An algorithmic solution to the Blotto game using multi-marginal
couplings
- URL: http://arxiv.org/abs/2202.07318v1
- Date: Tue, 15 Feb 2022 11:07:31 GMT
- Title: An algorithmic solution to the Blotto game using multi-marginal
couplings
- Authors: Vianney Perchet and Philippe Rigollet and Thibaut Le Gouic
- Abstract summary: We describe an efficient algorithm to compute solutions for the general two-player Blotto game on n battlefields with heterogeneous values.
Our algorithm samples from an eps-optimal solution in time O(n2 + eps-4) independently of budgets and battlefield values.
In the case of asymmetric values where optimal solutions need not exist but Nash equilibria do, our algorithm samples from an eps-Nash equilibrium with similar complexity.
- Score: 27.35514815248438
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We describe an efficient algorithm to compute solutions for the general
two-player Blotto game on n battlefields with heterogeneous values. While
explicit constructions for such solutions have been limited to specific,
largely symmetric or homogeneous, setups, this algorithmic resolution covers
the most general situation to date: value-asymmetric game with asymmetric
budget. The proposed algorithm rests on recent theoretical advances regarding
Sinkhorn iterations for matrix and tensor scaling. An important case which had
been out of reach of previous attempts is that of heterogeneous but symmetric
battlefield values with asymmetric budget. In this case, the Blotto game is
constant-sum so optimal solutions exist, and our algorithm samples from an
\eps-optimal solution in time O(n^2 + \eps^{-4}), independently of budgets and
battlefield values. In the case of asymmetric values where optimal solutions
need not exist but Nash equilibria do, our algorithm samples from an \eps-Nash
equilibrium with similar complexity but where implicit constants depend on
various parameters of the game such as battlefield values.
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