Two Notes on the Blotto Game
Two Notes on the Blotto Game
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关于 Blotto 游戏的两个注意事项
DOI：
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发表时间：
2012
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影响因子：
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通讯作者：
Jonathan Weinstein
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文献类型：
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作者：
Jonathan Weinstein
我们展示了一个新的平衡的经典Blotto游戏中，玩家分配一个单位的资源之间的三个坐标，并试图击败他们的对手在两个出三个。众所周知，如果每个坐标上的边际分布是U[0，（2/3）]，则混合策略将是均衡策略。这类分布的所有经典例子都有二维支持。在这里，我们展示了一个分布，它具有一维的支持，并且比以前的例子更容易描述。这个构造推广到在高维单纯形中也给出了具有相同性质的一维分布。作为我们的第二个注记，我们给出了当博弈被修改为局中人预算不相等时的均衡收益的一些结果。我们的研究结果提出了一个标准，在原来的对称游戏中的均衡选择，在鲁棒性方面的一个小的不对称资源。
We exhibit a new equilibrium of the classic Blotto game in which players allocate one unit of resources among three coordinates and try to defeat their opponent in two out of three. It is well known that a mixed strategy will be an equilibrium strategy if the marginal distribution on each coordinate is U[0,(2/3)]. All classic examples of such distributions have two-dimensional support. Here we exhibit a distribution which has one-dimensional support and is simpler to describe than previous examples. The construction generalizes to give one-dimensional distributions with the same property in higher-dimensional simplices as well.As our second note, we give some results on the equilibrium payoffs when the game is modified so that players have unequal budgets. Our results suggest a criterion for equilibrium selection in the original symmetric game, in terms of robustness with respect to a small asymmetry in resources.