Self-confirming Games: Unawareness, Discovery, and Equilibrium

Burkhard C. Schipper
(University of California, Davis)

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.

In Jérôme Lang: Proceedings Sixteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2017), Liverpool, UK, 24-26 July 2017, Electronic Proceedings in Theoretical Computer Science 251, pp. 470–488.
Published: 25th July 2017.

ArXived at: http://dx.doi.org/10.4204/EPTCS.251.35 bibtex PDF

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