Imitation with incomplete information in 2x2 games

TL;DR

This paper extends evolutionary game theory by modeling imitation with incomplete information, revealing how limited knowledge impacts strategy dynamics and favoring Grim Trigger over Tit-For-Tat in certain conditions.

Contribution

It introduces a generalized learning process for imitation with incomplete information, demonstrating significant effects on game dynamics and stationary states.

Findings

Incomplete information imitation alters strategy success.

Grim Trigger outperforms Tit-For-Tat under weak selection.

Dynamics are significantly affected by information availability.

Abstract

Evolutionary game theory has been an important tool for describing economic and social behaviour for decades. Approximate mean value equations describing the time evolution of strategy concentrations can be derived from the players' microscopic update rules. We show that they can be generalized to a learning process. As an example, we compare a restricted imitation process, in which unused parts of the role model's meta-strategy are hidden from the imitator, with the widely used imitation rule that allows the imitator to adopt the entire meta-strategy of the role model. This change in imitation behaviour greatly affects dynamics and stationary states in the iterated prisoner dilemma. Particularly we find Grim Trigger to be a more successful strategy than Tit-For-Tat especially in the weak selection regime.