Simultaneous Go via quantum collapse

TL;DR

This paper introduces a simplified, deterministic quantum-inspired version of the game Go, called SGo, which maintains strategic complexity and exhibits a mixed equilibrium strategy for draws.

Contribution

It presents SGo, a symmetric, deterministic, quantum-inspired adaptation of Go, removing traditional rules and demonstrating equilibrium strategies.

Findings

SGo has a mixed equilibrium strategy for draws.

SGo simplifies traditional Go while preserving key dynamics.

Deterministic quantum state reduction enables move sensitivity.

Abstract

We construct a symmetric, simultaneous, deterministic evolution game $SGo$, which is in a certain mathematical sense a symmetrization of the classical board game Go. $SGo$ is in some ways a simpler game than Go, as Komi, Ko and suicide rules are removed. On the other hand it has similar dynamics and move sensitivity, enabled by certain deterministic ``quantum state'' reduction, so that state evolution is deterministic. Using the argument of Nash, we show that $SGo$ has a mixed equilibrium strategy to draw on average.