What Can Ancient Roman Rebellions Teach Us About Game Theory?

Iberian Peninsula Rebellion

Around 75 BC a rebellion erupted on the Iberian Peninsula against ancient Rome, led by Quintus Sertorius. Rome sent two armies: one commanded by the elder aristocrat Metrius Pius and the other by the young, wealthy Pompey, who also held command over Pius.

Pius and Pompey faced strategic choices. Pius could either attack Hectulius to seize Leminius and then advance east to defeat the rebels, or first sail to Gades, rescue the besieged New Carthage, and later move to Lauro. Hectulius, Sertorius’s deputy, also had two options: march directly to New Carthage to confront Pius, or hold Leminius and block Pius at the River Baetis.

These decisions can be represented as a decision tree (see images).

Relation to Game Theory

The rebellion story illustrates strategic conflict: Hectulius must anticipate Pius’s reaction, and both aim to outthink the other, mirroring the core of game‑theoretic analysis.

The Nim Game

The Nim game is a simple yet complete game family. With three coins arranged in two rows (one in the first row, two in the second), players alternate removing at least one coin from a single row; the player taking the last coin wins.

Key questions include the optimal action sequence for each player, existence of a winning strategy, and which player can force a win.

Assuming Anna moves first and Barbara second, Anna has three possible first moves:

Remove 1 coin from the first row.

Remove 1 coin from the second row.

Remove 2 coins from the second row.

Analysis shows that removing 1 coin from the second row leaves Barbara with a single‑coin option in each row, guaranteeing Anna a win. Thus Anna’s optimal first move is to take 1 coin from the second row, after which she can capture the remaining coin(s) and secure victory.

Game Theory, Neoclassical Economics, and Mathematics

Neoclassical economics assumes rational agents operating within a regulated environment of property rights, monetary systems, and competitive markets. However, when competition is limited or property rights are ill‑defined, traditional models falter.

Game theory addresses this gap by modeling direct interactions among agents, turning strategic choices into mathematical optimization problems where each participant seeks to maximize payoff given others’ strategies.

The examples above demonstrate how historical conflicts and simple combinatorial games can illuminate the connections between game theory, economics, and mathematics.

References

Roger A. McCain, *Game Theory: An Introduction to Strategic Analysis* (translated by Lin Qian).