Extreme punishments characterize weak Pareto optimality

Abstract

In normal form games, we model the largely observed psychological phenomenon of systematic and extreme punishment after a deviation, regardless of the cost. After establishing basic properties, we show that this notion characterizes a weak form of Pareto optimality. Every Pareto optimal outcome can also be sustained by the threat of extreme punishment, which cannot be achieved in general through Nash equilibria strategies, nor with tit-for-tat strategies.