How damaging is zero-sum thinking to an agent's interests when the world is positive-sum?

TL;DR

This paper investigates the impact of zero-sum decision rules like maximin on agents' interests in positive-sum environments, challenging the view that they are always harmful compared to Nash equilibrium.

Contribution

It provides theoretical and empirical evidence that maximin can sometimes outperform Nash equilibrium in positive-sum games, highlighting the nuanced effects of zero-sum thinking.

Findings

Maximin can serve an agent's interests better than Nash in certain positive-sum games.

The class of games where maximin dominates Nash is as large as the class where Nash dominates maximin.

Maximin can outperform Nash in real pay-offs due to coordination failures and multiple equilibria.

Abstract

We study whether zero-sum decision rules, maximin and minimax, harm agents' interests in positive-sum strategic environments relative to Nash equilibrium behavior or, more generally, than best response behaviour. Contrary to an influential evolutionary view, we give illustrations where maximin serves an agent's interests better than Nash equilibrium behaviour. We also show that these illustration are not atypical or idiosyncratic because, in our main result, the class of such games where a maximin profile strictly Pareto dominates all Nash equilibria has the same cardinality as the class of games in which a Nash equilibrium strictly Pareto dominates all maximin profiles. Thus, neither behavior is generally superior. We further identify additional mechanisms favoring maximin over Nash equilibrium, including coordination failures under multiple equilibria, where maximin can outperform Nash play in realised-pay-off terms. A systematic analysis of strictly ordinal symmetric 3x3 games shows that these effects arise with non-trivial frequency. Our findings, therefore, suggest that the observed rise in zero-sum thinking in many rich countries, when associated with a maximin decision rule, will not be readily displaced through its generation of inferior pay-offs.