论文标题

多阶段一般乐透游戏的战略投资

Strategic investments in multi-stage General Lotto games

论文作者

Chandan, Rahul, Paarporn, Keith, Alizadeh, Mahnoosh, Marden, Jason R.

论文摘要

在对抗性互动中,通常需要一个人在多个时期做出战略决策,在这种情况下,做出较早的决策会影响球员的竞争地位以及如何在以后的阶段做出选择。在本文中,我们在一般乐透游戏中研究了这种情况,该场景对两个玩家之间的多个战场上的资源分配进行了建模。我们提出了一个两阶段的配方,其中一位参与者保留了可以在第一阶段在战场上进行战略性预分配的资源。然后,分配变成绑定,并向另一个玩家揭示。在第二阶段,玩家通过同时分配实时资源相互对抗来参与。本文的主要贡献提供了两阶段游戏中平衡收益的完整特征,揭示了性能与游戏每个阶段所消耗的资源之间的相互作用。我们发现,实时资源至少是预先分配资源的两倍。然后,当玩游戏开始之前购买每种类型的资源时,我们确定玩家的最佳投资,并且货币预算有限。

In adversarial interactions, one is often required to make strategic decisions over multiple periods of time, wherein decisions made earlier impact a player's competitive standing as well as how choices are made in later stages. In this paper, we study such scenarios in the context of General Lotto games, which models the competitive allocation of resources over multiple battlefields between two players. We propose a two-stage formulation where one of the players has reserved resources that can be strategically pre-allocated across the battlefields in the first stage. The pre-allocation then becomes binding and is revealed to the other player. In the second stage, the players engage by simultaneously allocating their real-time resources against each other. The main contribution in this paper provides complete characterizations of equilibrium payoffs in the two-stage game, revealing the interplay between performance and the amount of resources expended in each stage of the game. We find that real-time resources are at least twice as effective as pre-allocated resources. We then determine the player's optimal investment when there are linear costs associated with purchasing each type of resource before play begins, and there is a limited monetary budget.

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