A Characterization of Sequential Equilibrium through $\varepsilon$-Perfect $γ$-Sequential Equilibrium with Local Sequential Rationality and Its Computation
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866912293010276352 |
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| author | Cao, Yiyin Dang, Chuangyin |
| author_facet | Cao, Yiyin Dang, Chuangyin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_19493 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Characterization of Sequential Equilibrium through $\varepsilon$-Perfect $γ$-Sequential Equilibrium with Local Sequential Rationality and Its Computation Cao, Yiyin Dang, Chuangyin Theoretical Economics 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. |
| title | A Characterization of Sequential Equilibrium through $\varepsilon$-Perfect $γ$-Sequential Equilibrium with Local Sequential Rationality and Its Computation |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2503.19493 |