In this paper, we focus on computing an NE that optimizes a given objective function.

Self-play is a technique for machine learning in multi-agent systems where a learning algorithm learns by interacting with copies of itself. Self-play is useful for generating large quantities of data for learning, but has the drawback that the agents the learner will face post-training may have dramatically different behavior than the learner came to expect by interacting with itself. For the special case of two-player constant-sum games, self-play that reaches Nash equilibrium is guaranteed to produce strategies that perform well against any post-training opponent; however, no such guarantee exists for multiplayer games. We show that in games that approximately decompose into a set of two-player constant-sum games (called constant-sum polymatrix games) where global $\epsilon$-Nash equilibria are boundedly far from Nash equilibria in each subgame (called subgame stability), any no-external-regret algorithm that learns by self-play will produce a strategy with bounded vulnerability. For the first time, our results identify a structural property of multiplayer games that enable performance guarantees for the strategies produced by a broad class of self-play algorithms. We demonstrate our findings through experiments on Leduc poker.

In this paper we establish efficient and \emph{uncoupled} learning dynamics so that, when employed by all players in a general-sum multiplayer game, the \emph{swap regret} of each player after $T$ repetitions of the game is bounded by $O(\log T)$, improving over the prior best bounds of $O(\log^4 (T))$. At the same time, we guarantee optimal $O(\sqrt{T})$ swap regret in the adversarial regime as well. To obtain these results, our primary contribution is to show that when all players follow our dynamics with a \emph{time-invariant} learning rate, the \emph{second-order path lengths} of the dynamics up to time $T$ are bounded by $O(\log T)$, a fundamental property which could have further implications beyond near-optimally bounding the (swap) regret. Our proposed learning dynamics combine in a novel way \emph{optimistic} regularized learning with the use of \emph{self-concordant barriers}. Further, our analysis is remarkably simple, bypassing the cumbersome framework of higher-order smoothness recently developed by Daskalakis, Fishelson, and Golowich (NeurIPS'21).

In this paper, we focus on computing an NE that optimizes a given objective function.

After the great achievement of solving two-player zero-sum games, more and more AI researchers focus on solving multiplayer games. To facilitate the development of designing efficient learning algorithms for solving multiplayer games, we propose a multiplayer game platform for solving Urban Network Security Games (\textbf{UNSG}) that model real-world scenarios. That is, preventing criminal activity is a highly significant responsibility assigned to police officers in cities, and police officers have to allocate their limited security resources to interdict the escaping criminal when a crime takes place in a city. This interaction between multiple police officers and the escaping criminal can be modeled as a UNSG. The variants of UNSGs can model different real-world settings, e.g., whether real-time information is available or not, and whether police officers can communicate or not. The main challenges of solving this game include the large size of the game and the co-existence of cooperation and competition. While previous efforts have been made to tackle UNSGs, they have been hampered by performance and scalability issues. Therefore, we propose an open-source UNSG platform (\textbf{GraphChase}) for designing efficient learning algorithms for solving UNSGs. Specifically, GraphChase offers a unified and flexible game environment for modeling various variants of UNSGs, supporting the development, testing, and benchmarking of algorithms. We believe that GraphChase not only facilitates the development of efficient algorithms for solving real-world problems but also paves the way for significant advancements in algorithmic development for solving general multiplayer games.

Self-play is a technique for machine learning in multi-agent systems where a learning algorithm learns by interacting with copies of itself. Self-play is useful for generating large quantities of data for learning, but has the drawback that the agents the learner will face post-training may have dramatically different behavior than the learner came to expect by interacting with itself. For the special case of two-player constant-sum games, self-play that reaches Nash equilibrium is guaranteed to produce strategies that perform well against any post-training opponent; however, no such guarantee exists for multiplayer games. We show that in games that approximately decompose into a set of two-player constant-sum games (called constant-sum polymatrix games) where global \epsilon -Nash equilibria are boundedly far from Nash equilibria in each subgame (called subgame stability), any no-external-regret algorithm that learns by self-play will produce a strategy with bounded vulnerability. For the first time, our results identify a structural property of multiplayer games that enable performance guarantees for the strategies produced by a broad class of self-play algorithms.

In this paper we establish efficient and \emph{uncoupled} learning dynamics so that, when employed by all players in a general-sum multiplayer game, the \emph{swap regret} of each player after T repetitions of the game is bounded by O(\log T), improving over the prior best bounds of O(\log 4 (T)) . At the same time, we guarantee optimal O(\sqrt{T}) swap regret in the adversarial regime as well. To obtain these results, our primary contribution is to show that when all players follow our dynamics with a \emph{time-invariant} learning rate, the \emph{second-order path lengths} of the dynamics up to time T are bounded by O(\log T), a fundamental property which could have further implications beyond near-optimally bounding the (swap) regret. Our proposed learning dynamics combine in a novel way \emph{optimistic} regularized learning with the use of \emph{self-concordant barriers}. Further, our analysis is remarkably simple, bypassing the cumbersome framework of higher-order smoothness recently developed by Daskalakis, Fishelson, and Golowich (NeurIPS'21).

Trustworthiness reasoning is crucial in multiplayer games with incomplete information, enabling agents to identify potential allies and adversaries, thereby enhancing reasoning and decision-making processes. Traditional approaches relying on pre-trained models necessitate extensive domain-specific data and considerable reward feedback, with their lack of real-time adaptability hindering their effectiveness in dynamic environments. In this paper, we introduce the Graph Retrieval Augmented Reasoning (GRATR) framework, leveraging the Retrieval-Augmented Generation (RAG) technique to bolster trustworthiness reasoning in agents. GRATR constructs a dynamic trustworthiness graph, updating it in real-time with evidential information, and retrieves relevant trust data to augment the reasoning capabilities of Large Language Models (LLMs). We validate our approach through experiments on the multiplayer game "Werewolf," comparing GRATR against baseline LLM and LLM enhanced with Native RAG and Rerank RAG. Our results demonstrate that GRATR surpasses the baseline methods by over 30\% in winning rate, with superior reasoning performance. Moreover, GRATR effectively mitigates LLM hallucinations, such as identity and objective amnesia, and crucially, it renders the reasoning process more transparent and traceable through the use of the trustworthiness graph.

Multiplayer games, when the number of players exceeds two, present unique challenges that fundamentally distinguish them from the extensively studied two-player zero-sum games. These challenges arise from the non-uniqueness of equilibria and the risk of agents performing highly suboptimally when adopting equilibrium strategies. While a line of recent works developed learning systems successfully achieving human-level or even superhuman performance in popular multiplayer games such as Mahjong, Poker, and Diplomacy, two critical questions remain unaddressed: (1) What is the correct solution concept that AI agents should find? and (2) What is the general algorithmic framework that provably solves all games within this class? This paper takes the first step towards solving these unique challenges of multiplayer games by provably addressing both questions in multiplayer symmetric normal-form games. We also demonstrate that many meta-algorithms developed in prior practical systems for multiplayer games can fail to achieve even the basic goal of obtaining agent's equal share of the total reward.

Competency Questions (CQs) are a form of ontology functional requirements expressed as natural language questions. Inspecting CQs together with the axioms in an ontology provides critical insights into the intended scope and applicability of the ontology. CQs also underpin a number of tasks in the development of ontologies e.g. ontology reuse, ontology testing, requirement specification, and the definition of patterns that implement such requirements. Although CQs are integral to the majority of ontology engineering methodologies, the practice of publishing CQs alongside the ontological artefacts is not widely observed by the community. In this context, we present an experiment in retrofitting CQs from existing ontologies. We propose RETROFIT-CQs, a method to extract candidate CQs directly from ontologies using Generative AI. In the paper we present the pipeline that facilitates the extraction of CQs by leveraging Large Language Models (LLMs) and we discuss its application to a number of existing ontologies.