Self-confirming Games: Unawareness, Discovery, and Equilibrium

TL;DR

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

Contribution

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

Findings

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

Self-confirming equilibria can be achieved through these discovery processes.

Framework captures dynamic learning and unawareness in strategic interactions.

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 must 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 games with unawareness in which players are now aware of actions that they have previously 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 an extensive-form rationalizable self-confirming equilibrium. This notion of equilibrium can be interpreted as steady-state of a learning and discovery process.