Where Do Mistakes Lead? A Survey of Games with Incompetent Players

Abstract

Mathematical models often aim to describe a complicated mechanism in a cohesive and simple manner. However, reaching perfect balance between being simple enough or overly simplistic is a challenging task. Frequently, game-theoretic models have an underlying assumption that players, whenever they choose to execute a specific action, do so perfectly. In fact, it is rare that action execution perfectly coincides with intentions of individuals, giving rise to behavioural mistakes. The concept of incompetence of players was suggested to address this issue in game-theoretic settings. Under the assumption of incompetence, players have non-zero probabilities of executing a different strategy from the one they chose, leading to stochastic outcomes of the interactions. In this article, we survey results related to the concept of incompetence in classic as well as evolutionary game theory and provide several new results. We also suggest future extensions of the model and argue why it is important to take into account behavioural mistakes when analysing interactions among players in both economic and biological settings.

Shifts in evolutionary balance of phenotypes under environmental changes

“…We consider behavioural flexibility to be the potential expression of different phenotypes when organisms are exposed to unfamiliar environmental conditions. As this flexibility occurs due to the imperfect realization of the bacteria's 'expected' phenotype, it is referred to as incompetence [59][60][61] (see [62] for a recent survey of games with incompetent players). Incompetent bacteria may thus change their behavioural traits by switching to a different trait with some probability.…”