game-theoretic analysis

Game-theoretic power analysis traditionally relies on specific strategic forms and suffers from arbitrariness in utility function specification, undermining objectivity and cross-game comparability. Method: This paper proposes a game-form-agnostic geometric framework that maps players’ preferences into a standardized vector space. It eliminates utility-based subjectivity via canonical preference-space modeling and vectorized representation of relational postures. Power structure is then characterized through vector projection, centroid computation, and two structural metrics—hierarchicality (H) and reciprocity (R)—enabling dimensionality-reduced, quantitative, and comparative analysis. Results: Empirical application to the Prisoner’s Dilemma, Battle of the Sexes, and Cournot model demonstrates consistent cross-context representation of bargaining power, dependence, and reciprocity. The framework achieves, for the first time, geometric, quantitatively comparable, and dynamically tractable analysis of power structures in strategic interactions.

This paper addresses the decidability of winning strategy existence in finite combinatorial games. Methodologically, it introduces a general computational model based on equational logic, achieving the first deep integration of algebraic rewriting and equational programming to construct an executable and formally verifiable logical framework; automated strategy verification is realized via the OBJ-family of equational programming systems. The model enables experimental mathematical verification for multiple classic finite combinatorial games, including Nim and Kayles. Key contributions include: (i) establishing the first computable equational logic paradigm specifically designed for proving winning strategy existence—thereby transcending the limitations of traditional qualitative analysis; and (ii) significantly enhancing both the automation level and formal rigor of combinatorial game strategy reasoning, thereby providing a novel methodological pathway and empirical foundation for experimental mathematics in game theory.

Traditional game theory struggles to model bounded rationality and reasoning processes in LLM-based systems. Method: This paper proposes the LLM-Nash framework, explicitly modeling prompts as strategies to capture cognition-constrained reasoning behaviors of LLM agents, and introduces— for the first time—the notion of game-theoretic equilibrium in prompt space, enabling formal analysis of reasoning dynamics. The framework unifies game-theoretic modeling, LLM inference mechanisms, and cognitive modeling at the strategy level. Contribution/Results: Experiments demonstrate that the resulting reasoning equilibria systematically deviate from classical Nash equilibria, revealing structural effects of prompt design on behavioral convergence. This work establishes the first game-theoretic analytical paradigm and computationally tractable theoretical toolkit for LLM-agent interactions grounded in prompt-space modeling.

This work addresses the iterative volunteer’s dilemma by formalizing it, for the first time, as a stochastic concurrent multi-player game, and systematically conducting formal modeling, verification, and strategy synthesis. Methodologically, it integrates probabilistic model checking (using PRISM), multi-objective strategy synthesis, and parametric sensitivity analysis to verify correctness, decide reachability, synthesize optimal iterative strategies, and quantify correlations between local and global rewards over finite horizons. Key contributions include: (1) the first verifiable formal framework for stochastic concurrent games applied to social dilemmas; (2) parametric analysis supporting trade-offs among multiple reward objectives; and (3) quantitative characterization—across diverse configurations—of the inherent tension and evolutionary dynamics between individual incentives and collective welfare, thereby providing both theoretical foundations and computational tools for mechanism design.

This study addresses the stability of Nash equilibria under evolutionary dynamics in population games with strategy sets modeled as infinite-dimensional compact metric spaces. Methodologically, it extends dissipativity theory to infinite-dimensional evolutionary systems on the manifold of probability measures, establishing a general stability analysis framework applicable to arbitrary payoff structures. The approach integrates infinite-dimensional dynamical systems theory, monotone operator theory, and differential geometry of measure manifolds, enabling modular verification of dynamical mechanisms against payoff conditions. Theoretical contributions include: (i) unified derivation of stability criteria for multiple classical dynamics—including Brown–von Neumann–Nash and unbiased pairwise comparison dynamics; (ii) natural incorporation of generalized settings such as dynamic payoffs and monotone games; and (iii) successful application to novel continuous-time war-of-attrition games, demonstrating both the generality and practical applicability of the framework.

This study investigates symmetric Nash equilibria in two-player repeated additive games with finite action sets, focusing on reactive strategies that depend solely on the opponent’s previous move. By reformulating equilibrium conditions as a system of linear equalities and inequalities in strategy parameters, the work provides the first complete characterization of all such symmetric Nash equilibria and establishes a one-to-one correspondence between nonempty subsets of actions and equilibrium classes. Introducing the novel concept of “S-supported equilibria,” it proves that equilibria supported on the full action set coincide with the classical equalizer strategies. Integrating theoretical analysis with evolutionary simulations, the study further demonstrates that the evolutionary success of an equilibrium class is jointly determined by its emergence probability and robustness against invasion.

This study addresses a fundamental challenge in the formal verification of multi-agent systems: determining whether equilibrium strategies exist in multi-player graph games that satisfy given payoff constraints. The work provides a systematic investigation of the constrained existence problem under five distinct equilibrium concepts, integrating computational complexity theory, formal methods, and game theory to deliver a complete characterization of the associated complexity classes. In contrast to classical two-player zero-sum games, this research substantially extends the analytical framework by precisely delineating the computational boundaries of constrained equilibrium existence across different solution concepts, thereby establishing a rigorous theoretical foundation for verifying robustness in multi-agent systems.

This study investigates how participants’ understanding of equilibrium strategies transfers across different mechanisms. To this end, it introduces the concept of “strategic analogy,” which extends traditional notions of strategic equivalence by simultaneously remapping both actions and types. The paper develops a knowledge representation framework grounded in payoff comparisons to formally characterize strategic understanding. Integrating tools from mechanism design, equilibrium analysis, and knowledge representation, the work demonstrates that, provided a clear correspondence between actions and types is established, equilibrium reasoning can be effectively transferred across strategically analogous mechanisms. The proposed framework applies broadly to settings such as single-item auctions, scoring auctions, and nonlinear pricing with capacity constraints, offering both a theoretical foundation and practical pathways for cross-mechanism strategic transfer.

This study addresses the quantification of causal responsibility among agents in probabilistic multi-agent systems with respect to specific outcomes. By modeling the system as a concurrent stochastic multi-player game, the work proposes a responsibility metric grounded in counterfactual reasoning with backward-looking analysis. It introduces the Shapley value—adapted from cooperative game theory—for the first time into multi-agent responsibility attribution, integrating it with Nash equilibrium to balance individual rewards against assigned responsibilities. The resulting framework unifies formal verification and strategy synthesis to construct a responsibility-aware mechanism that satisfies fairness and consistency properties. Under stable strategies, this approach simultaneously optimizes each agent’s expected reward and its allocated share of responsibility.

This work addresses the long-standing challenge of Nash equilibrium existence in infinite games, which traditionally relies on strong assumptions and lacks a unified framework. By abandoning countable additivity and introducing finitely additive mixed strategies, the paper establishes—under the most general setting—that a Nash equilibrium exists for any nonempty set of players and any bounded utility functions. This result unifies existing equilibrium existence theorems and demonstrates that the equilibrium correspondence is nonempty, compact-valued, and upper hemicontinuous. The proof synthesizes tools from finitely additive measure theory, analysis of upper hemicontinuous correspondences, and finite approximation techniques, thereby enabling direct equilibrium analysis of infinite games previously considered intractable.