Economic Coercion and Strategic Autonomy: A Bayesian Game-Theoretic Analysis of U.S.-Canada Trade Relations

Abstract

This paper applies Bayesian game theory to analyze the January 2026 strategic confrontation between Canadian Prime Minister Mark Carney and U.S. President Donald Trump following Canada's trade agreement with China and Carney's Davos address. We model the interaction as a dynamic game of incomplete information where both leaders update beliefs about each other's resolve and preferences based on observed signals. Using backward induction and Bayesian Nash equilibrium analysis, we identify the conditions under which coercion succeeds versus strategic accommodation emerges. Our analysis reveals fundamental commitment problems on both sides and predicts a convergence toward moderate escalation with selective tariffs rather than Trump's threatened 100% tariff regime. The findings illuminate broader questions about the sustainability of hegemonic trade relationships when secondary powers pursue diversification strategies, and contribute to literatures on economic statecraft, alliance politics, and belief updating in high-stakes bargaining.

I. Introduction

The relationship between hegemonic powers and their economically dependent allies presents a fundamental puzzle in international political economy: under what conditions can dominant states use economic leverage to constrain ally autonomy, and when do such attempts trigger strategic realignment? This question has gained renewed urgency as the United States under President Donald Trump has deployed tariff threats against traditionally close partners, including Canada—with which it shares the world's largest bilateral trading relationship valued at $1.73 trillion annually.

On January 20, 2026, Canadian Prime Minister Mark Carney delivered a speech at the World Economic Forum in Davos that fundamentally challenged the premise of asymmetric economic integration. Denouncing what he termed the weaponization of trade interdependence, Carney declared: "You cannot live within the lie of mutual benefit through integration, when integration becomes the source of your subordination". This address followed Canada's announcement of a preliminary trade agreement with China allowing 49,000 Chinese electric vehicles into the Canadian market at reduced tariffs in exchange for restored access for Canadian canola, beef, and seafood exports .

Trump's response escalated rapidly. After initially stating the China deal was "a good thing", Trump reversed course following Carney's Davos speech, ultimately threatening on January 24, 2026 to impose 100% tariffs on all Canadian goods if the China agreement proceeded, warning that Canada would become a "drop-off port" for Chinese circumvention of U.S. tariffs. This threat represented an extraordinary escalation in U.S.-Canada relations, threatening to dismantle seven decades of deepening economic integration.

This paper makes three primary contributions to the literature on economic coercion and alliance politics. First, we develop a formal Bayesian game-theoretic model that explicitly incorporates belief updating as leaders observe each other's costly signals and cheap talk. Second, we demonstrate how incomplete information about resolve creates commitment problems that can lead rational actors toward mutually destructive outcomes. Third, we provide empirical predictions about equilibrium outcomes that can be tested against observed behavior in the coming months as the July 2026 USMCA review approaches.

Our analysis proceeds as follows. Section 2 reviews relevant theoretical literature on economic coercion, signaling games, and Bayesian updating in international relations. Section 3 develops our formal game-theoretic model with incomplete information. Section 4 presents the empirical context and timeline of belief-updating events from January 15-24, 2026. Section 5 analyzes equilibrium strategies and predictions. Section 6 discusses commitment problems and credibility issues. Section 7 examines extensions to multi-player coalition formation. Section 8 concludes with theoretical implications and policy recommendations.

II. Theoretical Framework and Literature Review

II.i. Economic Coercion and Asymmetric Interdependence

The literature on economic statecraft has long recognized that asymmetric trade dependence creates leverage opportunities for dominant states. Hirschman (1945) pioneered the analysis of trade as a tool of national power, arguing that countries with diversified trade portfolios can exploit partners who depend heavily on their markets. More recently, Farrell and Newman (2019) have conceptualized "weaponized interdependence" where states exploit network positions in globalized systems to achieve strategic objectives.

However, the effectiveness of economic coercion remains contested. Baldwin (1985) distinguished between "positive sanctions" (granting benefits) and "negative sanctions" (imposing costs), noting that the latter often fail due to implementation costs and domestic political resistance in the sender state. Drezner (2003) found that economic sanctions succeed in only 13-33% of cases, with effectiveness declining when target states can find alternative partners or when sender states face high costs from disrupted trade relationships.

The U.S.-Canada case presents a particularly challenging test for coercion theory. With 75% of Canadian exports destined for U.S. markets, Canada appears highly vulnerable. Yet Canada is simultaneously the top export destination for 36 U.S. states, and integrated supply chains mean that tariffs on Canadian inputs impose costs on U.S. manufacturers—fabricated metal producers experienced 30% profit declines during Q4 2024-Q2 2025 under existing selective tariffs (U.S. Census Bureau, 2025). This mutual vulnerability creates what Keohane and Nye (1977) termed "complex interdependence," where power asymmetries are less clear-cut than aggregate trade statistics suggest.

II.ii. Signaling and Reputation in International Bargaining

Our analysis draws heavily on signaling theory as developed by Spence (1973) and applied to international relations by Fearon (1994, 1997). In incomplete information games, actions serve dual purposes: they directly affect outcomes and they reveal information about private types. Leaders facing uncertainty about adversaries' resolve must infer intentions from observed behavior, distinguishing costly signals that credibly reveal information from cheap talk that any type could produce.

Schelling (1960) emphasized the importance of credible commitment in strategic interaction, noting that actors often face time-inconsistency problems where threatening is optimal ex ante but implementation is suboptimal ex post. This creates reputation dynamics: a leader who makes threats but fails to implement them suffers credibility loss that undermines future bargaining positions (Weisiger and Yarhi-Milo, 2015).

Trump's tariff threats illustrate this dilemma. His first administration (2017-2021) demonstrated willingness to impose tariffs on allies—successfully renegotiating NAFTA into USMCA by threatening automotive tariffs and implementing steel/aluminum tariffs despite allied objections (Bown, 2021). This history establishes Trump as a potentially high-resolve type. However, the 100% tariff threat on all Canadian goods would impose unprecedented costs on the U.S. economy, raising questions about whether this particular threat is credible or represents a bargaining position subject to moderation.

II.iii. Bayesian Updating and Learning in Strategic Contexts

Bayesian game theory, pioneered by Harsanyi (1967-68), provides a framework for analyzing strategic interaction under incomplete information. Players are uncertain about opponents' types (preferences, costs, resolve) and update beliefs according to Bayes' rule as they observe actions. A Bayesian Nash equilibrium requires that each player's strategy is optimal given their beliefs, and beliefs are consistent with equilibrium strategies (Fudenberg and Tirole, 1991).

Fey and Ramsay (2011) applied Bayesian updating to international crisis bargaining, showing how states learn about adversaries' willingness to fight through observed mobilization decisions and diplomatic communications. Slantchev (2003) demonstrated that incomplete information can prolong conflicts as actors engage in costly signaling to reveal resolve. Chadefaux (2011) found that wars often occur when one side misperceives the other's capabilities or resolve despite available information.

The Carney-Trump confrontation provides a natural setting for Bayesian analysis because both sides face genuine uncertainty. Trump cannot directly observe whether Canada's China partnership is limited or will expand substantially; whether Carney's Davos rhetoric reflects genuine commitment to strategic autonomy or domestic political posturing; or whether Canada can successfully diversify trade quickly enough to reduce U.S. leverage. Conversely, Carney cannot directly observe whether Trump's 100% tariff threat is genuine or represents an opening bargaining position; whether domestic political constraints will prevent implementation; or whether Trump prioritizes symbolic dominance over economic efficiency.

Each action—Carney's Davos speech, Trump's tariff threats, Canada's China deal—serves as a signal that updates the other side's beliefs. Our analysis formalizes this process and identifies the conditions under which beliefs converge toward accommodation versus escalation equilibria.

II.iv. Alliance Politics and Middle Power Coalitions

Recent scholarship on alliance politics has examined how secondary powers navigate relationships with dominant patrons when their interests diverge (Morrow, 1991; Snyder, 1997). The traditional view emphasized "entrapment" and "abandonment" risks: allies fear being dragged into unwanted conflicts or being left without support when needed (Snyder, 1984). However, Lake (2009) reconceptualized alliances as hierarchical relationships where dominant states provide security in exchange for subordinate states' policy compliance.

The question of whether subordinate allies can successfully pursue strategic autonomy has gained attention as the U.S. has become more unilateralist. Nexon and Wright (2007) analyzed how European states balanced between accepting U.S. leadership and asserting independence during the Iraq War. Kupchan (2012) argued that the era of uncontested U.S. hegemony has ended, creating space for middle powers to exercise greater autonomy.

Carney's Davos speech explicitly invoked middle power coalition formation, calling for countries to "act together" rather than individually accommodating great power demands. This raises coalition stability questions: can middle powers overcome free-rider problems where each benefits from others' resistance while avoiding costs themselves? Recent game-theoretic work on coalition formation (Ray and Vohra, 2015) suggests that stable coalitions require credible leadership and shared interests—conditions that may or may not obtain in this case.

III. Formal Model: A Bayesian Game of Coercion and Autonomy

 

III.i. Model Setup

We model the U.S.-Canada interaction as a two-player sequential game with incomplete information. The structure captures the essential strategic dynamics while maintaining analytical tractability.

Players: United States (U.S.) and Canada (C)

Timing:

1. Canada signs China trade agreement (observed)
2. Canada decides on Davos speech intensity s ∈ [0,1] where s=0 represents accommodation rhetoric and s=1 represents maximum defiance
3. U.S. observes s and updates beliefs about Canada's type
4. U.S. chooses tariff level t ∈ [0,1] where t=0 represents no tariffs and t=1 represents 100% tariffs
5. Canada observes t and decides whether to maintain (m=1) or cancel (m=0) the China agreement
6. Payoffs realize based on (s, t, m)

Types and Beliefs:

Canada has private information about its type θ_C ∈ {θ_C^H, θ_C^L}, where:

• θ_C^H (High autonomy valuation): Values strategic independence highly, willing to accept economic costs
• θ_C^L (Low autonomy valuation): Prioritizes economic stability, will accommodate under sufficient pressure

Let p = P(θ_C = θ_C^H) represent the U.S.'s prior belief that Canada is the high type.

The U.S. has private information about its type θ_U ∈ {θ_U^H, θ_U^L}, where:

• θ_U^H (High resolve): Will implement threatened tariffs even at economic cost
• θ_U^L (Low resolve): Makes threats strategically but seeks accommodation

Let q = P(θ_U = θ_U^H) represent Canada's prior belief that the U.S. is the high-resolve type.

III.ii. Payoff Structures

Canada's Strategic Calculus:

Canada's decision-making involves weighing multiple competing considerations. When Canada maintains its China partnership at a given level while the U.S. threatens tariffs, Canada receives benefits from trade diversification that reduce dependence on U.S. markets. The value Canada places on sovereignty signaling through strong rhetoric varies by type—high autonomy types value this symbolic resistance more than low autonomy types. Against these benefits, Canada must weigh the economic costs of U.S. tariffs, which increase proportionally with both the tariff rate and the extent of the China partnership. Additionally, if Canada backs down from strong initial rhetoric, it suffers credibility losses both domestically and internationally.

The critical distinction between Canadian types lies in how much they value sovereignty signaling relative to economic costs. High autonomy types are willing to accept greater economic pain to demonstrate independence, while low autonomy types prioritize economic stability.

U.S. Strategic Calculus:

The United States balances multiple objectives when deciding on tariff levels. Successfully coercing Canada to abandon or limit its China partnership provides direct strategic value by preventing circumvention of U.S.-China trade barriers. Imposing tariffs also sends deterrence signals to other allies considering similar diversification strategies. However, these benefits must be weighed against economic costs that increase more than proportionally with tariff rates—disrupting integrated supply chains imposes growing marginal costs as tariff levels rise from moderate to severe.

Critically, the U.S. also faces credibility costs if announced tariff levels differ substantially from implemented levels. High resolve types care deeply about reputation for following through on threats, while low resolve types are more willing to moderate implementation if economic costs prove high.

The key difference between U.S. types concerns willingness to bear economic costs to preserve credibility. High resolve types will implement costly tariffs to maintain reputation, while low resolve types will seek accommodation if implementation costs exceed benefits.

III.iii. Bayesian Updating Process

After observing Canada's speech intensity, the United States updates its beliefs about Canada's type using rational inference. If high autonomy types are more likely to deliver defiant speeches than low autonomy types, then observing a highly defiant speech increases the U.S. belief that Canada is the high autonomy type.

Specifically, the U.S. calculates the probability that Canada is high autonomy given the observed speech by considering: how likely would a high type be to give this speech, multiplied by the prior probability of high type, divided by the total probability of observing this speech across all types.

The logic is straightforward: if Carney delivers an extremely defiant speech (like the actual Davos address scoring approximately 0.85 on a defiance scale from zero to one), and if high autonomy types are much more likely to give such speeches, then the U.S. should substantially increase its belief that Canada is high autonomy.

Similarly, after observing a tariff threat, Canada updates its beliefs about U.S. resolve. Given Trump's announcement of one hundred percent tariffs—the maximum possible threat—Canada must assess whether this reflects genuine intent or a bargaining position. High resolve types are more likely to announce extreme threats they intend to implement, while low resolve types might announce extreme threats as negotiating tactics. The key inference challenge is determining which type Trump represents based on the pattern of threats and prior behavior.

III.iv. Equilibrium Concept

We seek Perfect Bayesian Equilibria where strategies and beliefs are mutually consistent. At each decision point, each player's strategy must maximize expected utility given their current beliefs about the other player's type. Beliefs must be updated rationally based on observed actions wherever possible. For actions that don't occur in equilibrium, beliefs must satisfy reasonable consistency requirements.

A Perfect Bayesian Equilibrium consists of complete strategies specifying what each type of each player does at every decision point, together with beliefs about the other player's type after every possible observed action, such that no player can improve their payoff by deviating given their beliefs, and beliefs are derived from strategies using rational updating on the equilibrium path.

III.v. Characterization of Equilibria

Separating Equilibrium: If the difference in how much high versus low autonomy types value sovereignty signaling is sufficiently large relative to the credibility loss from backing down, there exists a separating equilibrium where high autonomy Canada chooses maximum defiance while low autonomy Canada chooses accommodation. The U.S. perfectly infers Canada's type from observing the speech intensity.

The logic is that high autonomy types benefit enough from strong sovereignty signals that they willingly accept the risk of higher U.S. tariffs, while low autonomy types prefer to accommodate and avoid this risk. If these preferences differ sufficiently, the two types will naturally separate through their choice of rhetoric intensity. The U.S. can then respond appropriately to each type—harshly to high autonomy types (whose defiance threatens U.S. interests) and moderately to low autonomy types (who have already signaled willingness to accommodate).

The observed evidence—Carney's strong Davos speech followed by Trump's escalated threats—appears consistent with this separating equilibrium. Carney credibly revealed high autonomy preferences through costly defiant rhetoric, causing Trump to update beliefs and respond with severe tariff threats.

Pooling Equilibrium: If economic costs dominate sovereignty values for both Canadian types, there exists a pooling equilibrium where both types choose moderate speech intensity around 0.3 to 0.5 on the defiance scale. The U.S. learns nothing from observing this moderate rhetoric and maintains its prior belief about Canada's type. The U.S. then chooses tariff levels based on the expected value across Canadian types rather than tailoring responses to inferred types.

This equilibrium represents cautious diversification with diplomatic hedging—neither strongly defiant nor fully accommodating. However, this pattern does not match observed behavior, suggesting economic costs do not dominate sovereignty values sufficiently to produce pooling.

U.S. Commitment Problem: If U.S. economic costs from one hundred percent tariffs exceed the combined benefits from coercion success and deterrence signaling, then the U.S. faces time-inconsistency. Threatening maximum tariffs before observing Canadian actions is optimal because it might deter the China partnership. However, after Canada proceeds with the partnership, actually implementing one hundred percent tariffs becomes suboptimal due to excessive economic costs. This creates credibility problems that Canada can potentially exploit.

The empirical question is whether Trump faces this commitment problem or whether political and reputational factors make full implementation optimal despite economic costs.

IV. Empirical Context and Timeline Analysis

IV.i, Trade Dependence and Economic Costs

Canada's asymmetric trade dependence creates the fundamental vulnerability that enables U.S. coercion. As of 2024, 75% of Canadian merchandise exports ($350 billion) flowed to U.S. markets, while Canada accounted for 17% of U.S. imports ($412 billion) (Statistics Canada, 2025; U.S. Census Bureau, 2025). However, this aggregate asymmetry masks sectoral interdependencies that constrain U.S. freedom of action.

The energy sector illustrates this complexity. Canada supplies 60% of U.S. crude oil imports (4.3 million barrels daily), 85% of aluminum imports, and substantial natural gas supplies (U.S. Energy Information Administration, 2025). Tariffs on these inputs would raise costs for U.S. refiners and manufacturers. In the automotive sector, vehicles cross the U.S.-Canada border seven times on average during production, meaning tariffs impose cumulative costs on integrated supply chains (International Trade Administration, 2024).

Empirical estimates of tariff impacts support the view that 100% tariffs would be mutually destructive. The Bank of Canada's (2025) scenario analysis projects that full-scale trade war would reduce Canadian GDP growth from 1.2% to 0.8% in 2025 and potentially negative growth in 2026. For the U.S., disruptions to supply chains during existing selective tariffs reduced profits in fabricated metals by 30%, machinery by 13%, and electrical equipment by 11% during Q4 2024-Q2 2025 (U.S. Census Bureau, 2025). The Congressional Budget Office has not released estimates for 100% Canadian tariffs, but extrapolating from these sectoral effects suggests GDP impacts of 0.3-0.5 percentage points.

IV.ii. Timeline of Belief-Updating Events

January 15-16, 2026: Canada-China Agreement Announcement

Canada announced a preliminary trade agreement addressing tariff disputes that had disrupted $7 billion in annual trade. Key provisions included:

• Canada would allow 49,000 Chinese electric vehicles at 6.1% tariff (down from 100%), rising to 70,000 over five years
• China would reduce canola seed tariffs from 84% to 15%, restoring $4 billion market
• China would resume imports of Canadian canola meal, beef, lobster, crab, and other products worth $2.6 billion annually
• Steel and aluminum remissions extended and expanded

Bayesian Interpretation: This action sends a costly signal. Unlike mere diplomatic rhetoric, Canada committed actual economic resources and market access. The signal's costliness comes from U.S. retaliation risk, making it more credible as a revelation of Canada's preference for diversification.

Trump's initial response—"That's what he should be doing. It's a good thing for him to sign a trade deal" (Reuters, January 16, 2026)—suggested moderate updated beliefs: P(θ_C = θ_C^H | China deal) ≈ 0.40, below the threshold that would trigger immediate retaliation.

January 20, 2026: Carney's Davos Speech

Carney's World Economic Forum address represented the pivotal signal that transformed U.S. beliefs. Without explicitly naming Trump, Carney declared: "We are in the midst of a rupture, not a transition" and condemned the weaponization of economic integration. He called for middle powers to "act together" rather than individually accommodate great power demands.

The speech's reception provided independent validation of its significance. Finnish President Alexander Stubb called it "one of the best speeches we've heard." NATO Secretary General Mark Rutte stated it provided "evidence that Canada is back." Australian Treasurer Jim Chalmers described it as "stunning, impactful." California Governor Gavin Newsom reported that "numerous U.S. leaders sent me the transcript saying 'Wow'" (various sources, January 20-21, 2026).

Bayesian Update: This costly signal—staking international reputation and domestic political capital—credibly revealed Carney as type θ_C^H (high autonomy valuation). The U.S.'s posterior belief sharply increased: P(θ_C = θ_C^H | Davos speech) ≈ 0.70-0.75.

January 21, 2026: Trump's Initial Response

Trump responded by asserting asymmetric dependence: "Canada lives because of the United States. Remember that, Mark, the next time you make your statements" (Reuters, January 21, 2026).

This response served dual purposes: it attempted to reframe the narrative around Canadian vulnerability while signaling displeasure. For Canada, this provided information about U.S. sensitivity to Carney's autonomy claims, updating: P(θ_U = θ_U^H | aggressive rhetoric) ≈ 0.55-0.60.

January 22-23, 2026: Board of Peace Revocation

Trump formally revoked Canada's invitation to the "Board of Peace"—a proposed international organization for nations contributing to the Global Gateway initiative. This diplomatic sanction imposed reputational costs on the U.S. (isolating a traditional ally) while punishing Canada symbolically.

Carney's counter-response—"Canada doesn't live because of the United States. Canada thrives because we are Canadian"—reinforced the high-autonomy signal, further updating beliefs.

January 24, 2026: 100% Tariff Threat

Trump threatened immediate 100% tariffs on all Canadian goods if the China deal proceeded: "If Canada makes a deal with China, it will immediately be hit with a 100% Tariff against all Canadian goods and products coming into the U.S.A." He justified this by claiming Canada would become a "drop-off port" for Chinese circumvention.

Bayesian Inference Problem: Canada faces the critical question: Is this threat credible, or does Trump face a commitment problem where implementing is suboptimal ex post?

Evidence for Credibility:

• Trump implemented threatened tariffs in first term (steel, aluminum, NAFTA renegotiation)
• Reputation costs from non-implementation: δ_U(θ_U^H) · |1.0 - 0| are substantial
• Political base demands tough stance

Evidence Against Credibility:

• Economic costs γ_U · (1.0)² are unprecedented—full supply chain disruption
• Legal constraints: Congressional resolutions to terminate tariff emergency (S.J.Res. 37, 77)
• Supreme Court reviewing IEEPA tariff authority
• Initial approval of China deal contradicts later threat
• Already-signed deal means threat requires retroactive cancellation

Canadian Government Response: Trade Minister Dominic LeBlanc attempted to de-escalate: "There is no pursuit of a free trade deal with China. What was achieved was resolution on several important tariff issues" (Canadian Press, January 24, 2026). This signals willingness to clarify scope and limit expansion—consistent with moderate-type behavior even if Carney himself is high type (potential principal-agent dynamic within Canadian government).

IV.iii. Estimated Posterior Beliefs (January 24, 2026)

Based on the observed sequence of signals and assuming rational Bayesian updating:

U.S. Beliefs About Canada:

• P(θ_C = θ_C^H | all signals) ≈ 0.70: High confidence Canada seeks strategic autonomy
• P(Canada will expand China partnership | current trajectory) ≈ 0.50: Moderate uncertainty
• P(Canada will cancel China deal | 100% threat) ≈ 0.35-0.40: Low-to-moderate expectation of capitulation

Canadian Beliefs About U.S.:

• P(θ_U = θ_U^H | all signals) ≈ 0.60-0.65: Moderate-to-high confidence Trump will implement threats
• P(100% tariff implementation | proceed with China) ≈ 0.55-0.65: Substantial uncertainty remains
• P(USMCA withdrawal | current trajectory) ≈ 0.30-0.35: Moderate risk

These posterior beliefs shape equilibrium strategies, analyzed in the next section.

V. Equilibrium Analysis and Predictions

V.i. Backward Induction from USMCA Review

The July 1, 2026 USMCA review deadline provides a natural terminal node for backward induction. Both parties prefer agreement renewal to collapse, but with different reservation values.

Terminal Payoffs (July 2026):

If USMCA renewed with modifications:

• Canada: Moderate economic stability but U.S.-favorable terms
• U.S.: Maintains regional integration with enhanced leverage

If USMCA collapses:

• Canada: Severe short-term costs ($350B exports at risk) but long-term diversification necessity
• U.S.: Supply chain disruption, inflation pressures, loss of preferential access to Canadian resources

The mutual preference for renewal creates bargaining space, but the distribution of surplus depends on relative bargaining power determined by current actions.

V.ii. Candidate Equilibria at Current Stage

Equilibrium 1: Coercion Success (Subgame Perfect Moderate)

Strategies:

• Canada: Maintains China deal structure but provides transparency mechanisms, limits expansion, offers USMCA concessions on automotive content and digital services
• U.S.: Accepts modified arrangement, imposes selective sector-specific tariffs (15-35%), continues USMCA negotiations

Beliefs:

• U.S. believes: P(Canada will significantly expand China partnership) ≈ 0.30
• Canada believes: P(U.S. will implement >50% tariffs) ≈ 0.25

Payoffs:

• Canada: U_C ≈ (3, 2) - preserves partial diversification with limited tariff costs
• U.S.: U_U ≈ (2, 4) - demonstrates power without full economic disruption

Probability Assessment: 35% based on mutual incentives for moderate de-escalation

Equilibrium 2: Mutual Escalation (Both Hardline)

Strategies:

• Canada: Proceeds with China deal unchanged, expands to additional partners, imposes counter-tariffs on U.S. goods, leads middle power coalition
• U.S.: Implements 75-100% tariffs, withdraws from USMCA or demands major restructuring, pursues diplomatic isolation

Beliefs:

• U.S. believes: P(Canada will capitulate under pressure) ≈ 0.20
• Canada believes: P(U.S. bluffing) ≈ 0.20

Payoffs:

• Canada: U_C ≈ (-2, 5) - severe economic costs but maximum sovereignty credibility
• U.S.: U_U ≈ (1, -1) - symbolic victory but economic self-harm

Probability Assessment: 25% - high-risk outcome requiring miscalculation or non-economic motivations

Equilibrium 3: Strategic Accommodation (Nash Bargaining)

Strategies:

• Canada: Continues China deal with enhanced transparency, provides assurances on circumvention prevention, offers meaningful USMCA concessions
• U.S.: Accepts limited China partnership as fait accompli, focuses tariffs on specific circumvention-risk sectors (EVs, electronics), negotiates USMCA renewal constructively

Beliefs:

• Both parties recognize mutual vulnerability and update toward moderate types
• U.S. believes: P(Canada accepts reasonable constraints) ≈ 0.60
• Canada believes: P(U.S. accepts limited diversification) ≈ 0.55

Payoffs:

• Canada: U_C ≈ (4, 3) - achieves diversification within risk tolerance
• U.S.: U_U ≈ (3, 3) - maintains regional integration while securing concessions

Probability Assessment: 30% - requires rational bargaining and belief convergence

Equilibrium 4: Trump Commitment Failure

Strategies:

• Canada: Calls bluff, proceeds with all plans
• U.S.: Makes threats but implements only token tariffs or delays indefinitely

Beliefs:

• Canada believes: P(θ_U = θ_U^L | observed inconsistencies) ≈ 0.60

Payoffs:

• Canada: U_C ≈ (5, 4) - maximum gains
• U.S.: U_U ≈ (0, 2) - credibility loss, future leverage reduced

Probability Assessment: 10% - low probability given Trump's historical follow-through

V.iii. Most Likely Equilibrium Path

Combining the probability assessments and analyzing incentives at each decision node, we predict convergence toward Equilibrium 1 (Coercion Success - Moderate) or Equilibrium 3 (Strategic Accommodation) with combined probability of 65%.

Mechanism:

1. Canada recognizes that P(substantial tariffs | proceed unchanged) ≈ 0.60 is sufficiently high to make unmodified continuation dominated
2. U.S. recognizes that γ_U · (1.0)² > expected benefits, making full 100% tariff implementation suboptimal
3. Both parties engage in mutual belief updating toward moderate types through iterative signaling
4. Bargaining converges on compromise: limited China partnership + transparency + selective U.S. tariffs + USMCA renewal with modifications

Timeline Prediction:

• February-March 2026: Intensive bilateral negotiations; Canada provides detailed circumvention prevention proposals
• April-May 2026: U.S. announces sector-specific tariffs (25-40%) on high-risk categories (EVs, electronics); maintains USMCA framework
• June 2026: USMCA review negotiations conclude with U.S. securing:
  • Tightened automotive rules of origin (70% → 75% North American content)
  • Canadian digital services tax elimination or modification
  • Enhanced Chinese investment screening coordination
  • Labor/environmental enforcement mechanisms
• July 1, 2026: Modified USMCA formally renewed

Alternative Scenario (25% probability): If Trump faces overwhelming domestic political pressure to implement full threats or if Carney cannot compromise without losing minority government confidence, Equilibrium 2 (Mutual Escalation) emerges with severe economic consequences for both parties.

VI. Commitment Problems and Credibility Analysis

VI.i. Trump's Time-Inconsistency Problem

The fundamental commitment problem Trump faces is that the optimal strategy before Canada acts (threatening severe tariffs to induce Canadian compliance) diverges from the optimal strategy after Canada proceeds (implementing moderate tariffs to avoid economic self-harm).

Trump faces commitment failure if the tariff level that maximizes expected utility when making threats (which accounts for the probability that threats will deter Canadian action) differs from the tariff level that maximizes utility when actually implementing (given that deterrence has already failed and only costs and benefits of actual implementation matter).

Specifically, when making initial threats, Trump should announce the highest credible tariff level because higher threats increase the probability Canada backs down. At this stage, the expected utility calculation weights potential deterrence benefits heavily. However, once Canada proceeds with the China deal, the deterrence benefit disappears—Canada has already acted. At the implementation stage, Trump must weigh only the direct costs of tariffs (supply chain disruption, inflation, manufacturing input costs) against coercion benefits (forcing Canada to cancel the deal) and reputation benefits (maintaining credibility for future threats).

If economic costs from one hundred percent tariffs are sufficiently high, then implementation becomes suboptimal even though the threat was optimal. This is the classic time-inconsistency problem in strategic commitment.

Empirical Evidence for Commitment Problem:

1. Stated vs. Implemented Tariffs: Trump's pattern in Term 1 showed frequent moderation between threat and implementation. He threatened to withdraw from NAFTA entirely but settled for renegotiation. He threatened 25% auto tariffs but implemented 10% on specific components.

2. Economic Cost Calculations: Based on prior tariff impacts, 100% tariffs on $350 billion Canadian goods would raise U.S. consumer prices by 1-1.5%, disrupt critical supply chains (60% of crude oil, 85% of aluminum), and reduce GDP growth by 0.3-0.5 percentage points. These costs create strong ex post incentives to moderate implementation.

3. Legal Constraints: The U.S. Senate passed two resolutions (S.J.Res. 37, S.J.Res. 77) seeking to terminate tariff national emergency declarations. While these failed to override presidential authority, they signal Congressional opposition that constrains implementation.

4. Initial Inconsistency: Trump initially approved the China deal on January 16, then reversed to threaten 100% tariffs on January 24. This inconsistency suggests either incomplete information processing or strategic positioning rather than fixed resolve.

Reputation Dynamics: Despite these pressures toward moderation, Trump's reputation for implementing major threats creates countervailing credibility concerns. The reputational cost of non-implementation—the damage to credibility from announcing one hundred percent tariffs but implementing only moderate levels—may be large enough that the credibility loss exceeds the economic savings from moderation.

Whether Trump will actually implement extreme tariffs depends on whether reputational costs from backing down exceed economic costs from following through. Our assessment is that Trump will implement tariffs in the twenty-five to fifty percent range rather than the threatened one hundred percent, representing partial commitment that balances credibility maintenance with economic rationality.

VI.ii. Carney's Political Constraints

Canada faces a different commitment problem: Carney's minority government creates principal-agent dynamics between the Prime Minister's strategic preferences and parliamentary support requirements.

Domestic Political Structure:

• Liberal minority government requires Conservative or NDP support
• Ontario Premier Doug Ford opposes China deal, threatens provincial trade barriers
• Prairie Premiers support canola market access restoration
• Quebec Premier François Legault focused on provincial autonomy issues
• Manufacturing-dependent Ontario seats crucial for confidence votes

Trade Minister's De-escalation Signal: Dominic LeBlanc's January 24 clarification—"There is no pursuit of a free trade deal with China"—may represent a signal that cabinet moderates can constrain Carney's autonomy strategy even if Carney himself is high type.

Commitment Mechanism: Carney can credibly commit to limited diversification because backing down too far would:

• Undermine international leadership credibility established at Davos
• Fail to deliver economic benefits to agricultural exporters (key constituencies)
• Expose vulnerability to future U.S. pressure
• Weaken Canada's USMCA negotiating position

However, Carney cannot credibly commit to unlimited escalation because minority government status creates veto players who prioritize economic stability.

VI.iii. Observable Implications for Credibility Assessment

To distinguish between credible commitment and strategic bluffing, observers should monitor:

Indicators of Trump High Resolve (θ_U^H):

• Implementation of preliminary tariff actions on specific sectors
• Coordination with USTR on legal preparation for broad tariffs
• White House communications emphasizing circumvention concerns rather than punishment rhetoric
• Engagement with Congressional allies on IEEPA authority defense

Indicators of Trump Low Resolve (θ_U^L):

• Shifting to other policy priorities (Greenland, NATO, domestic issues)
• Opening channels for bilateral negotiation without preconditions
• Emphasis on USMCA benefits and supply chain integration
• Acceptance of Canadian transparency proposals

Indicators of Carney Commitment:

• Concrete moves to expand China partnership beyond current agreement
• Additional middle power coalition-building activities
• Parliamentary support building for trade diversification
• Budget allocations for tariff-impact mitigation

Indicators of Carney Flexibility:

• Detailed transparency protocols offered to U.S.
• Limits on Chinese EV imports below agreement ceiling
• USMCA concession signals on automotive content, digital taxes
• Reduced public rhetoric on U.S. coercion

As of January 24, 2026, the evidence suggests mixed signals from both sides, consistent with our prediction of convergence toward moderate equilibria rather than extreme outcomes.

VII. Extensions: Coalition Formation and Multi-Player Dynamics

VII.i. Middle Power Coalition as a Public Good Problem

Carney's Davos speech invoked a "middle powers" coalition strategy. This creates a multi-country public good problem where each country benefits from collective resistance to great power coercion but individually prefers to free-ride on others' costly actions.

Structure of the Problem: Consider multiple middle power countries, each deciding how much to contribute to coalition resistance through costly actions like diversifying trade away from the dominant power or publicly supporting other coalition members. Each country's contribution imposes individual costs but generates collective benefits that all coalition members share. Total coalition strength increases with the sum of all countries' contributions, and this collective strength provides benefits to all members regardless of their individual contribution levels.

The benefit each country receives from coalition strength follows a pattern of diminishing marginal returns—the first units of coalition strength provide large benefits, but additional strength provides progressively smaller gains. Meanwhile, each country bears the full cost of its own contribution.

Free Rider Problem: Each country's individually optimal strategy is to contribute nothing, letting other countries bear the costs while enjoying the collective benefits of coalition strength. However, if all countries reason this way, total coalition strength equals zero and the coalition fails to form. This represents the classic collective action problem in coalition formation.

Solutions to Coordination Failure:

First, leadership provision by a large player can overcome free riding. If one country (Canada) is large enough that its individual benefits from coalition strength exceed its costs even when contributing alone, it will provide leadership by making disproportionate contributions. Carney's prominent role at Davos represents this leadership mechanism.

Second, repeated interaction over time allows countries to sustain cooperation through reciprocity. If countries interact repeatedly, they can use trigger strategies where defectors face exclusion from future coalition benefits, making cooperation individually rational even though one-shot defection would be optimal.

Third, selective incentives can supplement collective benefits. The coalition can provide private benefits exclusively to contributors, such as preferential market access among coalition members, making contribution individually beneficial independent of the public good aspect.

Empirical Assessment: The coalition's stability depends on whether Canada's leadership provision is sustainable given U.S. pressure. If the U.S. successfully coerces Canada through severe tariffs, Canada's willingness to bear leadership costs collapses and the coalition unravels. This creates a "demonstration effect" where Trump's strategy aims not just at Canada but at deterring other middle powers from similar strategies by showing that coalition leadership brings punishment rather than support.

VII.ii. Three-Player Strategic Triangle: U.S.-Canada-China

The U.S.-Canada bilateral game is embedded in a strategic triangle including China. We model this as a three-player game where each pair has bilateral relationships affecting the third party.

Preference Orderings:

U.S.: (Canada fully integrated, China isolated) > (Canada partially diversified, managed China competition) > (Canada-China partnership) > (China dominance)

Canada: (Balanced partnerships with both) > (Diversified partnerships) > (U.S. dependence only) > (Isolation)

China: (Canada partnership) > (U.S.-Canada division) > (U.S.-Canada integration) > (Containment)

Strategic Dynamics: China has incentives to offer attractive terms to Canada precisely because doing so creates U.S.-Canada tensions. The canola tariff reduction from 84% to 15% represents a strategic subsidy designed to pull Canada away from exclusive U.S. alignment.

Nash Equilibrium Analysis: We analyze simultaneous-move strategies where each player chooses partnership intensity with others.

Let x_UC represent U.S.-Canada partnership intensity, x_CC represent Canada-China intensity, and x_UC represent U.S.-China intensity (exogenously hostile in current environment).

Result: No pure-strategy Nash equilibrium exists under current parameters because:

• If Canada chooses high x_CC (strong China partnership), U.S. best response is low x_UC (punish with tariffs)
• If U.S. chooses low x_UC, Canada best response is high x_CC (diversify due to insecurity)
• If Canada chooses high x_CC, China best response is high x_CC (reciprocate)
• This creates a cycle without stable equilibrium

Mixed-Strategy Equilibrium: Canada randomizes over partnership levels, U.S. randomizes over punishment levels. This explains observed volatility and uncertainty.

Stability Condition: Equilibrium stabilizes only if one player can credibly commit to a fixed strategy. The USMCA review deadline may serve this function by forcing crystallization of strategies by July 2026.

VII.iii. European Union as Fourth Player

The EU's response to Carney's Davos speech—highly positive reception from leaders like Stubb and Rutte—suggests the EU may coordinate with Canada to resist U.S. unilateralism. This creates a four-player game with coalition possibilities.

Potential Coalitions:

• {Canada, EU} vs. U.S.: Middle power resistance
• {U.S., Canada, EU} vs. China: Democratic alliance (historical pattern)
• {U.S., EU} + Canada accommodation: Status quo restoration

The coalition that forms depends on U.S. strategy. Excessive coercion against Canada pushes the {Canada, EU} coalition toward formation. This creates a strategic constraint on U.S. escalation: Trump must weigh benefits of coercing Canada against costs of damaging transatlantic cohesion.

Game-Theoretic Implication: The presence of potential coalition partners increases Canada's bargaining power because it creates outside options. Canada's threat to "act together" with other middle powers is only credible if the EU and others demonstrate willingness to support Canada materially, not just rhetorically.

Current Assessment: EU support remains primarily rhetorical. Without concrete trade or financial support mechanisms, Canada's coalition threat has limited credibility, increasing U.S. bargaining power.

VIII. Policy Implications and Recommendations

VIII.i. For Canadian Policymakers

Our game-theoretic analysis suggests Canada's optimal strategy involves maintaining the China partnership while mitigating U.S. concerns through transparency and limits on expansion.

Recommended Strategy:

First, regarding China partnership management, maintain the current agreement structure but establish rigorous anti-circumvention protocols. Provide the U.S. with visibility into Chinese electric vehicle imports and enforce strict rules of origin to prevent "drop-off port" concerns that drive U.S. threat escalation.

Second, on USMCA negotiation positioning, offer meaningful but non-critical concessions including accepting modestly higher automotive content requirements (seventy-five percent versus current seventy percent), modifying (not eliminating) the digital services tax to exempt small and medium U.S. firms, enhancing coordination on Chinese investment screening, and accepting labor enforcement mechanisms if reciprocal.

Third, accelerate diversification by aggressively pursuing the announced twelve trade agreements to reduce U.S. dependence from seventy-five percent to sixty-five to seventy percent by 2027. Priority regions should include the EU for a comprehensive agreement, the UK for expansion of existing arrangements, CPTPP for deeper integration, and ASEAN for new agreements.

Fourth, move beyond rhetorical coalition support to concrete coordination with the EU, Australia, and Japan on trade facilitation among middle powers, joint investment in supply chain diversification, shared defense burden for Arctic and North Atlantic regions, and coordinated responses to great power coercion.

Fifth, address Ontario manufacturing concerns while delivering benefits to Prairie agriculture through budgeting significant support (fifteen to twenty billion dollars) for tariff-impacted industries to maintain political sustainability of the diversification strategy.

Sixth, meet the two percent NATO spending target (approximately seventy-three billion dollars) to reduce U.S. leverage on security issues, removing one dimension of U.S. criticism and strengthening Canada's bargaining position.

Expected Outcome: This strategy yields moderate diversification within acceptable economic risk, maintains the USMCA framework with modifications, and establishes Canada as a credible middle power leader. It accepts some U.S. tariffs in the fifteen to thirty-five percent sectoral range as an unavoidable cost of autonomy, while avoiding the catastrophic scenario of one hundred percent tariffs on all goods.

VIII.ii. For U.S. Policymakers

Our analysis suggests that extreme coercion (one hundred percent tariffs) is likely suboptimal for achieving U.S. strategic objectives. A more nuanced approach would better serve U.S. interests while preserving valuable alliance relationships and economic integration.

Recommended Strategy:

First, implement calibrated tariff responses focused specifically on circumvention-risk sectors: thirty to forty percent on Chinese electric vehicles entering through Canada, twenty-five to thirty-five percent on electronics with potential transshipment issues, while maintaining USMCA-compliant goods tariff-free. This generates total tariff revenue of fifteen to twenty-five billion dollars, which is economically manageable for both countries while addressing genuine security concerns.

Second, pursue USMCA renewal with modifications that secure meaningful gains including tighter rules of origin in automotive to seventy-five percent North American content, enhanced digital trade provisions, a joint Chinese investment screening framework, and dispute settlement mechanism reforms.

Third, recognize that integrated North American supply chains serve U.S. interests through energy security (sixty percent of crude oil from Canada), critical minerals (aluminum, copper, nickel), and manufacturing inputs (steel, auto parts). Disruption costs from extreme tariffs exceed coercion benefits.

Fourth, regarding alliance management, distinguish between adversaries like China and allies pursuing partial diversification like Canada. Excessive coercion of allies damages U.S. credibility and soft power, pushes middle powers toward China, undermines NATO cohesion, and reduces allied willingness to support U.S. initiatives elsewhere.

Fifth, establish credible commitment mechanisms through clear, enforceable redlines rather than sweeping threats. Define acceptable versus unacceptable levels of China partnership, specify circumvention prevention requirements, create monitoring mechanisms with Canadian buy-in, and implement automatic graduated responses to violations rather than all-or-nothing ultimatums.

Sixth, achieve strategic clarity by deciding whether U.S. grand strategy prioritizes China containment (which requires allied cooperation, implying acceptance of limited allied China trade) or economic nationalism (which implies accepting reduced allied support). Current inconsistency undermines both objectives.

Expected Outcome: This strategy maintains substantial U.S. leverage over Canada, secures favorable USMCA terms, prevents significant circumvention, and preserves alliance value for broader strategic competition with China. It accepts limited Canadian diversification as an unavoidable consequence of prior U.S. unilateralism rather than treating it as intolerable defiance.

VIII.iii. Broader Theoretical Implications

The Carney-Trump confrontation illuminates several important theoretical questions:

1. Limits of Asymmetric Interdependence as Leverage

Traditional theories emphasized that asymmetric trade dependence creates coercive opportunities for dominant states. Our analysis reveals important limitations:

• Mutual vulnerability in integrated supply chains constrains dominant state freedom of action
• Secondary powers can pursue gradual diversification that shifts dependence ratios over time
• Extreme coercion risks triggering rapid realignment that undermines long-term influence

2. Reputation and Credibility in Contemporary International Relations

Trump's approach represents a challenge to conventional wisdom about reputation:

• Frequent threats followed by partial implementation may paradoxically enhance credibility in some dimensions (willingness to use coercion) while undermining it in others (follow-through on specific threats)
• The optimal level of threat implementation may be partial rather than complete to maintain flexibility
• Reputation effects may be domain-specific rather than general

3. Middle Power Agency in Great Power Competition

The traditional view of middle powers as passive objects of great power competition requires revision:

• Middle powers can actively pursue coalition formation and diversification strategies
• Strategic autonomy remains viable even under asymmetric dependence
• Effective leadership (Carney's Davos speech) can coordinate dispersed middle power interests
• However, coalition stability requires institutional mechanisms, not just rhetorical alignment

4. Economic Statecraft in an Era of Complex Interdependence

The case suggests that economic coercion in highly integrated relationships faces inherent limitations:

• Sender states cannot easily isolate costs to target while exempting themselves
• Credible threats must account for domestic political costs of implementation
• Targets can engage in "strategic hedging" that gradually reduces vulnerability
• Optimal coercion involves targeted instruments rather than blunt economy-wide measures

IX. Conclusion

This paper has analyzed the January 2026 U.S.-Canada confrontation through the lens of Bayesian game theory, modeling how both sides update beliefs based on observed signals and adjust strategies accordingly. Our analysis yields several key findings:

Theoretical Contributions:

First, we demonstrate how incomplete information about resolve and preferences creates commitment problems that can lead rational actors toward inefficient outcomes. Trump faces time-inconsistency between optimal ex ante threats and ex post implementation; Carney faces domestic political constraints that limit credible commitment to maximum escalation.

Second, we show how costly signals (China trade deal, Davos speech, tariff implementations) credibly reveal private information while cheap talk (rhetorical threats, insults) has limited informational content. The sequence of signals from January 15-24, 2026 generated substantial belief updating on both sides, transforming initial uncertainty into moderate confidence about each side's type.

Third, we extend standard two-player models to analyze coalition formation dynamics and multi-player strategic triangles, showing how the presence of third parties (China, EU) affects bilateral bargaining power and equilibrium selection.

Empirical Predictions:

Our equilibrium analysis predicts convergence toward moderate outcomes rather than extreme escalation:

• Canada will likely maintain its China partnership but with transparency measures and limited expansion
• U.S. will likely implement selective tariffs (25-40%) on specific sectors rather than blanket 100% tariffs
• USMCA will be renewed by July 2026 with modifications favorable to U.S. on automotive content, digital services, and Chinese investment screening
• Canada will achieve partial diversification, reducing U.S. trade dependence from 75% to 65-70% over 2026-2027

We assign 65% probability to these moderate accommodation outcomes, 25% to mutual escalation scenarios with severe economic consequences, and 10% to Trump commitment failure where threats prove empty.

Policy Implications:

For Canada, optimal strategy involves maintaining strategic autonomy claims while providing sufficient assurances to reduce tariff risks below the threshold that would make continuation dominated. This requires sophisticated diplomacy that distinguishes between symbolic resistance and substantive concessions.

For the United States, optimal strategy involves selective coercion focused on genuine security concerns (circumvention prevention) rather than symbolic dominance displays. Extreme coercion risks damaging integrated supply chains, undermining alliance cohesion, and accelerating Canadian diversification—all contrary to U.S. strategic interests.

Limitations and Future Research:

Our analysis abstracts from several complicating factors that merit further investigation:

• Domestic political dynamics within both countries beyond simple majority/minority status
• The role of specific interest groups (automotive manufacturers, energy companies, agricultural exporters) in shaping government preferences
• Learning dynamics over multiple rounds of interaction beyond the current episode
• Potential intervention by international institutions (WTO, NATO) in constraining unilateral action

Future research should examine whether the patterns observed in this case generalize to other asymmetric alliance relationships, particularly U.S. relations with European allies, Japan, South Korea, and Australia facing similar pressures to accommodate U.S. unilateralism while pursuing strategic autonomy.

The Carney-Trump confrontation may represent an inflection point in the transformation of the U.S.-led order from hierarchical hegemony toward a more multipolar system where middle powers exercise greater agency. Whether this transformation proceeds smoothly through negotiated accommodation or disruptively through escalation and breakdown depends critically on whether both sides update beliefs rationally, recognize mutual vulnerability, and converge toward the moderate equilibria our analysis identifies as Pareto-superior to extreme alternatives.

The July 2026 USMCA review will provide a crucial test of these predictions and reveal whether rational Bayesian updating or commitment failures and miscalculation determine the future of North American economic integration.