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125. Computing quasi-perfect equilibria: from a characterization to a differentiable path-following method
Invited abstract in session TD-40: Tools and algorithms for equilibrium detection, stream Interfaces Between Optimization, Hierarchical Problems and Equilibrium Detection with Applications.
Tuesday, 14:30-16:00Room: 96 (building: 306)
Authors (first author is the speaker)
| 1. | Chuangyin Dang
|
| Systems Engineering, City University of Hong Kong | |
| 2. | Yiyin Cao
|
| Department of advanced design and systems engineering, City University of Hong Kong |
Abstract
As a different paradigm from Selten's perfection for rationality on strategy perturbation, the concept of quasi-perfect equilibrium was formulated by van Damme through backward induction for finite extensive-form games with perfect recall. The admissibility of quasi-perfect equilibrium gains itself an advantage over Selten's perfect equilibrium. Nevertheless, the formulation provides insufficient information on how to find such an equilibrium so that its existence was derived from the existence of a normal-form proper equilibrium (sufficient but unnecessary). To address this issue, this paper develops with a separation technique an equivalent definition of quasi-perfect equilibrium through the introduction of epsilon-quasi-perfect equilibrium and establishes directly the existence of a quasi-perfect equilibrium. To demonstrate its computational effectiveness, we illustrate with simple examples how one can employ the definition to analytically find all the quasi-perfect equilibria. As a byproduct, we acquire an equivalent definition of sequential equilibrium. A further application of the definition leads to a differentiable path-following method to compute quasi-perfect equilibria.
Keywords
- Game Theory
- Continuous Optimization
- Programming, Nonlinear
Status: accepted
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