Discovery and Equilibrium in Games with Unawareness

TL;DR

This paper introduces a framework for understanding how players discover new actions in games with unawareness, leading to a self-confirming equilibrium through rationalizable discovery processes.

Contribution

It defines discovery processes in games with unawareness and proves the existence of self-confirming equilibria as steady-states of these processes.

Findings

Existence of rationalizable discovery processes leading to self-confirming equilibria.

Framework accommodates players discovering new actions during play.

Equilibrium interpreted as a steady-state of discovery and learning.

Abstract

Equilibrium notions for games with unawareness in the literature cannot be interpreted as steady-states of a learning process because players may discover novel actions during play. In this sense, many games with unawareness are "self-destroying" as a player's representation of the game may change after playing it once. We define discovery processes where at each state there is an extensive-form game with unawareness that together with the players' play determines the transition to possibly another extensive-form game with unawareness in which players are now aware of actions that they have discovered. A discovery process is rationalizable if players play extensive-form rationalizable strategies in each game with unawareness. We show that for any game with unawareness there is a rationalizable discovery process that leads to a self-confirming game that possesses a self-confirming equilibrium in extensive-form rationalizable conjectures. This notion of equilibrium can be interpreted as steady-state of both a discovery and learning process.