Quantifying in extensive games

Abstract

Recently, there have been a lot of approaches that uses a modal logic to model and reason about games. It seems natural to study quantification whenever games are modeled by means of the modal approach. In this work, we use a first-order modal logic, namely Game Analysis Logic (GAL), in order to study the alternatives of quantification for the most used solution concepts, namely Nash Equilibrium (NE) and subgame perfect equilibrium (SPE), for extensive games. We also characterize these concepts by means of the structure of an extensive game according to the different ways of quantification. Despite the fact that quantifying in a modal context might be troublesome, we show that for NE and SPE the alternatives are equivalent each other.