arXiv subjects

Yiyin Cao

Publications and source records attributed to Yiyin Cao.

6 recordsLinked to original sources

arXiv2026

A Sequence-Form Formulation of Logistic Quantal Response Equilibrium in Extensive-Form Games for Selecting Nash Equilibria

For an extensive-form game, logistic quantal response equilibrium (QRE) is defined with respect to its associated normal form and provides a natural equilibrium-selection mechanism as the rationality parameter tends to infinity. However, direct computation of logistic QRE in the normal form is generally impractical because the strategy space grows exponentially in the number of information sets. To address this difficulty, we construct a dilated-entropy-barrier artificial game in the sequence form and prove that its Nash equilibria characterize the corresponding logistic QREs. Building on this characterization, we further develop a sequence-form formulation of logistic QRE relative to a totally mixed strategy profile. This formulation gives rise to a differentiable path-following method for tracing the associated logit-QRE path, and we establish the existence of the corresponding smooth path. By recasting the dilated-entropy terms as the standard entropy terms, we additionally derive an equivalent smooth path. Numerical experiments illustrate the equilibrium-selection process of the proposed methods and evaluate their computational performance.

cs.GT↗

arXiv2026

Characterization and Computation of Normal-Form Proper Equilibria in Extensive-Form Games via the Sequence-Form Representation

Normal-form proper equilibrium, introduced by Myerson as a refinement of normal-form perfect equilibrium, occupies a distinctive position in the equilibrium analysis of extensive-form games because its more stringent perturbation structure entails the sequential rationality. However, the size of the normal-form representation grows exponentially with the number of parallel information sets, making the direct determination of normal-form proper equilibria intractable. To address this challenge, we develop a compact sequence-form proper equilibrium by redefining the expected payoffs over sequences, and we prove that it coincides with the normal-form proper equilibrium via strategic equivalence. To facilitate computation, we further introduce an alternative representation by defining a class of perturbed games based on an $\varepsilon$-permutahedron over sequences. Building on this representation, we introduce two differentiable path-following methods for computing normal-form proper equilibria. These methods rely on artificial sequence-form games whose expected payoff functions incorporate logarithmic or entropy regularization through an auxiliary variable. We prove the existence of a smooth equilibrium path induced by each artificial game, starting from an arbitrary positive realization plan and converging to a normal-form proper equilibrium of the original game as the auxiliary variable approaches zero. Finally, our experimental results demonstrate the effectiveness and efficiency of the proposed methods.

cs.GT↗

arXiv2025

A Sequence-Form Characterization and Differentiable Path-Following Method for Computing Normal-Form Perfect Equilibria in Extensive-Form Games

The sequence form, owing to its compact and holistic strategy representation, has demonstrated significant efficiency in computing normal-form perfect equilibria for two-player extensive-form games with perfect recall. Nevertheless, the examination of $n$-player games remains underexplored. To tackle this challenge, we present a sequence-form characterization of normal-form perfect equilibria for $n$-player extensive-form games, achieved through a class of perturbed games formulated in sequence form. Based on this characterization, we develop a differentiable path-following method for computing normal-form perfect equilibria and prove its convergence. This method formulates an artificial logarithmic-barrier game in sequence form, introducing an additional variable to regulate the impact of logarithmic-barrier terms on the payoff functions, as well as the transition of the strategy space. We prove the existence of a smooth equilibrium path defined by the artificial game, starting from an arbitrary positive realization plan and converging to a normal-form perfect equilibrium of the original game as the additional variable approaches zero. Furthermore, we extend Harsanyi's linear and logarithmic tracing procedures to the sequence form and develop two alternative methods for computing normal-form perfect equilibria. Numerical experiments further substantiate the effectiveness and computational efficiency of our methods.

cs.GT↗

arXiv2025

A Characterization of Reny's Weakly Sequentially Rational Equilibrium through $\varepsilon$-Perfect $γ$-Weakly Sequentially Rational Equilibrium

A weakening of sequential rationality of sequential equilibrium yields Reny's (1992) weakly sequentially rational equilibrium (WSRE) in extensive-form games. WSRE requires Kreps and Wilson's (1982) consistent assessment to satisfy global rationality of nonconvex payoff functions at every information set reachable by a player's own strategy. The consistent assessment demands a convergent sequence of totally mixed behavioral strategy profiles and associated Bayesian beliefs. Nonetheless, due to the nonconvexity, proving the existence of WSRE required invoking the existence of a normal-form perfect equilibrium, which is sufficient but not necessary. Furthermore, Reny's WSRE definition does not fully specify how to construct the convergent sequence. To overcome these challenges, this paper develops a characterization of WSRE through $\varepsilon$-perfect $γ$-WSRE with local sequential rationality, which is accomplished by incorporating an extra behavioral strategy profile. For any given $γ>0$, we generate a perfect $γ$-WSRE as a limit point of a sequence of $\varepsilon_k$-perfect $γ$-WSRE with $\varepsilon_k\to 0$. A WSRE is then acquired from a limit point of a sequence of perfect $γ_q$-WSRE with $γ_q\to 0$. This characterization enables analytical identification of all WSREs in small extensive-form games and a direct proof of the existence of WSRE. An application of the characterization yields a polynomial system that serves as a necessary and sufficient condition for verifying whether a totally mixed assessment is an $\varepsilon$-perfect $γ$-WSRE. Exploiting the system, we devise differentiable path-following methods to compute WSREs by establishing the existence of smooth paths, which are secured from the equilibrium systems of barrier and penalty extensive-form games. Comprehensive numerical results further confirm the efficiency of the methods.

econ.TH↗

arXiv2025

A Characterization of Nash Equilibrium in Behavioral Strategies through Local Sequential Rationality

The concept of Nash equilibrium in behavioral strategies (NashEBS) was formulated By Nash~\cite{Nash (1951)} for an extensive-form game through global rationality of nonconvex payoff functions. Kuhn's payoff equivalence theorem resolves the nonconvexity issue, but it overlooks that one Nash equilibrium of the associated normal-form game can correspond to infinitely many NashEBSs of an extensive-form game. To remedy this multiplicity, the traditional approach as documented in Myerson~\cite{Myerson (1991)} involves a two-step process: identifying a Nash equilibrium of the agent normal-form representation, followed by verifying whether the corresponding mixed strategy profile is a Nash equilibrium of the associated normal-form game, which often scales exponentially with the size of the extensive-form game tree. In response to these challenges, this paper develops a characterization of NashEBS through the incorporation of an extra behavioral strategy profile and beliefs, which meet local sequential rationality of linear payoff functions and self-independent consistency. This characterization allows one to analytically determine all NashEBSs for small extensive-form games. Building upon this characterization, we acquire a polynomial system serving as a necessary and sufficient condition for determining whether a behavioral strategy profile is a NashEBS. An application of the characterization yields differentiable path-following methods for computing such an equilibrium.

econ.TH↗

arXiv2025

A Characterization of Sequential Equilibrium through $\varepsilon$-Perfect $γ$-Sequential Equilibrium with Local Sequential Rationality and Its Computation

Sequential equilibrium requires a consistent assessment and sequential rationality, where the consistent assessment emerges from a convergent sequence of totally mixed behavioral strategies and associated beliefs. However, the original definition lacks explicit guidance on constructing such convergent sequences. To overcome this difficulty, this paper presents a characterization of sequential equilibrium by introducing $\varepsilon$-perfect $γ$-sequential equilibrium with local sequential rationality. For any $γ>0$, we establish a perfect $γ$-sequential equilibrium as a limit point of a sequence of $\varepsilon_k$-perfect $γ$-sequential equilibrium with $\varepsilon_k\to 0$. A sequential equilibrium is then derived from a limit point of a sequence of perfect $γ_q$-sequential equilibrium with $γ_q\to 0$. This characterization systematizes the construction of convergent sequences and enables the analytical determination of sequential equilibria and the development of a polynomial system serving as a necessary and sufficient condition for $\varepsilon$-perfect $γ$-sequential equilibrium. Exploiting the characterization, we develop a differentiable path-following method to compute a sequential equilibrium.

econ.TH↗