Quantum Walk Algorithm to Compute Subgame Perfect Equilibrium in Finite Two-player Sequential Games

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Arish Pitchai 1,* A V Reddy 1 Nickolas Sarvarimuthu 1

1. Dept. of Computer Applications, National Institute of Technology Tiruchirappalli, Trichy 620015, India

* Corresponding author.

DOI: https://doi.org/10.5815/ijmsc.2016.03.03

Received: 16 Apr. 2016 / Revised: 2 May 2016 / Accepted: 31 May 2016 / Published: 8 Jul. 2016

Index Terms

Quantum Game Theory, Sequential Games, Subgame Perfect Equilibrium, Quantum Random Walk, Backward Induction, Two-player Games, Quantum Algorithm, Quantum Computing


Subgame Perfect Equilibrium (SGPE) is a refined version of Nash equilibrium used in games of sequential nature. Computational complexity of classical approaches to compute SGPE grows exponentially with the increase in height of the game tree. In this paper, we present a quantum algorithm based on discrete-time quantum walk to compute Subgame Perfect Equilibrium (SGPE) in a finite two-player sequential game. A full-width game tree of average branching factor b and height h has nodes in it. The proposed algorithm uses oracle queries to backtrack to the solution. The resultant speed-up is times better than the best known classical approach, Zermelo's algorithm.

Cite This Paper

Arish Pitchai, A V Reddy, Nickolas Savarimuthu,"Quantum Walk Algorithm to Compute Subgame Perfect Equilibrium in Finite Two-player Sequential Games", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.2, No.3, pp.32-40, 2016.DOI: 10.5815/ijmsc.2016.03.03


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