Sequential Equilibria in a Class of Infinite Extensive Form Games

TL;DR

This paper extends the concept of sequential equilibrium to a class of infinite extensive form games with continuous information, proving existence and consistency with finite game definitions.

Contribution

It introduces a new definition of sequential equilibrium for infinite games with continuous information and shows its existence and alignment with finite game equilibria.

Findings

Sequential equilibria exist in the defined class of infinite games.

The new definition refines Nash equilibria.

In finite games, the new definition matches traditional sequential equilibrium.

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.