How damaging is zero-sum thinking to an agent's interests when the world is positive-sum?
New research challenges the assumption that zero-sum strategies always underperform in positive-sum environments.
Economists Shaun Hargreaves Heap and Mehmet Mars Seven challenge a long-held assumption in game theory: that zero-sum thinking (using maximin or minimax decision rules) necessarily harms agents in positive-sum environments. In their paper "How damaging is zero-sum thinking to an agent's interests when the world is positive-sum?" (arXiv:2604.19359), they compare these strategies to Nash equilibrium and best-response behaviors. Surprisingly, they provide illustrations where maximin serves an agent's interests better than Nash equilibrium, contradicting the influential evolutionary view that zero-sum strategies are always inferior.
Their main result shows that the class of games where a maximin profile strictly Pareto dominates all Nash equilibria has the same cardinality as the class where Nash equilibrium dominates maximin—meaning neither strategy is generally superior. They identify mechanisms like coordination failures under multiple equilibria, where maximin can yield higher realized payoffs. A systematic analysis of strictly ordinal symmetric 3x3 games confirms these effects occur with non-trivial frequency. The findings suggest the observed rise in zero-sum thinking in many rich countries may not be readily displaced by its supposed inferior payoffs, as it can be rational in certain contexts.
- Maximin can outperform Nash equilibrium in some positive-sum games, contrary to evolutionary views.
- The class of games where maximin dominates Nash has the same cardinality as the reverse—no strategy is universally superior.
- Coordination failures under multiple equilibria allow maximin to yield higher realized payoffs in symmetric 3x3 games.
Why It Matters
This challenges the assumption that zero-sum thinking is always irrational, with implications for economic policy and AI strategy design.