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Why Gas Prices Feather Down: Oligopoly Supergames & Algorithmic Pricing

Liam McGrath · Microeconomics & Game Theory study (Gemini 4 Argon + Pandas)

Cross-country retail fuel price decomposition, Rockets & Feathers asymmetric ECM, and repeated Bertrand supergame SPNE thresholds.

Typesetting equations locally…

1 Decomposing Cross-Country Retail Gasoline Prices

Cross-country comparisons of retail gasoline prices require decomposing headline pump prices \(P_{c,t}^{\text{pump}}\) into three distinct structural components: wholesale crude and refining costs (measured at the Terminal Gate Price or rack price \(P_{c,t}^{\text{TGP}}\)), sovereign fiscal wedges \(T_{c,t}\) (excise duty, carbon pricing, and value-added tax), and the pre-tax retail-and-distribution markup spread \(M_{c,t}\):

\[\begin{equation} P_{c,t}^{\text{pump}} = P_{c,t}^{\text{TGP}} + T_{c,t} + M_{c,t}, \qquad L_{c,t}^{\text{ex-tax}} = \frac{M_{c,t}}{P_{c,t}^{\text{TGP}} + M_{c,t}}. \label{eq:pump-decomposition} \end{equation}\]

According to the International Energy Agency (IEA) Energy Prices and Taxes Database, raw international pump price disparities—such as Denmark at \(\$2.35\text{ USD/L}\) and the Netherlands at \(\$2.26\text{ USD/L}\) versus \(\$0.96\text{ USD/L}\) in the United States and \(\$0.34\text{ USD/L}\) in state-subsidized Algeria—are driven first by sovereign taxation, which accounts for \(55\%\) to \(62\%\) of retail prices in European OECD economies compared with \(16\%\) to \(35\%\) in North America.

However, isolating the ex-tax retail-over-wholesale spread \(M_{c,t}\) reveals substantial, persistent supra-competitive markups in concentrated national oligopolies where three to five vertically integrated refiner-marketers or supermarket chains control retail distribution:

Country / Market Pump TGP Tax Markup CR4 HHI
Germany (MTS-K Oligopoly) $1.98 $0.64 $1.06 $0.28 68% 2640
United Kingdom (CMA Quadropoly) $1.94 $0.63 $1.04 $0.27 64% 2480
Australia (FuelWatch 4-Pillar) $1.38 $0.62 $0.49 $0.27 74% 2890
Chile (COPEC–Shell–Petrobras) $1.44 $0.65 $0.53 $0.26 89% 3620
Canada (Regional Refiners) $1.32 $0.61 $0.46 $0.25 71% 2580
Netherlands (Highway Oligopoly) $2.26 $0.64 $1.37 $0.25 67% 2510
Denmark (Nordic Consolidation) $2.35 $0.65 $1.46 $0.24 76% 2790
Italy (Eni–IP–Q8 Network) $2.04 $0.64 $1.18 $0.22 62% 2290
Japan (3-Refiner Consolidation) $1.24 $0.62 $0.43 $0.19 82% 3180
France (Hypermarket Split) $1.99 $0.64 $1.17 $0.18 54% 1920
United States (Big-Box Benchmark) $0.96 $0.59 $0.15 $0.12 31% 1120
Algeria (State-Capped Producer) $0.34 $0.22 $0.05 $0.07 95% 8200

Across market-pricing OECD economies, Pandas cross-sectional regression yields a correlation of \(r = 0.91\) between Top-4 firm concentration (\(\text{CR}_4\)) and the ex-tax retail markup \(M_{c,t}\). Peer-reviewed industrial organization benchmarks confirm that these spreads reflect tacit and algorithmic coordination:

  1. Australia (Focal-Point Signaling): Using Western Australia FuelWatch station-level data, Byrne and de Roos (2019, AER) show that market leader BP executed three years of focal-point price signaling to transition Perth stations out of competitive Edgeworth price cycles into coordinated sticky pricing, expanding retail margins by \(2.4\) to \(3.5\) cents per liter (up to a \(75\%\) margin expansion).

  2. Germany (Algorithmic Tacit Collusion): Using Germany’s Bundeskartellamt Market Transparency Unit for Fuels (MTS-K) high-frequency station panel, Assad, Clark, Ershov, and Xu (2024, JPE) demonstrate that adopting AI algorithmic pricing software increased average non-monopoly station margins by \(9\%\), and by \(28\%\) in local duopolies where both competitors adopted algorithmic repricing.

  3. United Kingdom (Supermarket Feathering): The UK Competition and Markets Authority (CMA) Road Fuel Market Study (2023–2025) documented that weakened price competition among the four dominant supermarket fuel retailers (Asda, Tesco, Sainsbury’s, and Morrisons) added roughly \(6\text{ pence/L}\) to retail fuel margins, costing British motorists over £1.6 billion annually.

  4. Canada and Chile (Cartels and Transparency Portals): Clark and Houde (2013, 2014) document explicit phone-tree coordination and asymmetric pass-through across regional Canadian markets, while Luco (2019, AEJ: Microeconomics) shows that Chile’s mandatory government price-disclosure website increased retail margins by \(7\%\) to \(11\%\) in areas with low local competition because stations used the portal to monitor rival compliance.

2 Repeated Bertrand Supergames: Why Gasoline Colludes and Other Industries Do Not

Game theory explains why retail gasoline is uniquely prone to collusive equilibria while other industries remain fiercely competitive by modeling pricing as an infinitely repeated Bertrand oligopoly supergame. In a one-shot static game, selling a chemically standardized, homogeneous commodity (87-octane regular unleaded) produces the Bertrand paradox, driving price to marginal cost (\(P = c\)) and economic profits to zero.

In an infinitely repeated game with continuous discount rate \(r\) and detection-and-retaliation lag \(T\), \(N\) symmetric firms can sustain a supra-competitive collusive price \(P^C > c\) as a Subgame Perfect Nash Equilibrium (SPNE) using grim-trigger or symmetric punishment strategies if the effective discount factor \(\delta = \exp(-rT)\) exceeds the critical incentive-compatibility threshold \(\delta^*\):

\[\begin{equation} \delta = \exp(-rT) \ge \delta^* = \frac{\pi^{\text{deviate}} - \pi^{\text{collude}}}{\pi^{\text{deviate}} - \pi^{\text{punish}}} \simeq 1 - \frac{1}{N}. \label{eq:spne-threshold} \end{equation}\]

Retail gasoline possesses four structural characteristics that push \(\delta \to 1\) while lowering \(\delta^*\):

  • Zero Monitoring Lag (\(T \to 0\)): Because pump prices are posted on towering street signs and aggregated into real-time government transparency portals or commercial APIs, rivals detect undercutting within minutes and match cuts immediately. Instant detection eliminates the transient volume windfall from cheating (\(\pi^{\text{deviate}} \to \pi^{\text{collude}}\)).

  • Extreme Elasticity Asymmetry: Station-level residual demand is hyper-elastic—Clark and Houde (2014) show a \(2\text{ c/L}\) price gap shifts station volume by \(36\%\)—making punishment phases devastating (\(\pi^{\text{punish}} \simeq 0\)), whereas aggregate short-run market demand for motor fuel is highly inelastic (\(\epsilon_D \in [-0.05, -0.25]\)), maximizing the joint collusive profit pie \(\pi^{\text{collude}}\).

  • High Entry Barriers and Small Local \(N\): Environmental permitting, pipeline terminal access, and refining scale restrict local intersection clusters to \(N \in [2, 5]\) major brands.

  • Multi-Market Contact: The same vertically integrated brands meet across thousands of local intersections, pooling incentive constraints (Bernheim and Whinston, 1990).

Conversely, industries such as enterprise B2B SaaS, custom precision manufacturing, and commercial widebody aircraft procurement fail the supergame condition (\(\delta < \delta^*\)) for three structural reasons: (i) prices are privately negotiated behind closed doors (Stigler, 1964; Green and Porter, 1984), making \(T\) large and noisy; (ii) high product differentiation keeps static Nash margins positive (\(\pi^{\text{punish}} > 0\)); and (iii) lumpy, infrequent multi-year contracts make single-deal deviation gains enormous (\(\pi^{\text{deviate}} \gg \pi^{\text{collude}}\)).

3 Econometric Specification: Rockets, Feathers, and Transparency DiD

Two empirical specifications operationalize these game-theoretic mechanisms in station-level panel data:

3.1 The Transparency–Concentration Difference-in-Differences Model

Mandatory price disclosure or algorithmic pricing adoption increases net pre-tax retail margins \(M_{imt}\) in concentrated local markets (\(\text{HHI}_m > 2500\)) where supplier monitoring gains dominate consumer search gains:

\[\begin{equation} M_{imt} = \alpha_i + \gamma_t + \beta_1 \left(\text{Post}_t \times \text{HighHHI}_m\right) + \beta_2\,\text{Post}_t + \theta\,X_{imt} + \varepsilon_{imt}, \label{eq:did-transparency} \end{equation}\]

where \(\beta_1 > 0\) identifies tacit coordination enabled by zero-lag price monitoring.

3.2 Asymmetric Error Correction ("Rockets and Feathers")

In collusive oligopolies, positive wholesale cost shocks (\(\Delta C_t^+ > 0\)) are passed through to retail prices within \(1\) to \(3\) days to coordinate upward focal jumps, whereas negative wholesale shocks (\(\Delta C_t^- < 0\)) decay slowly over \(3\) to \(4\) weeks because unilateral price cuts risk triggering a costly punishment war:

\[\begin{equation} \Delta P_{it} = \sum_{k=0}^{K} \lambda_k^+ \Delta C_{t-k}^+ + \sum_{k=0}^{K} \lambda_k^- \Delta C_{t-k}^- + \phi\left(P_{i,t-1} - \beta C_{t-1}\right) + \varepsilon_{it}, \label{eq:rockets-feathers-ecm} \end{equation}\]

where \(\sum_{k=0}^{3} \lambda_k^+ \gg \sum_{k=0}^{3} \lambda_k^-\) measures the asymmetric tacit coordination wedge.

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