game-theoretic 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 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.

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 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 paper addresses the ambiguous boundary between “strategic” and “non-strategic” behavior in behavioral game theory—particularly the lack of a rigorous, formal definition of non-strategic behavior under bounded rationality. To resolve this, we introduce the first axiomatic characterization of non-strategic behavior: actions that do not model others’ beliefs or decision processes. Our definition subsumes all canonical non-strategic rules in the literature—including Nash indifference, level-0 reasoning in cognitive hierarchy models, and reactive heuristics—and is provably disjoint from any strategic behavior in a mathematically precise sense. Methodologically, we integrate tools from game theory, formal logic, and decision theory, constructing an axiom system and establishing separation via model-theoretic proofs. The resulting framework provides the first universally applicable and decidable formal foundation for modeling bounded rationality, designing multi-agent systems, and advancing cognitive hierarchy theory.

This study addresses the challenge of equilibrium nonexistence in multi-principal, multi-team settings, where strategic externalities induce interdependence among incentive-compatible mechanisms and potential discontinuities in the mechanism correspondence. To overcome this limitation of classical models, the authors develop a novel framework that jointly characterizes the outcome distribution along honest obedience paths and the feasible sets attainable through unilateral deviations, integrating mechanism design theory, game theory, and set-valued analysis. Within this framework, they establish rigorous conditions for equilibrium existence in environments featuring team production and agency problems, thereby significantly extending the applicability of Myerson’s classic model to more complex, realistic multi-principal contexts.

Existing approaches to modeling concurrent multi-agent systems struggle to balance expressiveness and tractability. This work proposes a novel modeling paradigm based on circuit representations, integrating formal methods, game-theoretic equilibrium concepts, and computational complexity theory to overcome the expressiveness limitations and intractability inherent in explicit models for equilibrium analysis. Within this framework, we provide a complete characterization of the complexity bounds—both upper and lower—for equilibrium realizability and verification problems. Our results demonstrate that the proposed circuit-based model is provably superior in theoretical expressiveness and computational properties compared to conventional explicit representations.

This study investigates a mean-payoff bidding game played by two agents on a graph, where the right to move a token is determined each round through an auction, generating an infinite path whose long-run average payoff defines the players’ utilities. Focusing on the actual trajectories induced when both players employ adversarial optimal strategies, the work provides the first formal analysis of such non-antagonistic dynamics and establishes that, under certain conditions, the resulting trajectories eventually become periodic. By integrating tools from game theory, automata theory, and explicit constructions of optimal strategies, the paper addresses the complex dynamics arising in infinite state spaces and presents an efficient algorithm to compute the mean-payoff utilities for each player along the eventual periodic trajectory.

This study investigates multi-player discrete-bidding graph games, where token ownership is determined each turn via auction. It extends classical two-player bidding games to a multi-player coalition setting, integrating game-theoretic analysis, graph game models, and discrete budget mechanisms. The work establishes that such games are determined under mild tie-breaking rules, proves the universal existence of pure-strategy Nash equilibria for qualitative objectives, and demonstrates that the decision problem of determining winning strategies is PSPACE-hard—even when budgets are encoded in unary—marking a stark contrast to the NP ∩ coNP complexity known for the two-player case.