Cooking Poisons: Thinking Laterally with Game Theory
Timothy Y. Chow
TL;DR
This paper reframes Rabin's lateral-thinking puzzle as a two-player, two-poison game and examines both the intended and alternative Cooked solutions through a game-theoretic lens. By formalizing strategies A–D and considering multiple poison-strength orderings, it derives payoff structures that are not zero-sum and identifies three Nash equilibria, including mixed and asymmetric outcomes, along with a non-equilibrium strategy that guarantees a baseline survival. The work highlights how lateral-thinking puzzles can be fruitfully analyzed with standard game-theoretic concepts, while also exposing limitations when multiple equilibria exist. It also suggests avenues for extending the model (more poisons) and for empirical exploration via tournaments, echoing themes from Axelrod’s iterated games. Overall, the paper demonstrates a rich interplay between creative reasoning and formal strategic analysis, with implications for broader puzzle design and decision-making under uncertainty.
Abstract
We revive an old lateral-thinking puzzle by Michael Rabin, involving poisons with strange properties. We show that the puzzle admits several unintended solutions that are just as interesting as the intended solution. Analyzing these alternative solutions using game theory yields surprisingly subtle results and several unanswered questions.