The Value of Compromising Strategic Intent in General Lotto Games

TL;DR

This work investigates how partial revelation of an opponent's strategic intent affects outcomes in General Lotto games by introducing a binary information channel (GLI) where the Breaker observes whether the Attacker's allocation exceeds a threshold $\tau$ and conditions its response accordingly. The authors derive a comprehensive analytical characterization of equilibrium payoffs and strategies for GLI across all budgets $X_A,X_B$ and thresholds $\tau$, leveraging a decomposition into sub-games with posterior strategies and an optimization over mixture weights. Numerical results demonstrate that the binary sensor can substantially improve the Breaker’s performance relative to the classic GL, with the payoff gains depending on the relative budgets and the chosen threshold; the improvements persist across parameter regimes and converge to the standard GL as $\tau$ becomes very small or very large. This work provides exact analytical tools for evaluating information-enabled security policies in competitive resource allocation and suggests future directions for richer signaling and adaptive sensor design.

Abstract

Resource allocation in adversarial environments is a fundamental challenge across various domains, from corporate competition to military strategy. This article examines the impact of compromising an opponent's strategic intent in the context of General Lotto games, a class of resource allocation problems. We consider a scenario where one player, termed the "Breaker", has access to partial information about their opponent's strategy through a binary sensor. This sensor reveals whether the opponent's allocated resources exceed a certain threshold. Our analysis provides a comprehensive characterization of equilibrium strategies and payoffs for both players under this information structure. Through numerical studies, we demonstrate that the information provided by the sensor can significantly improve the Breaker's performance.

Figures (5)

• Figure 1: The highlighted scenario captures a strategic environment where two players, referred to as the Attacker and Breaker, must decide how to allocate their limited assets ($X_A$ and $X_B$ respectively) over a given contest. In the classic General Lotto setting, each agent simultaneously chooses their allocation strategy to optimize their performance guarantees without any knowledge of their opponent's allocation strategy. This work extends this classic framework by introducing an information asymmetry that favors the Breaker as highlighted above. Specifically, we consider a setting where the Breaker is able to observe a binary signal indicating whether the Attacker's allocated assets, i.e., the realization of the Attacker's randomized allocation strategy, are above or below a given threshold value. The Breaker can then condition their allocation strategy on this observed information.
• Figure 2: Numerical instance of a General Lotto Game and a General Lotto Game with Binary Information. Note that placing a sensor that reveals if the realization is above or below $\tau=13$ generates a $\sim 13\%$ improvement to player $B$'s payoff.
• Figure 3: Value of the function $U_B^*(X_A,X_B,\tau)$ over the regions described in Equations \ref{['eq:ua:i']}-\ref{['eq:ua:ix']} in the $(X_A,X_B)$-plane.
• Figure 4: Value of the function $U_B^*(X_A,X_B,\tau)$ as a function of $\tau$ for a different $(X_A,X_B)$ pairs. The dashed lines represent the payoff obtained by player $B$ in a General Lotto game $U_B^*(X_A,X_B)$. Also, we highlight the maximizer of each curve with a marker.
• Figure 5: Equilibrium payoff for the Upper Bounded General Lotto game. It can be noticed that, using previous results, do not allow us to have the equilibrium payoff for all possible values of $\tau$.

Theorems & Definitions (10)

• Theorem 1: Hart_2008
• Theorem 2
• Definition 1
• Definition 2: Upper Bounded General Lotto Game
• Definition 3: Lower Bounded General Lotto Game
• Lemma 1
• Theorem 3
• Theorem 4
• Lemma 2
• Corollary 1