刻画 Blotty 博弈中信息与实力的相互作用
Characterizing the interplay between information and strength in Blotto games
AI总结：
本文研究 Colonel Blotto 博弈中的信息不对称性，刻画了双战场和三战场设定下的唯一均衡收益与策略，并量化了信息价值，揭示了对抗环境中信息与实力的相互作用。
摘要：
本文研究了 Colonel Blotto 博弈中的信息不对称性，这是一种两名玩家在一组战场上进行竞争性资源分配的博弈论模型。战场估值具有随机性。两名玩家中有一名确切知道这些估值，另一名仅知道战场实现的分布。然而，拥有信息的玩家可分配的资源较少。我们刻画了 Colonel Blotty 博弈在双战场设定下的唯一均衡收益。随后，我们关注 Colonel Blotto 博弈的常见变体 General Lotto 博弈中的三战场设定。我们刻画了其唯一的均衡收益和混合均衡策略。我们量化了信息的价值，即非对称信息博弈与完全信息博弈之间均衡收益的差异。我们发现信息严格提升了信息知情玩家的性能保障。然而，提升的幅度随信息知情玩家的实力以及博弈参数而变化。我们的分析突显了对抗性环境中实力与信息之间的相互作用。
英文摘要：
In this paper, we investigate informational asymmetries in the Colonel Blotto game, a game-theoretic model of competitive resource allocation between two players over a set of battlefields. The battlefield valuations are subject to randomness. One of the two players knows the valuations with certainty. The other knows only a distribution on the battlefield realizations. However, the informed player has fewer resources to allocate. We characterize unique equilibrium payoffs in a two battlefield setup of the Colonel Blotto game. We then focus on a three battlefield setup in the General Lotto game, a popular variant of the Colonel Blotto game. We characterize the unique equilibrium payoffs and mixed equilibrium strategies. We quantify the value of information - the difference in equilibrium payoff between the asymmetric information game and complete information game. We find information strictly improves the informed player's performance guarantee. However, the magnitude of improvement varies with the informed player's strength as well as the game parameters. Our analysis highlights the interplay between strength and information in adversarial environments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
