Game Theory — Pure Strategy in Oil Industry
Discussing and illustrating simplified game. A strategic situation with pure strategy.
OP is an organization formed by group of multinational oil production countries. It has a market share of around 44% of global crude oil supply. The members will comply with the cartel, to ensure the stabilization of oil supply and price fluctuation in the market. Members are expected to act in mutual interest. The problem arises as there is economic incentive for the members to cheat. This is a simultaneous move and infinitely repeated game with complete information. The complete payoff matrix is available for analysis. The players are choosing their strategy without knowledge of opponent’s choice and the game will be repeating when the supply-demand and oil price are fluctuating beyond the favorable range that may crash the oil market. A similar but simplified game is illustrated.
Players: Firm A and Firm B
Strategic situation is a situation where the outcome for a player does not depend only on what he does, but also what others do.
Assuming the production restriction of 50 barrels per firm was imposed, the global oil price was USD 50/barrel before the pandemic. Following the outbreak of pandemic, most of the countries are locked down, the oil demand declines. There is supply surplus and the storage space tightens, hence the price drops dramatically. OP members were committed to cut the production to sustain the market price. The oligopoly oil market is simplified, such that OP members are dominating the market and there are only two firms participating in the cartel. They are producing at different fixed costs as shown in Table 1.
The oil price increases as the total production reduced, and vice versa (Table 2).
The production is now restricted to 35 barrels/firm. The production is modelled as in Table 3 with respect to firms’ strategies. The profit of each firm is computed in payoff matrix (Table 4), as profit = production*(price — cost).
There is no strategy that is always the best or the worst for a firm regardless of the strategy by another firm. When firm B chooses to cheat, firm A has better payoff by cooperating and worse payoff by cheating. When firm B chooses to cooperate, firm A has better payoff by cheating and worsen by cooperating. Similar scenario observed when we switch the players, but at different payoff values. Therefore, we say that there is dominant or dominated strategy for neither firm.
If both firms cheat, (Cheat, Cheat), the oil price continues to decline and supply increases, they will experience the worse outcome of lower profit. ‘Cheat’ will not be an ideal strategy for either firm if they expect opponent to cheat. They gain increased profit of (USD 2100, USD 1820) when both cut the production, (Cooperate, Cooperate), but this is not the strategy that maximize the profit attainable by a firm, considering the choice of another firm to cooperate.
The firms are looking for optimal strategy such that they have no incentive to deviate from their initial choice of action when the opponent remains in their strategy, a Nash equilibrium. (Cheat, Cooperate) and (Cooperate, Cheat) are the Nash equilibria for the case.
Observing the payoff matrix, when counterparty is cooperating, the payoff received by the firm to cheat is much higher than that to cooperate. Hence, when a firm cooperates, another firm has incentive to cheat to maximize their profit. As the counterparty is reducing the production, the firm tends to increase production taking up a larger market share and attain a higher profit.
For strategy (Cheat, Cooperate), considering firm A plays a strategy ‘Cheat’, firm B has no incremental benefit by switching from ‘Cooperate’ to ‘Cheat’, due to the lower payoff of USD 660 as compared to USD 1400 in the Nash equilibrium. When firm B is cooperating, there is no incentive for firm A to change its strategy of ‘Cheat’, as the strategy deviation will not be beneficial to the firm and cause a profit reduction from USD 2365 to USD 2100. The same situation is applicable to the strategy (Cooperate, Cheat), but of different amount for each firm, due to the difference in production cost. Neither of these equilibria is better for both firms than the other, each Nash equilibrium is preferred by different player.
The situation is similar as the coordination game, ‘The battle of Sexes’. None of the pure strategy Nash equilibrium is mutual best response for both players. Different player prefers different equilibrium. The situation discussed described part of the reason in real-world case where there is news reporting on the OP members cheat for higher return. The payoff received by each firm depends on their decision, as well as the opponent’s choice, both of their decisions bring impact to the total supply and hence the oil price. Nevertheless, the real world cases are much more complicated and cover a wider range of influencing factors. Since there are nonmember oil production countries contribute more than half of global supply, a more in-depth study needs to be conducted on the strategic decision by the OP members, considering the influences those non-member firms, including the elasticity of supply and the on-going negotiation or price war between members and non-member countries.