← 研踪 PaperTrailarXiv:2611.05221 · v1
Efficient Equilibrium Computation in Colonel Blotto Games
首次提交 2026-11-04 01:06
版本更新 2026-11-04 01:06
雷达观测 2026-11-04 23:39
摘要
Colonel Blotto is a fundamental resource-allocation game in which two players divide their budgets across battlefields, and the higher allocation on each battlefield wins its value. The problem of computing an equilibrium efficiently has remained unresolved for its classical continuous version with arbitrary budgets and with values that may vary across battlefields but are the same for both players. We give a fully polynomial-time approximation scheme that computes an $\varepsilon$-Nash equilibrium in time polynomial in the input length and $1/\varepsilon$, and nearly linear in the input length for fixed $\varepsilon$. For sufficiently balanced budgets and battlefield values, we also compute exact equilibria in linear time.
作者备注：75 pages
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v1 · 2026-11-04 01:06 · 最新观测版本
Efficient Equilibrium Computation in Colonel Blotto Games
Colonel Blotto is a fundamental resource-allocation game in which two players divide their budgets across battlefields, and the higher allocation on each battlefield wins its value. The problem of computing an equilibrium efficiently has remained unresolved for its classical continuous version with arbitrary budgets and with values that may vary across battlefields but are the same for both players. We give a fully polynomial-time approximation scheme that computes an $\varepsilon$-Nash equilibrium in time polynomial in the input length and $1/\varepsilon$, and nearly linear in the input length for fixed $\varepsilon$. For sufficiently balanced budgets and battlefield values, we also compute exact equilibria in linear time.
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