Can Evolutionary Game Theory Explain the US‑China Trade War?

Recent headlines about US President Trump imposing tariffs and China’s strong retaliation illustrate a conflict without literal weapons, yet one that involves many actors such as exporters and investors. From a mathematical modeling perspective, this situation can be examined with evolutionary game theory , which captures dynamic, population‑level strategy competition.

Basic Concepts of Evolutionary Game Theory

Traditional game theory focuses on rational agents choosing optimal strategies under fixed rules to reach a Nash equilibrium, assuming complete information. In reality, agents have limited rationality and the environment changes, requiring a dynamic description.

Evolutionary game theory (Evolutionary Game Theory) borrows biological evolution mechanisms: successful strategies proliferate through reproduction, while unsuccessful ones fade, without agents consciously maximizing utility. Strategies better adapted to the environment gain dominance via replicator dynamics or similar equations.

2. Evolutionarily Stable Strategy (ESS)

An ESS is a strategy that (1) is a Nash equilibrium when everyone adopts it, and (2) resists invasion by alternative strategies offering equal payoff, maintaining a slight advantage that stabilizes the population.

Applied to nations, a policy such as protectionism that yields high short‑term gains may be imitated, but if its costs become too high, the strategy loses adaptability and is replaced by a more stable alternative.

Common Evolutionary Game Models

1. Hawk‑Dove Game

The classic hawk‑dove model analyzes whether individuals choose aggressive (hawk) or submissive (dove) behavior when competing for limited resources.

Payoffs are described as:

When two hawks meet, both risk injury, yielding an average payoff.

When a hawk meets a dove, the hawk captures the entire resource while the dove gets zero.

When two doves meet, they avoid conflict and share the resource, receiving a modest payoff.

If the proportion of hawks in the population is x and doves 1‑x , expected payoffs can be calculated, and a mixed‑strategy equilibrium emerges when the two expected payoffs are equal.

When conflict costs exceed resource benefits, aggressive hawk strategies may win short‑term but cannot dominate long‑term; a mixed strategy balancing aggression and restraint becomes evolutionarily stable.

2. Numerical Setting and Equilibrium Solving

By assigning concrete values to resource benefits and conflict costs, the payoff matrix can be populated, and solving for the point where hawk and dove expected payoffs are equal yields the equilibrium proportion of each strategy.

The result often shows a 50‑50 split, indicating that neither pure aggression nor pure submission is sustainable; a balanced mix is optimal.

Replicator Dynamics

In real societies, strategy distributions are rarely at equilibrium initially; they evolve over time toward stability.

Replicator dynamics describe how the proportion of a strategy changes according to its payoff relative to the population average: if a strategy’s payoff exceeds the average, its share grows; otherwise, it declines, eventually approaching the equilibrium point.

International Situation as a Hawk‑Dove Metaphor

The current US‑China trade war, global geopolitical tensions, and major‑power strategic contests can be abstracted as a special hawk‑dove game.

Hawk strategies represent tariffs, technology bans, alliance pressure, and other hard‑line measures.

Dove strategies favor cooperation, negotiation, and conflict avoidance.

Extreme hawk tactics raise conflict costs quickly and are unsustainable; extreme dove tactics risk losing strategic resources. Nations tend toward mixed strategies that balance firmness with flexibility.

Thus, the ongoing “no‑smoke” international battle is not a single impulsive decision but a long‑term adaptive competition where successful strategies survive through payoff‑driven replication.

Because the game never ends, evolution never stops. (Author: Wang Haihua)