A Characterisation of Nash Equilibrium in Behavioural Strategies through Local Sequential Rationality and Self-Independent Beliefs
12 Jul 2024
12:30 -14:00
Times are shown in local time.
Open to: All
Room W2.02 (Cambridge Judge Business School)
Trumpington St
Cambridge
CB2 1AG
United Kingdom
Join our Operations and Technology Management seminar
Speaker: Cao Yiyin, City University of Hong Kong
About the seminar topic
The concept of a Nash equilibrium in behavioural strategies was formulated for an extensive-form game with perfect recall through global rationality. This formulation contains nonconvex payoff functions and establishes the existence of Nash equilibria through the associated normal-form game. Importantly, the formulation of Nash equilibrium based on global rationality is essentially independent of the structure of game trees and beliefs.
Furthermore, applying this formulation to find Nash equilibria can present challenges. In order to address the limitations and enable the direct identification of Nash equilibria from extensive-form games, without relying on the associated normal-form game, our paper presents a novel characterisation of Nash equilibrium in behavioural strategies. This characterisation is achieved through local sequential rationality and self-independent beliefs.
By introducing an auxiliary behavioural strategy profile, our characterisation ensures global rationality by leveraging local sequential rationality that involves conditional expected payoffs at every information set. Moreover, this characterisation leads naturally to a polynomial system that serves as a necessary and sufficient condition for a Nash equilibrium.
As a by-product, we secure from the characterisation a differentiable path-following method for computing a Nash equilibrium. Comprehensive numerical experiments further confirm the effectiveness and efficiency of our method.
Speaker bio
Cao Yiyin is a doctoral candidate at City University of Hong Kong.
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No registration required. If you have any questions about this seminar, please email Luke Slater.