Prisoners Dilemma Payoff Outcome Quiz

The Prisoners Dilemma requires a specific payoff ordering: T (temptation) is greater than C (mutual cooperation) is greater than D (mutual defection) is greater than S (sucker payoff). This ordering ensures defection strictly dominates cooperation individually while mutual cooperation produces higher payoffs for both than mutual defection. If any part of this ordering changed, the game would no longer be a Prisoners Dilemma and different strategic predictions would follow.

Defecting earns Firm 1 a payoff of 9 when Firm 2 cooperates (versus 6 from cooperation) and 2 when Firm 2 defects (versus 0 from cooperation). In both scenarios, defecting produces a higher payoff for Firm 1. Defection therefore strictly dominates cooperation for Firm 1. By symmetric logic, defection is also dominant for Firm 2. Both firms defect at the Nash equilibrium, earning (2,2), even though mutual cooperation would yield (6,6).

The sucker payoff is the worst individual outcome in the Prisoners Dilemma. It results from the most vulnerable position: choosing to cooperate while being exploited by a defecting rival. The payoff ordering requires that the sucker payoff is strictly less than mutual defection, which is strictly less than mutual cooperation, which is strictly less than the temptation payoff. This ordering is what makes cooperation individually risky and defection individually dominant, even though mutual cooperation produces better outcomes for both.

The cooperative outcome (6,6) is Pareto superior to the Nash equilibrium (2,2): both players are strictly better off under mutual cooperation, and neither player is worse off. The Nash equilibrium is therefore Pareto inferior. However, the Pareto superior outcome is not achievable through individual rational play because each player has a unilateral incentive to defect. This gap between the Nash equilibrium and the Pareto optimum is the central economic insight of the Prisoners Dilemma.

The payoff ordering in the Prisoners Dilemma requires that mutual defection produces a higher payoff than the sucker payoff from cooperating while the rival defects. The sucker payoff is the worst outcome in the matrix. A player who cooperates while the rival defects is being fully exploited and earns the minimum payoff. A player who defects while the rival also defects earns the mutual defection payoff, which is strictly greater than the sucker payoff by the formal definition of the Prisoners Dilemma structure.

The condition that 2C exceeds T plus S ensures that mutual cooperation produces more total value than what two players could obtain by alternating between exploiting and being exploited. Without this condition, players might sustain a strategy of taking turns defecting. With it, stable mutual cooperation is collectively superior even to alternating strategies, which matters for identifying cooperation as the uniquely optimal collective outcome in both single-shot and repeated versions of the game.

The temptation payoff is the highest individual outcome in the Prisoners Dilemma, mutual cooperation beats mutual defection for both players collectively, and the sucker payoff is the worst individual outcome. The claim that the Nash equilibrium is Pareto superior to the cooperative outcome is false: the Nash equilibrium at mutual defection is Pareto inferior since both players earn strictly less than they would under mutual cooperation, which is the defining welfare problem the Prisoners Dilemma creates.

The student correctly identifies that (4,4) is Pareto superior to (1,1), but fails to account for the dominant strategy structure. Each player earns more from defection whether the rival cooperates (6 versus 4) or defects (1 versus 0). Individual rationality drives both players to defect, producing (1,1), even though both would prefer (4,4). Recognizing that good collective outcomes can fail to emerge from individually rational choices is the core insight that the Prisoners Dilemma payoff structure illustrates.

The dominant strategy to defect relies on the temptation payoff being greater than the mutual cooperation payoff. If the temptation payoff fell below mutual cooperation, a player would no longer earn more by defecting when the rival cooperates. This would eliminate defection as a dominant strategy and transform the game into a different structure, such as a stag hunt or coordination game. The specific payoff ordering is what defines the Prisoners Dilemma and produces its characteristic strategic dynamics.

The payoff ordering 7 greater than 5 greater than 3 greater than 1 satisfies all Prisoners Dilemma conditions: temptation exceeds mutual cooperation, mutual cooperation exceeds mutual defection, and mutual defection exceeds the sucker payoff. Defecting yields 7 versus 5 when the rival cooperates, and 3 versus 1 when the rival defects. Defection dominates for both players. The Nash equilibrium is mutual defection at (3,3), even though both players prefer (5,5). The sucker payoff need not be negative to satisfy the Prisoners Dilemma conditions.

Nash equilibrium requires that no player can improve their payoff by unilaterally deviating. At the cooperative outcome, each player earns more by switching to defection while the rival cooperates (the temptation payoff exceeds the cooperation payoff). This unilateral deviation incentive means the cooperative outcome fails the Nash equilibrium test. Both players have incentives to defect, preventing cooperation from being self-enforcing and explaining why mutual defection is the only Nash equilibrium despite being collectively inferior.

By definition, mutual cooperation payoffs (C+C) exceed mutual defection payoffs (D+D) in the Prisoners Dilemma since C is greater than D for each player. The total social value of cooperation is strictly greater than the total social value of mutual defection. This is the source of the welfare loss produced by the Prisoners Dilemma: individually rational behavior destroys social value by driving both players to defect even though cooperation would generate more total payoff that could, in principle, make everyone better off.

When the temptation payoff falls below the mutual cooperation payoff, defecting while the rival cooperates no longer provides an advantage over mutual cooperation. Cooperation now earns 6 compared to defection's 4 when the rival cooperates, and 6 compared to 2 when the rival defects. Cooperation dominates defection for both players. The Prisoners Dilemma structure is eliminated and replaced by one where cooperation is the dominant strategy, demonstrating how modifying the payoff structure can change strategic behavior fundamentally.

The Prisoners Dilemma structure requires the specific payoff ordering T greater than C greater than D greater than S. Increasing the temptation payoff while maintaining this ordering preserves the structure. Proportional scaling preserves ordinal rankings and therefore preserves the strategic structure. Increasing the sucker payoff above mutual defection would change D greater than S to S greater than or equal to D, violating the required ordering. Decreasing cooperation below defection would change C greater than D to C less than D, also eliminating the Prisoners Dilemma structure.

Standard game theory assumes players maximize only their own monetary payoff. In practice, many people value fairness, altruism, and reciprocity. When these social preferences are incorporated, the effective payoff from mutual cooperation may exceed the effective payoff from defection because the social cost of exploiting another player reduces the utility of the temptation payoff. Behavioral economics recognizes that social preferences can make cooperation individually rational even in single-shot games, explaining observed cooperation rates above the standard theory prediction.