In today's interconnected global economy, trade wars and tariff policies can have far‐reaching impacts on domestic and international markets. This blog article is intended to foster a discussion and give fellow decision modelers and strategists (Decision Superheroes) a simple framework to understand the system dynamics of a trade war. The models were coded in Julia and all the files are available on Github.

Understanding Trade Wars

A trade war occurs when countries impose tariffs or other trade barriers on each other in response to perceived unfair trade practices or imbalances. Rather than negotiating, countries engage in tit-for-tat measures, which can escalate and hurt both economies by reducing international trade and increasing prices for consumers. In this context, these measures revolve mostly around tariffs, counter tariffs and export taxes.
Tariffs are taxes imposed on imported goods. They serve multiple purposes:

• Revenue Generation: Governments collect money from imported goods.
• Protectionism: Tariffs can help protect domestic industries by making imported goods more expensive compared to local products.
• Political Leverage: Tariffs can be used as a tool in diplomatic or trade negotiations.

Counter tariffs (or retaliatory tariffs) are tariffs imposed in response to tariffs set by another country. When one nation raises tariffs on imports, the affected country might retaliate with its own tariffs, escalating into a trade war. Another approach is to use export taxes which are levied on goods leaving a country. Unlike tariffs, which are applied to imports, export taxes reduce the competitiveness of domestic goods abroad. They can be used to conserve valuable resources or ensure domestic supply but might also discourage exports.
Historically, many nations have used high tariffs as a way to protect emerging industries:

• United States in the 19th Century: During the early years of industrialization, the U.S. maintained relatively high tariffs (sometimes over 40%) to shield its young manufacturing sector from established European competitors. This protection helped stimulate domestic industrial growth but also led to higher consumer prices.
• Import Substitution Industrialization (ISI) in Latin America: In the mid-20th century, many Latin American countries imposed high tariffs to foster domestic industries by reducing reliance on imports. Although this strategy initially boosted local production, over time it sometimes resulted in inefficiencies, lower competitiveness, and economic stagnation due to a lack of innovation and exposure to global markets.

In contrast, countries with lower tariffs tend to experience more dynamic competition and integration into the global economy:

• Post-World War II Europe: The establishment of the European Economic Community (EEC) and later the European Union (EU) led to a significant reduction in internal tariffs. This integration promoted increased trade, efficiency gains, and overall economic growth.
• East Asian Economies: Countries like South Korea and Taiwan, after initially protecting some nascent industries, gradually reduced tariffs and opened up to international trade. This transition was accompanied by rapid industrialization, technological transfer, and export-led growth, which propelled them to high levels of economic development.

Model Overview and Starting Assumptions

In this post, we explore a simplified simulation model that uses a dynamic, game‐theoretic approach to analyze trade interactions between the United States and its major trading partners. Our model combines elements of the classic prisoner’s dilemma. The prisoner's dilemma is a classic game theory scenario where two players must independently choose to cooperate or defect without knowing what the other will do. If both cooperate, they receive a moderate benefit; if one defects while the other cooperates, the defector gains a high benefit while the cooperator gets little or nothing; and if both defect, both end up worse off than if they had cooperated.

This model is useful for understanding trade wars because countries face a similar decision. When two nations decide whether to impose tariffs (defect) or maintain free trade (cooperate), both can benefit from mutual cooperation. However, the temptation to impose tariffs in hopes of gaining short-term advantage can lead to retaliatory measures (counter tariffs) and a trade war, ultimately harming both economies. Thus, the prisoner's dilemma captures the inherent conflict between short-term self-interest and long-term mutual benefit in trade policies.

The simulation focuses on five key trading partners of the US. The baseline bilateral trade data (in billions of dollars) between the US and a partner is defined as follows:

const trade_data = Dict( 
    "Canada" => TradeData(250.0, 300.0),
    "Mexico" => TradeData(200.0, 350.0),
    "China" => TradeData(130.0, 450.0),
    "Japan" => TradeData(60.0, 140.0),
    "European Union" => TradeData(376.0, 545.0)
)
  

In this example, the US exports 250 billion dollars to Canada while importing 300 billion dollars. Similar trade figures are provided for Mexico, China, Japan, and the European Union.

Tariff Rate Assumptions

To model the uncertainty and variability of tariff policies, the simulation uses a triangular distribution for effective tariff rates:

tri_dist = TriangularDist(5.0, 50.0, 25.0)
  

This distribution is defined as a triangular distribution with a minimum of 5%, a maximum of 50%, and a most likely (mode) value of 25%. In each round, if a party defects (i.e. imposes tariffs), the effective tariff rate is randomly sampled from this distribution.The triangular distribution is especially useful in low-information settings because it allows us to incorporate expert judgment—by specifying a minimum, maximum, and most likely value—into the model. On the otherhand, if you are ot willing to make a guess at the most likely value,a uniform distribution assumes all outcomes are equally likely, it does not capture a preferred or most likely outcome, which can be critical in reflecting real-world scenarios.

GDP Data

The model also accounts for the economic size of each country by incorporating GDP data (in billions of dollars) from datacommons.org:

const gdp_data = Dict(
    "US" => 27700.0,
    "Canada" => 2200.0,
    "Mexico" => 1790.0,
    "China" => 17800.0,
    "Japan" => 4200.0,
    "European Union" => 18600.0
)
  

These figures help us translate the simulation's "payoffs" into impacts on each country's economy as a percentage of GDP.

Simulation Approach

At its core, our simulation models bilateral trade interactions as a repeated game resembling the prisoner’s dilemma. For example in this round, you can see the previous strategy and how each party decided to act given past decisions:

--- Round 4 ---

Partner: Mexico
Previous actions: US = cooperate, Mexico = cooperate
Chosen strategies: US -> cooperate, Mexico -> cooperate
Effective tariff rates this round: US faces 0.0% from Mexico, Mexico faces 0.0% from US
Round payoff: US = 10.5, Mexico = 10.5
Cumulative totals for Mexico: US = 38.5, Mexico = 38.5

Partner: China
Previous actions: US = defect, China = cooperate
Chosen strategies: US -> cooperate, China -> cooperate
Effective tariff rates this round: US faces 0.0% from China, China faces 0.0% from US
Round payoff: US = 13.5, China = 13.5
Cumulative totals for China: US = 58.5, China = 36.0

Partner: European Union
Previous actions: US = cooperate, European Union = defect
Chosen strategies: US -> defect, European Union -> cooperate
Effective tariff rates this round: US faces 0.0% from European Union, European Union faces 43.79% from US
Round payoff: US = 27.25, European Union = 0.0
Cumulative totals for European Union: US = 70.85, European Union = 43.6

Partner: Canada
Previous actions: US = defect, Canada = cooperate
Chosen strategies: US -> cooperate, Canada -> cooperate
Effective tariff rates this round: US faces 0.0% from Canada, Canada faces 0.0% from US
Round payoff: US = 9.0, Canada = 9.0
Cumulative totals for Canada: US = 42.0, Canada = 27.0

Partner: Japan
Previous actions: US = defect, Japan = cooperate
Chosen strategies: US -> cooperate, Japan -> defect
Effective tariff rates this round: US faces 28.38% from Japan, Japan faces 0.0% from US
Round payoff: US = 0.0, Japan = 7.0
Cumulative totals for Japan: US = 15.4, Japan = 15.4

After running five rounds, each round accounting for the previous action, we obtain the following outcomes.

After 5 rounds (with normalization factor = 100.0):
Overall US cumulative payoff (normalized, 'billion-dollar units'): 208.1  
US cumulative payoff by country:
    - Mexico: 49.0
    - China: 36.0
    - European Union: 76.3
    - Canada: 30.0
    - Japan: 16.8
    Total US cumulative payoff (sum over all partners): 208.1
Partner cumulative payoff:
    - Mexico: 31.5
    - China: 58.5
    - European Union: 49.05
    - Canada: 45.0
    - Japan: 9.8
    Total partner cumulative payoff (sum over all partners): 193.85
Estimated percentage impact on GDP per country:
    - US impact (with Mexico): 0.1769% of US GDP
    - Mexico impact (with US): 1.7598% of Mexico GDP
    - US impact (with China): 0.13% of US GDP
    - China impact (with US): 0.3287% of China GDP
    - US impact (with European Union): 0.2755% of US GDP
    - European Union impact (with US): 0.2637% of European Union GDP
    - US impact (with Canada): 0.1083% of US GDP
    - Canada impact (with US): 2.0455% of Canada GDP
    - US impact (with Japan): 0.0606% of US GDP
    - Japan impact (with US): 0.2333% of Japan GDP
Total US impact across all partners: 0.7513% of US GDP
Average effective tariff rates per round:
    - US facing Mexico: 13.66% per round on average
    - Mexico facing US: 14.74% per round on average
    - US facing China: 14.07% per round on average
    - China facing US: 10.8% per round on average
    - US facing European Union: 10.43% per round on average
    - European Union facing US: 20.13% per round on average
    - US facing Canada: 20.26% per round on average
    - Canada facing US: 11.22% per round on average
    - US facing Japan: 17.7% per round on average
    - Japan facing US: 22.33% per round on average
  
julia> 

• Strategy Choice: Both the US and its partner choose between cooperating (no tariffs) or defecting (imposing tariffs). The decision is influenced by the opponent’s previous action. For example, if the opponent defected in the last round, there is an 80% chance to retaliate with defection; if they cooperated, there is only a 20% chance of defection.
• Payoff Calculation: Payoffs are computed based on a simple payoff matrix: mutual cooperation yields 3x the normalized trade volume; defection when the opponent cooperates yields 5x; and mutual defection results in 1x. The trade volume is normalized by dividing by 100, so the raw trade data remains comparable to GDP.
• Tariff Application: When a party defects, a tariff rate is sampled from the triangular distribution defined above. These effective tariffs are accumulated over simulation rounds to compute average tariff rates.
• Economic Impact: The cumulative payoffs are interpreted as economic gains or losses. Dividing these by the country's GDP gives us an estimate of the impact on the overall economy.

Simulation Results

Now let's take this to the next level by simulating 5 tariff rounds for all 5 trading blocks 1000 times using Monte Carlo simulation. We obtained the following summary statistics for key US metrics:

Overall US Cumulative Payoff

• Mean: 223.75 (normalized billion-dollar units)
• Median: 225.20
• Minimum: 129.35
• Maximum: 291.50

These figures represent the aggregated payoff the US receives from all bilateral interactions over the simulation period.

 

 

Overall US Average Tariff Rate

• Mean: 9.56%
• Median: 9.31%
• Minimum: 0.00%
• Maximum: 22.27%

This metric is the average effective tariff rate the US faces across all its trading partners.

 

 

Overall US Impact on GDP

• Mean: 0.81%
• Median: 0.81%
• Minimum: 0.47%
• Maximum: 1.05%

The overall impact on US GDP is calculated by comparing the cumulative payoff to the US GDP (27,700 billion dollars), indicating a modest short-term effect.

 

 

Discussion and Limitations

Although our simulation indicates that imposing tariffs might yield short-term gains for the US, several limitations must be considered:

Simplistic Assumptions:
The model uses a basic payoff matrix and a probability-based strategy selection mechanism that simplifies decision-making into binary outcomes (cooperate or defect). In the real world, trade dynamics are influenced by many more factors. Supply chain integration, regulatory frameworks, political pressures, and long-term strategic shifts all play critical roles. For example, a country might choose to impose tariffs not only for immediate protection but also to achieve longer-term geopolitical objectives. Such complexities are not captured by our simplified model, meaning that while the simulation can offer insights into short-term behaviors, it does not fully reflect the multifaceted nature of international trade.

Market Substitution Effects:
Our simulation assumes that if tariffs are imposed, the trade relationships remain constant. However, in practice, when tariffs make certain goods more expensive, trading partners often respond by finding alternative markets or suppliers. This market substitution can significantly alter trade flows over time. For instance, if the US imposes tariffs on steel imports, its trading partners may pivot to selling that steel to other countries or investing in domestic production alternatives. The model’s failure to account for these substitution effects means it likely underestimates the long-term negative impacts of a trade war—loss of market share and the erosion of established trade relationships can lead to more severe economic consequences than the short-term gains would suggest.

Static Trade Data:
In our simulation, the baseline trade figures and GDP data are fixed inputs. This static approach does not reflect the dynamic nature of real economies, where trade volumes, market shares, and GDP figures evolve over time in response to technological innovations, policy changes, and shifting consumer preferences. Over a prolonged period, these evolving factors can dramatically alter the balance of trade, meaning that a model based on static data may not accurately predict long-term outcomes.

Short-Term Focus:
Finally, the simulation captures a snapshot of interactions over a limited number of rounds. This short-term focus may reveal immediate benefits from imposing tariffs, such as increased revenue or temporary protection for domestic industries. However, it neglects the long-term consequences that can accumulate over time. Long-term outcomes might include lost markets, reduced global competitiveness, and the costly need to reconfigure supply chains. These effects are typically much more damaging than the initial gains observed in a short-term scenario.

In summary, while the simulation offers a valuable framework for understanding the immediate trade-offs in a tariff war, its simplistic assumptions, lack of market substitution dynamics, static data inputs, and short-term focus mean that the long-term consequences could be far more severe than the model suggests.

In conclusion...

Our dynamic trade war simulation offers a simplified framework to understand the potential effects of tariff policies on bilateral trade and the broader economy. While short-term gains might appear to justify tariff impositions, our model suggests that the long-term impacts, especially when accounting for market substitution and lost trade opportunities, could be considerably more damaging.

Future work could expand on this model by incorporating adaptive strategies, dynamic trade and GDP data, and substitution effects to provide a more comprehensive picture of the long-term outcomes of trade wars.

This post serves as an initial exploration of trade war dynamics using a primitive simulation model, and further research is needed to fully capture the complex interactions in global trade.