Centipedes Leap into the Quantum Realm

TL;DR

This paper explores how applying quantum strategies to the centipede game results in superior equilibria and outcomes compared to classical solutions, supported by quantum computing implementation.

Contribution

It introduces two new quantum Nash equilibria for the centipede game and demonstrates their advantages through quantum algorithm implementation.

Findings

Quantum strategies yield better payoffs than classical backward induction.

Quantum Nash equilibria outperform classical solutions in the centipede game.

Implementation on Qiskit confirms improved modeling of real-life game outcomes.

Abstract

The centipede game is a two-player non-zero-sum game. Each turn, a player can choose whether they want to take or pass a growing reward. The classical, rational solution of this game shows defection in the first round, when in reality, players cooperate much more often. Inspired by prior work employing quantum strategies in the prisoners dilemma, we showed that when similar quantum mechanics principles are applied to the centipede game, it leads to two new quantum Nash equilibria that are superior to the classical solution. Furthermore, by implementing our algorithm on Qiskit, we confirmed that leveraging quantum strategies, rather than strategies like backward induction, to solve the centipede game provided better payoffs for both players and more accurately modeled the games real-life outcomes. Ultimately, we propose a generalized conjecture for similarly structured quantum games.