In contrast, in a game theoretic setting, myopic strategic interactions among players lead to a Nash equilibrium or locally optimal configuration rather than highest scoring global configuration.

Strategy logic (SL) is a powerful temporal logic that enables first-class reasoning over strategic behavior in multi-agent systems (MAS). In many MASs, the agents (and their strategies) cannot observe the global state of the system, leading to many extensions of SL centered around imperfect information, such as strategy logic with imperfect information (SL$_\mathit{ii}$). Along orthogonal lines, researchers have studied the combination of strategic behavior and hyperproperties. Hyperproperties are system properties that relate multiple executions in a system and commonly arise when specifying security policies. Hyper Strategy Logic (HyperSL) is a temporal logic that combines quantification over strategies with the ability to express hyperproperties on the executions of different strategy profiles. In this paper, we study the relation between SL$_\mathit{ii}$ and HyperSL. Our main result is that both logics (restricted to formulas where no state formulas are nested within path formulas) are equivalent in the sense that we can encode SL$_\mathit{ii}$ instances into HyperSL instances and vice versa. For the former direction, we build on the well-known observation that imperfect information is a hyperproperty. For the latter direction, we construct a self-composition of MASs and show how we can simulate hyperproperties using imperfect information.

Large Language Models (LLMs) are increasingly deployed across diverse contexts to support decision-making. While existing evaluations effectively probe latent model capabilities, they often overlook the impact of context framing on perceived rational decision-making. In this study, we introduce a novel evaluation framework that systematically varies evaluation instances across key features and procedurally generates vignettes to create highly varied scenarios. By analyzing decision-making patterns across different contexts with the same underlying game structure, we uncover significant contextual variability in LLM responses. Our findings demonstrate that this variability is largely predictable yet highly sensitive to framing effects. Our results underscore the need for dynamic, context-aware evaluation methodologies for real-world deployments.

In this study, we introduce Modular State-based Stackelberg Games (Mod-SbSG), a novel game structure developed for distributed self-learning in modular manufacturing systems. Mod-SbSG enhances cooperative decision-making among self-learning agents within production systems by integrating State-based Potential Games (SbPG) with Stackelberg games. This hierarchical structure assigns more important modules of the manufacturing system a first-mover advantage, while less important modules respond optimally to the leaders' decisions. This decision-making process differs from typical multi-agent learning algorithms in manufacturing systems, where decisions are made simultaneously. We provide convergence guarantees for the novel game structure and design learning algorithms to account for the hierarchical game structure. We further analyse the effects of single-leader/multiple-follower and multiple-leader/multiple-follower scenarios within a Mod-SbSG. To assess its effectiveness, we implement and test Mod-SbSG in an industrial control setting using two laboratory-scale testbeds featuring sequential and serial-parallel processes. The proposed approach delivers promising results compared to the vanilla SbPG, which reduces overflow by 97.1%, and in some cases, prevents overflow entirely. Additionally, it decreases power consumption by 5-13% while satisfying the production demand, which significantly improves potential (global objective) values.

The rapid advancement of large language models (LLMs) has accelerated their application in reasoning, with strategic reasoning drawing increasing attention. To evaluate the strategic reasoning capabilities of LLMs, game theory, with its concise structure, has become the preferred approach for many researchers. However, current research typically focuses on a limited selection of games, resulting in low coverage of game types. Additionally, classic game scenarios carry risks of data leakage, and the benchmarks used often lack extensibility, rendering them inadequate for evaluating state-of-the-art models. Specifically, we incorporate all 144 game types summarized by the Robinson-Goforth topology of 2 2 games, which are constructed as classic games in our benchmark. Furthermore, we employ synthetic data generation techniques to create diverse, higher-quality game scenarios through topic guidance and human inspection for each classic game, which we refer to as story-based games. Lastly, to provide a sustainable evaluation framework adaptable to increasingly powerful LLMs, we treat the aforementioned games as atomic units and organize them into more complex forms through sequential, parallel, and nested structures. We conducted a comprehensive evaluation of mainstream LLMs, covering tests on rational reasoning, reasoning robustness, Theory-of-Mind capabilities, and reasoning in complex game forms. The results revealed that LLMs still have flaws in the accuracy and consistency of strategic reasoning processes, and their levels of mastery over Theory-of-Mind also vary. These achievements are largely attributed to LLMs' ability to assimilate vast amounts of knowledge during training, emerging with the capacity to organize information at a coarse level and link knowledge at a finegrained level through their internal representations (Min et al., 2023; Zhao et al., 2023). These core capabilities have driven the success of LLMs in numerous reasoning tasks, including mathematical reasoning (Hendrycks et al., 2021; Zhang et al., 2023), commonsense reasoning (Sap et al., 2019; Bisk et al., 2020), logical reasoning (Lei et al., 2023), and strategic reasoning (Lorè & Heydari, Work done during an internship at the University of Hong Kong. The dataset and evaluation codes will be available at https://github.com/PinkEx/TMGBench. Among these, strategic reasoning has attracted considerable attention due to its multi-agent nature and close association with social intelligence (Gandhi et al., 2023). Strategic reasoning refers to the cognitive process of anticipating, planning, and responding to others' actions to achieve specific objectives within competitive or cooperative contexts (Zhang et al., 2024a).

Structured prediction methods have been remarkably successful in learning mappings between input observations and output configurations [1; 2; 3]. The central guiding formulation involves learning a scoring function that recovers the configuration as the highest scoring assignment. In contrast, in a game theoretic setting, myopic strategic interactions among players lead to a Nash equilibrium or locally optimal configuration rather than highest scoring global configuration. Learning games therefore involves, at best, enforcement of local consistency constraints as recently advocated [4].

This article describes a novel game structure for autonomously optimizing decentralized manufacturing systems with multi-objective optimization challenges, namely Distributed Stackelberg Strategies in State-Based Potential Games (DS2-SbPG). DS2-SbPG integrates potential games and Stackelberg games, which improves the cooperative trade-off capabilities of potential games and the multi-objective optimization handling by Stackelberg games. Notably, all training procedures remain conducted in a fully distributed manner. DS2-SbPG offers a promising solution to finding optimal trade-offs between objectives by eliminating the complexities of setting up combined objective optimization functions for individual players in self-learning domains, particularly in real-world industrial settings with diverse and numerous objectives between the sub-systems. We further prove that DS2-SbPG constitutes a dynamic potential game that results in corresponding converge guarantees. Experimental validation conducted on a laboratory-scale testbed highlights the efficacy of DS2-SbPG and its two variants, such as DS2-SbPG for single-leader-follower and Stack DS2-SbPG for multi-leader-follower. The results show significant reductions in power consumption and improvements in overall performance, which signals the potential of DS2-SbPG in real-world applications.

This paper investigates the strategic decision-making capabilities of three Large Language Models (LLMs): GPT-3.5, GPT-4, and LLaMa-2, within the framework of game theory. Utilizing four canonical two-player games -- Prisoner's Dilemma, Stag Hunt, Snowdrift, and Prisoner's Delight -- we explore how these models navigate social dilemmas, situations where players can either cooperate for a collective benefit or defect for individual gain. Crucially, we extend our analysis to examine the role of contextual framing, such as diplomatic relations or casual friendships, in shaping the models' decisions. Our findings reveal a complex landscape: while GPT-3.5 is highly sensitive to contextual framing, it shows limited ability to engage in abstract strategic reasoning. Both GPT-4 and LLaMa-2 adjust their strategies based on game structure and context, but LLaMa-2 exhibits a more nuanced understanding of the games' underlying mechanics. These results highlight the current limitations and varied proficiencies of LLMs in strategic decision-making, cautioning against their unqualified use in tasks requiring complex strategic reasoning.

We study the problem of synthesizing strategies for a mobile sensor network to conduct surveillance in partnership with static alarm triggers. We formulate the problem as a multi-agent reactive synthesis problem with surveillance objectives specified as temporal logic formulas. In order to avoid the state space blow-up arising from a centralized strategy computation, we propose a method to decentralize the surveillance strategy synthesis by decomposing the multi-agent game into subgames that can be solved independently. We also decompose the global surveillance specification into local specifications for each sensor, and show that if the sensors satisfy their local surveillance specifications, then the sensor network as a whole will satisfy the global surveillance objective. Thus, our method is able to guarantee global surveillance properties in a mobile sensor network while synthesizing completely decentralized strategies with no need for coordination between the sensors. We also present a case study in which we demonstrate an application of decentralized surveillance strategy synthesis.

In timeline-based planning, domains are described as sets of independent, but interacting, components, whose behaviour over time (the set of timelines) is governed by a set of temporal constraints. A distinguishing feature of timeline-based planning systems is the ability to integrate planning with execution by synthesising control strategies for flexible plans. However, flexible plans can only represent temporal uncertainty, while more complex forms of nondeterminism are needed to deal with a wider range of realistic problems. In this paper, we propose a novel game-theoretic approach to timeline-based planning problems, generalising the state of the art while uniformly handling temporal uncertainty and nondeterminism. We define a general concept of timeline-based game and we show that the notion of winning strategy for these games is strictly more general than that of control strategy for dynamically controllable flexible plans. Moreover, we show that the problem of establishing the existence of such winning strategies is decidable using a doubly exponential amount of space.