The Art of Concession in General Lotto Games

Success in adversarial environments often requires investment into additional resources in order to improve one’s competitive position. But, can intentionally decreasing one’s own competitiveness ever provide strategic benefits in such settings? In this paper, we focus on characterizing the role of “concessions” as a component of strategic decision making. Specifically, we investigate whether a player can gain an advantage by either conceding budgetary resources or conceding valuable prizes to an opponent. While one might na¨ıvely assume that the player cannot, our work demonstrates that – perhaps surprisingly – concessions do offer strategic benefits when made correctly. In the context of General Lotto games, we first show that neither budgetary concessions nor value concessions can be advantageous to either player in a 1-vs.-1 scenario. However, in settings where two players compete against a common adversary, we find opportunities for one of the two players to improve her payoff by conceding a prize to the adversary. We provide a set of sufficient conditions under which such concessions exist

Focality and Asymmetry in Multi-battle Contests

This article examines behavior in two-person constant-sum Colonel Blotto games in which each player maximizes the expected total value of the battlefields won. A lottery contest success function is employed in each battlefield. Recent experimental research on such games provides only partial support for Nash equilibrium behavior. We hypothesize that the salience of battlefields affects strategic behavior (the salient target hypothesis). We present a controlled test of this hypothesis – against Nash predictions – when the sources of salience come from certain asymmetries in either battlefield values or labels (as in Schelling (1960)). In both cases, subjects over-allocate the resource to the salient battlefields relative to the Nash prediction. However, the effect is stronger with salient values. In the absence of salience, we replicate previous results in the literature supporting the Nash prediction

Bandit Learning for Dynamic Colonel Blotto Game with a Budget Constraint

We consider a dynamic Colonel Blotto game (CBG) in which one of the players is the learner and has limited troops (budget) to allocate over a finite time horizon. At each stage, the learner strategically determines the budget distribution among the battlefields based on past observations. The other player is the adversary, who chooses its budget allocation strategies randomly from some fixed unknown distribution. The learner's objective is to minimize its regret, which is the difference between the payoff of the best mixed strategy and the realized payoff by following a learning algorithm. The dynamic CBG is analyzed under the framework of combinatorial bandit and bandit with knapsacks. We first convert the dynamic CBG with budget constraint to a path planning problem on a graph. We then devise an efficient dynamic policy for the learner that uses a combinatorial bandit algorithm Edge on the path planning graph as a subroutine for another algorithm LagrangeBwK. It is shown that under the proposed policy, the learner's regret is bounded with high probability by a term sublinear in time horizon $T$ and polynomial with respect to other parameters

Strategically Revealing Intentions in General Lotto Games

Strategic decision-making in uncertain and adversarial environments is crucial for the security of modern systems and infrastructures. A salient feature of many optimal decision-making policies is a level of unpredictability, or randomness, which helps to keep an adversary uncertain about the system’s behavior. This paper seeks to explore decision-making policies on the other end of the spectrum – namely, whether there are benefits in revealing one’s strategic intentions to an opponent before engaging in competition.We study these scenarios in a well-studied model of competitive resource allocation problem known as General Lotto games. In the classic formulation, two competing players simultaneously allocate their assets to a set of battlefields, and the resulting payoffs are derived in a zero-sum fashion. Here, we consider a multi-step extension where one of the players has the option to publicly pre-commit assets in a binding fashion to battlefields before play begins. In response, the opponent decides which of these battlefields to secure (or abandon) by matching the pre-commitment with its own assets. They then engage in a General Lotto game over the remaining set of battlefields. Interestingly, this paper highlights many scenarios where strategically revealing intentions can actually significantly improve one’s payoff. This runs contrary to the conventional wisdom that randomness should be a central component of decision-making in adversarial environments

Strategically Revealing Intentions in General Lotto Games

Strategic decision-making in uncertain and adversarial environments is crucial for the security of modern systems and infrastructures. A salient feature of many optimal decision-making policies is a level of unpredictability, or randomness, which helps to keep an adversary uncertain about the system’s behavior. This paper seeks to explore decision-making policies on the other end of the spectrum – namely, whether there are benefits in revealing one’s strategic intentions to an opponent before engaging in competition.We study these scenarios in a well-studied model of competitive resource allocation problem known as General Lotto games. In the classic formulation, two competing players simultaneously allocate their assets to a set of battlefields, and the resulting payoffs are derived in a zero-sum fashion. Here, we consider a multi-step extension where one of the players has the option to publicly pre-commit assets in a binding fashion to battlefields before play begins. In response, the opponent decides which of these battlefields to secure (or abandon) by matching the pre-commitment with its own assets. They then engage in a General Lotto game over the remaining set of battlefields. Interestingly, this paper highlights many scenarios where strategically revealing intentions can actually significantly improve one’s payoff. This runs contrary to the conventional wisdom that randomness should be a central component of decision-making in adversarial environments

Focality and Asymmetry in Multi-battle Contests

This article examines the influence of focality in Colonel Blotto games with a lottery contest success function (CSF), where the equilibrium is unique and in pure strategies. We hypothesise that the salience of battlefields affects strategic behaviour (the salient target hypothesis) and present a controlled test of this hypothesis against Nash predictions, checking the robustness of equilibrium play. When the sources of salience come from asymmetries in battlefield values or labels (as in Schelling, 1960), subjects over-allocate the resource to the salient battlefields relative to the Nash prediction. However, the effect is stronger with salient values. In the absence of salience, we find support for the Nash prediction

Game Theory in Distributed Systems Security: Foundations, Challenges, and Future Directions

Many of our critical infrastructure systems and personal computing systems have a distributed computing systems structure. The incentives to attack them have been growing rapidly as has their attack surface due to increasing levels of connectedness. Therefore, we feel it is time to bring in rigorous reasoning to secure such systems. The distributed system security and the game theory technical communities can come together to effectively address this challenge. In this article, we lay out the foundations from each that we can build upon to achieve our goals. Next, we describe a set of research challenges for the community, organized into three categories -- analytical, systems, and integration challenges, each with "short term" time horizon (2-3 years) and "long term" (5-10 years) items. This article was conceived of through a community discussion at the 2022 NSF SaTC PI meeting.Comment: 11 pages in IEEE Computer Society magazine format, including references and author bios. There is 1 figur

Dynamic Adversarial Resource Allocation: the dDAB Game

This work proposes a dynamic and adversarial resource allocation problem in a graph environment, which is referred to as the dynamic Defender-Attacker Blotto (dDAB) game. A team of defender robots is tasked to ensure numerical advantage at every node in the graph against a team of attacker robots. The engagement is formulated as a discrete-time dynamic game, where the two teams reallocate their robots in sequence and each robot can move at most one hop at each time step. The game terminates with the attacker's victory if any node has more attacker robots than defender robots. Our goal is to identify the necessary and sufficient number of defender robots to guarantee defense. Through a reachability analysis, we first solve the problem for the case where the attacker team stays as a single group. The results are then generalized to the case where the attacker team can freely split and merge into subteams. Crucially, our analysis indicates that there is no incentive for the attacker team to split, which significantly reduces the search space for the attacker's winning strategies and also enables us to design defender counter-strategies using superposition. We also present an efficient numerical algorithm to identify the necessary and sufficient number of defender robots to defend a given graph. Finally, we present illustrative examples to verify the efficacy of the proposed framework

Strategic and Stochastic Approaches to Modeling the Structure of Multi-Layer and Interdependent Networks

Examples of complex networks abound in both the natural world (e.g., ecological, social and economic systems), and in engineered applications (e.g., the Internet, the power grid, etc.). The topological structure of such networks plays a fundamental role in their functioning, dictating properties such as the speed of information diffusion, the influence of powerful or vulnerable nodes, and the ability of the nodes to take collective actions. There are two main schools of thought for investigating the structure of complex networks. Early research on this topic primarily adopted a stochastic perspective, postulating that the links between nodes are formed randomly. In an alternative perspective, it has been argued that optimization (rather than pure randomness) plays a key role in network formation. In such settings, edges are formed strategically (either by a designer or by the nodes themselves) in order to maximize certain utility functions. The classical literature on the structure of networks has predominantly focused on single layer networks where there is a single set of edges between nodes. However, there is an increasing realization that many real-world networks have either multi-layer or interdependent structure. While the former considers multiple layers of relationships between the same set of nodes, the latter deals with networks-of-networks consisting of interdependencies between different subnetworks. This thesis focuses on the analysis of the structure of multi-layer and interdependent networks via strategic and stochastic approaches. In the strategic multi-layer network formation setting, each layer represents a different type of relationship between the nodes and is designed to maximize some utility that depends on its own topology and those of the other layers. By viewing the designer of each layer as a player in a multi-layer network formation game, we show that hub-and-spoke networks that are commonly observed in transportation systems arise as a Nash equilibrium. Extending this analysis to interdependent networks where there are different sets of nodes, we introduce a network design game where the objective of the players is to design the interconnections between the nodes of two different networks, G1 and G2. In this game, each player is associated with a node in G1 and has functional dependencies on certain nodes in G2. Besides showing that finding a best response of a player is NP-hard and characterizing some useful properties of the best response actions of the players, we prove existence of pure Nash equilibria in this game under certain conditions. In order to obtain further insights into the structure of interdependent networks with an arbitrary number of subnetworks, we consider a model for random interdependent networks where each edge between two different subnetworks is formed with probability p. We investigate certain spectral and structural properties of such networks, with corresponding implications for certain variants of consensus dynamics on those networks. In particular, we study a property known as r-robustness, which is a strong indicator of the ability of a network, including interdependent networks, to tolerate structural perturbations and dynamical attacks

COMPLETELY POSITIVE AND CO-POSITIVE PROGRAMMING: APPLICATIONS IN DISRUPTION RISK MANAGEMENT, POST DISASTER HUMANITARIAN LOGISTICS AND HOMELAND SECURITY GAMES

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