix algorithm with the double oracle
algorithm we obtain an algorithm for computing NE in the models in question
that achieves a significant speed-up as compared to the standard, LP-based,
approach. We also introduce a heuristic to further speed up the process.
Overall, our approach offers an efficient and novel method for computing NE in
a specific class of conflicts, with potential practical applications in various
fields.
