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

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  • Yiyin Cao
  • Chuangyin Dang

Abstract

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 $\gamma$-sequential equilibrium with local sequential rationality. For any $\gamma>0$, we establish a perfect $\gamma$-sequential equilibrium as a limit point of a sequence of $\varepsilon_k$-perfect $\gamma$-sequential equilibrium with $\varepsilon_k\to 0$. A sequential equilibrium is then derived from a limit point of a sequence of perfect $\gamma_q$-sequential equilibrium with $\gamma_q\to 0$. 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 $\gamma$-sequential equilibrium. Exploiting the characterization, we develop a differentiable path-following method to compute a sequential equilibrium.

Suggested Citation

  • Yiyin Cao & Chuangyin Dang, 2025. "A Characterization of Sequential Equilibrium through $\varepsilon$-Perfect $\gamma$-Sequential Equilibrium with Local Sequential Rationality and Its Computation," Papers 2503.19493, arXiv.org.
  • Handle: RePEc:arx:papers:2503.19493
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    2. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
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