Sequential Equilibria in a Class of Infinite Extensive Form Games
Michael Greinecker, Martin Meier, Konrad Podczeck
TLDR
This paper defines sequential equilibrium for a new class of infinite extensive-form games, ensuring existence and refinement of Nash equilibria.
Key contributions
- Introduces a new class of infinite extensive-form games with continuous information.
- Defines a natural sequential equilibrium concept for this new class of infinite games.
- Proves existence of sequential equilibria in this class, which refine Nash equilibria.
- Ensures the definition is consistent with traditional sequential equilibrium in finite games.
Why it matters
Sequential equilibrium is a fundamental concept in game theory, previously undefined for games with continuous actions. This work extends its applicability to infinite extensive-form games, enabling analysis of more realistic and complex strategic interactions.
Original Abstract
Sequential equilibrium is one of the most fundamental refinements of Nash equilibrium for games in extensive form. However, it is not defined for extensive-form games in which a player can choose among a continuum of actions. We define a class of infinite extensive form games in which information behaves continuously as a function of past actions and define a natural notion of sequential equilibrium for this class. Sequential equilibria exist in this class and refine Nash equilibria. In standard finite extensive-form games, our definition selects the same strategy profiles as the traditional notion of sequential equilibrium.
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