The price-setting game involving three firms, as detailed in Figure 8.21, exemplifies a prisoners' dilemma. While all firms would achieve a better outcome with a cartel agreement to set high prices, the arrangement is unsustainable. The payoff matrix reveals that each firm has a dominant incentive to defect. For example, if Firms B and C maintain a high price, Firm A can boost its profit from \$60 to \$72 by lowering its price. This action would force the other firms to lower their prices as well, leading to the cartel's collapse.

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This node details the payoff structure for firms in a three-firm market, viewed from Firm A's perspective and assuming Firms B and C behave identically. If all three firms set a high price, the market is shared equally, with each firm selling 20 units and earning a profit of \$60. If they all set a low price, each sells 24 units and makes a profit of \$24. When pricing is mixed, the total market sales of 72 units and the corresponding \$72 profit are divided equally among the firms that chose the lower price, while any firm charging a high price sells nothing and earns zero profit.

Payoff Scenarios in a Three-Firm Market (Figure 8.21)

A prisoners' dilemma is a type of game, and a classic example of a simultaneous game, where players choose their actions concurrently. It features a dominant strategy equilibrium, but this outcome is paradoxically worse for all players than an alternative, cooperative outcome. This means the Nash equilibrium in a prisoners' dilemma is not Pareto efficient.

Prisoners' Dilemma

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The Three-Firm Price-Setting Game as a Prisoners' Dilemma

Considering the three-firm price-setting game scenario, what would be the resulting market dynamics if two of the firms, B and C, were to set their prices independently rather than acting in unison?

Price-Setting Dynamics When Cartel Members Act Independently

The name 'prisoners' dilemma' originates from a classic story about two prisoners, Thelma and Louise, who may have committed a crime together. Each prisoner must choose a strategy: either to 'Accuse' their partner, implicating them, or to 'Deny' their involvement. The outcomes, or payoffs, in this scenario are represented by years of prison time, meaning both individuals prefer outcomes with lower numerical values.

Origin of the Term 'Prisoners' Dilemma'

In economic analyses of the prisoners' dilemma, standard terminology is used to describe the players' strategies. The strategy that is mutually beneficial if chosen by all players, analogous to 'Deny' in the classic story, is called 'Cooperate'. The dominant strategy, which is individually rational but leads to a worse collective outcome, analogous to 'Accuse', is termed 'Defect'.

Standard Terminology in Prisoners' Dilemma: Cooperate vs. Defect

This is a hypothetical prisoners' dilemma scenario involving two foreign exchange traders, Dimitrios and Ameera, who work at an international investment bank. They are under investigation by the police for alleged market manipulation. Each trader must decide simultaneously, and without consulting the other, whether to accuse their colleague or deny the crime. The consequences of their choices are measured in years of prison time, representing negative payoffs, with Dimitrios's outcome listed first and Ameera's second in a payoff table.

The Dimitrios and Ameera Market Manipulation Case: A Prisoners' Dilemma Example

The (T, T) allocation, which is the dominant strategy equilibrium in the pest control game, is a Pareto inefficient outcome. This is demonstrated by comparing it to the (I, I) allocation. The (T, T) outcome yields payoffs of (2, 2), while the (I, I) outcome results in higher payoffs of (3, 3) for both farmers. Because the (I, I) allocation makes both individuals better off, it Pareto-dominates (T, T). Graphically, this is shown by the point for (I, I) being located in the Pareto improvement zone relative to (T, T), which is the area 'above and to the right'. This situation, where a mutually better outcome exists but is not achieved through independent self-interested actions, is a hallmark of a prisoners' dilemma.

Comparison of (T,T) and (I,I) Allocations: Pareto Inefficiency of the (T,T) Outcome

In a prisoners' dilemma, players often fail to reach the mutually beneficial 'cooperative' outcome. The fundamental reason for this is that the cooperative allocation does not Pareto-dominate all other possible outcomes. Because of this, an individual player can achieve an even better personal payoff by unilaterally changing their strategy ('defecting') while the other player 'cooperates'. This potential for a higher individual gain creates the incentive to not choose the cooperative strategy.

Incentive to Defect from the Cooperative Outcome in a Prisoners' Dilemma

In both real-world scenarios and experimental settings, individuals frequently choose to cooperate in prisoners' dilemma games, which demonstrates that cooperative equilibria are possible outcomes. This behavior contradicts the prediction that purely self-interested players will always defect. Social preferences, particularly altruism, are a primary explanation for this cooperation, as seen in historical examples of mutual cooperation over free-riding, such as shared irrigation systems and the Montreal Protocol.

Explaining Observed Cooperation in the Prisoners' Dilemma

A cartel's stability is constantly threatened by the inherent self-interest of its members. Each firm has a strong incentive to 'defect' from a collusive agreement by secretly lowering its price to capture a larger portion of the market. [5] This situation often creates a prisoners' dilemma, where the collective failure to cooperate leads to lower profits for all participating firms. While this outcome is unfavorable for the cartel members, it is beneficial for consumers who gain from the lower, more competitive prices that emerge when the cartel collapses. [2]

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