Game Theory

How hard is it to achieve consensus in a social network under uncertainty? In this paper we model this problem as a social graph of agents where each vertex is initially colored red or blue. The goal of the agents is to achieve consensus, which is when the colors of all agents align. Agents attempt to do this locally through steps in which an agent changes their color to the color of the majority of their neighbors. In real life, agents may not know exactly how many of their neighbors are red or blue, which introduces uncertainty into this process. Modeling uncertainty as perturbations of relative magnitude $1+\varepsilon$ to these color neighbor counts, we show that even small values of $\varepsilon$ greatly hinder the ability to achieve consensus in a social network. We prove theoretically tight upper and lower bounds on the price of uncertainty, a metric defined in previous work by Balcan et al. to quantify the effect of uncertainty in network games.

Recent advancements in financial problem-solving have leveraged LLMs and agent-based systems, with a primary focus on trading and financial modeling. However, credit assessment remains an underexplored challenge, traditionally dependent on rule-based methods and statistical models. In this paper, we introduce MASCA, an LLM-driven multi-agent system designed to enhance credit evaluation by mirroring real-world decision-making processes. The framework employs a layered architecture where specialized LLM-based agents collaboratively tackle sub-tasks. Additionally, we integrate contrastive learning for risk and reward assessment to optimize decision-making. We further present a signaling game theory perspective on hierarchical multi-agent systems, offering theoretical insights into their structure and interactions. Our paper also includes a detailed bias analysis in credit assessment, addressing fairness concerns. Experimental results demonstrate that MASCA outperforms baseline approaches, highlighting the effectiveness of hierarchical LLM-based multi-agent systems in financial applications, particularly in credit scoring.

Classical game-theoretic models typically assume rational agents, complete information, and common knowledge of payoffs - assumptions that are often violated in real-world MAS characterized by uncertainty, misaligned perceptions, and nested beliefs. To overcome these limitations, researchers have proposed extensions that incorporate models of cognitive constraints, subjective beliefs, and heterogeneous reasoning. Among these, hypergame theory extends the classical paradigm by explicitly modeling agents' subjective perceptions of the strategic scenario, known as perceptual games, in which agents may hold divergent beliefs about the structure, payoffs, or available actions. We present a systematic review of agent-compatible applications of hypergame theory, examining how its descriptive capabilities have been adapted to dynamic and interactive MAS contexts. We analyze 49 selected studies from cybersecurity, robotics, social simulation, communications, and general game-theoretic modeling. Building on a formal introduction to hypergame theory and its two major extensions - hierarchical hypergames and HNF - we develop agent-compatibility criteria and an agent-based classification framework to assess integration patterns and practical applicability. Our analysis reveals prevailing tendencies, including the prevalence of hierarchical and graph-based models in deceptive reasoning and the simplification of extensive theoretical frameworks in practical applications. We identify structural gaps, including the limited adoption of HNF-based models, the lack of formal hypergame languages, and unexplored opportunities for modeling human-agent and agent-agent misalignment. By synthesizing trends, challenges, and open research directions, this review provides a new roadmap for applying hypergame theory to enhance the realism and effectiveness of strategic modeling in dynamic multi-agent environments.

The serious games between humans and AI have only just begun. Evolutionary Game Theory (EGT) models the competitive and cooperative strategies of biological entities. EGT could help predict the potential evolutionary equilibrium of humans and AI. The objective of this work was to examine EGT models relevant to human-AI interaction, evolution, and co-evolution. Of thirteen EGT models considered, three were examined: the Hawk-Dove Game, Iterated Prisoner's Dilemma, and the War of Attrition. This selection was based on the widespread acceptance and clear relevance of these models to potential human-AI evolutionary dynamics and co-evolutionary trajectories. The Hawk-Dove Game predicts balanced mixed-strategy equilibria based on the costs of conflict. Iterated Prisoner's Dilemma suggests that repeated interaction may lead to cognitive co-evolution. The War of Attrition suggests that competition for resources may result in strategic co-evolution, asymmetric equilibria, and conventions on sharing resources. Each model was examined from the perspective of human and AI decision-making, from psychological and biological perspectives, and from an AI viewpoint. AI is being shaped by human input and is evolving in response to it. So too, neuroplasticity allows the human brain to evolve in response to stimuli. If humans and AI converge in future, what might be the result of human neuroplasticity combined with an ever-evolving AI? There are profound ethical and cognitive implications. EGT may provide a suitable framework to understand and predict human-AI interaction, evolution, and co-evolution. However, future research should extend beyond EGT and explore additional frameworks, empirical validation methods, and interdisciplinary perspectives. In the spirit of further exploration, an illustrative computational simulation is provided.

In the current practices of machine learning, the evaluation of forecasts has become a cornerstone of scientific progress. A multitude of evaluation metrics have been suggested and used to qualify "good" forecasts. What do those metrics share? How are they related? In this work, we use a protocol borrowed from game-theoretic probability to show that a large part of evaluation metrics can be viewed as averaged outcomes of fair gambles. Intuitively, a fair gambler is one which a forecaster would expect to fail. Hence, the gambler's ability to gain disproves the quality of the forecast. Standard evaluation metrics are then variants of choices of such fair gambles. In particular, this choice is structured along two dimensions, one of which separates calibration-type and regret-type metrics. In particular, this framework sheds light on the relationship of calibration and regret showing a theoretical equivalence in their ability to evaluate when being scaled appropriately, but the incomparability of obtained scores.