A Level-K Theory for Private Information Games

24 Pages Posted: 9 Aug 2017 Last revised: 4 Oct 2018

See all articles by Marco Serena

Marco Serena

Max Planck Institute for Tax Law and Public Finance

Date Written: August 8, 2017

Abstract

In a Bayesian Nash Equilibrium (BNE) of a private information game players form reciprocal beliefs over types (i.e., payoff-relevant parameters) of the form "I believe that you believe that I believe...", and so on, ad infinitum. We propose a level-k theory for private information games where a player of level of reasoning k forms "equilibrium beliefs" up to the k{th}-order, and "non-equilibrium beliefs" from the (k 1){th} -order onwards. Equilibrium beliefs follow the distribution of types, as in a BNE. Non-equilibrium beliefs ignore the distribution of types and are rather heuristic projections of one own's type onto the rival, of the form "my rival is of my type." As a result, k→∞ coincides with the definition of a BNE, and k=0 coincides with the Nash equilibrium of the symmetric-type complete information version of the game. Finally, we illustrate our belief-based level-k theory through a simple game.

Keywords: K-level Reasoning, Private Information

JEL Classification: C72, D83

Suggested Citation

Serena, Marco, A Level-K Theory for Private Information Games (August 8, 2017). Working Paper of the Max Planck Institute for Tax Law and Public Finance No. 2018-12. Available at SSRN: https://ssrn.com/abstract=3015167 or http://dx.doi.org/10.2139/ssrn.3015167

Marco Serena (Contact Author)

Max Planck Institute for Tax Law and Public Finance ( email )

Marstallplatz 1
Munich, 80539
Germany

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