Can revealing one's competitive capabilities to an opponent offer strategic benefits? In this paper, we address this question in the context of General Lotto games, a class of two-player competitive resource allocation models. We consider an asymmetric information setting where the opponent is uncertain about the resource budget of the other player, and holds a prior belief on its value. We assume the other player, called the signaler, is able to send a noisy signal about its budget to the opponent. With its updated belief, the opponent then must decide to invest in costly resources that it will deploy against the signaler's resource budget in a General Lotto game. We derive the subgame perfect equilibrium to this extensive-form game. In particular, we identify necessary and sufficient conditions for which a signaling policy improves the signaler's resulting performance in comparison to the scenario where it does not send any signal. Moreover, we provide the optimal signaling policy when these conditions are met. Notably we find that for some scenarios, the signaler can effectively double its performance.
翻译:普通彩票游戏中战略性地揭示能力
翻译后的摘要:
本文探讨了在对手面前揭示自己竞争能力是否能够提供战略优势。在这篇论文中,我们关注了普通彩票游戏中的这个问题,这是一种两个玩家竞争性资源分配模型。我们考虑了一个不对称的信息设置,对手对另一个玩家的资源预算有不确定性,并对其价值持有先验信念。我们假设另一个玩家,称为信号者,能够向对手发送关于其预算的嘈杂信号。根据更新后的信念,对手必须决定是否投资昂贵的资源,并在普通彩票游戏中用于对抗信号者的资源预算。我们推导了这个广义形式博弈的次博弈完美平衡。特别的,我们确定了当一些条件得到满足时,发信号策略将如何提高信号者的结果表现,且提供了最优发信号策略。值得注意的是,我们发现,在某些情况下,信号者能够有效地提高其表现达到两倍。