Pizza Race Problem

TL;DR

This paper analyzes a real-time pizza sharing game where two players eat slices simultaneously, proving the starting player can secure at least 40% of the pizza, with implications for strategic sharing under timing constraints.

Contribution

It introduces a new real-time variant of the pizza sharing problem and establishes a lower bound on the starting player's share in this setting.

Findings

Starting player can always eat at least 40% of the pizza.

The problem differs from the classic alternating turn model.

Potential for improved strategies beyond the proven bound.

Abstract

This paper deals with a problem in which two players share a previously sliced pizza and try to eat as much amount of pizza as they can. It takes time to eat each piece of pizza and both players eat pizza at the same rate. One is allowed to take a next piece only after the person has finished eating the piece on hand. Also, after the first piece is taken, one can only take a piece which is adjacent to already-taken piece. This paper shows that, in this real time setting, the starting player can always eat at least two-fifth of the total size of the pizza. However, this may not be the best possible amount the starting player can eat. It is a modified problem from an original one where two players takes piece alternatively instead.