论文标题
离散的Richman出生得分游戏
Discrete Richman-bidding Scoring Games
论文作者
论文摘要
我们在所谓的Richman Auctions（Lazarus etal。1996）的框架内研究零和组合游戏，即，我们修改了交替的Play评分规则集累积减法（CS）（Cohensius等人，2019年），类似于分散的出价方案（类似于Develin和Payne和Payne 2010）。球员竞标，出价最高的球员赢得了这一举动，并将获胜的竞标交给了另一个球员。新游戏被称为竞标累积减法（BCS）。在所谓的统一游戏中，玩家完全从一堆相同的项目中删除了一项，直到堆为空，并且他们的动作有助于共同的分数，该分数会根据最大化的球员是否赢得了转弯。我们表明，对于更大的游戏，有一个独特的竞标均衡，这在文献中概括了标准得分游戏。我们证明，对于所有足够大的堆尺寸，统一BC的平衡结果最终是周期性的，并具有2个周期，我们表明，周期性最新出现在总预算中的尺寸二次尺寸的最新量。
We study zero-sum (combinatorial) games, within the framework of so-called Richman auctions (Lazarus et al. 1996) namely, we modify the alternating play scoring ruleset Cumulative Subtraction (CS) (Cohensius et al. 2019), to a discrete bidding scheme (similar to Develin and Payne 2010). Players bid to move and the player with the highest bid wins the move, and hands over the winning bidding amount to the other player. The new game is dubbed Bidding Cumulative Subtraction (BCS). In so-called unitary games, players remove exactly one item out of a single heap of identical items, until the heap is empty, and their actions contribute to a common score, which increases or decreases by one unit depending on whether the maximizing player won the turn or not. We show that there is a unique bidding equilibrium for a much larger class of games, that generalize standard scoring play in the literature. We prove that for all sufficiently large heap sizes, the equilibrium outcomes of unitary BCS are eventually periodic, with period 2, and we show that the periodicity appears at the latest for heaps of sizes quadratic in the total budget.
