Super-additive cooperation

The study investigates two prominent evolutionary hypotheses for why humans cooperate in one-shot social dilemmas: (1) repeated interactions (direct reciprocity) shaping an ancestral psychology that treats even first encounters as the start of long-term relationships with reputational concerns, particularly activated by ingroup cues; and (2) intergroup competition (group selection) favoring groups with more cooperators despite within-group advantages to selfishness. The authors note both hypotheses make overlapping predictions (more cooperation with ingroup, less with outgroup) and rest on assumptions about ancestral social life that are difficult to verify. The research question is which mechanism—or their combination—can robustly explain the evolution of one-shot cooperation. Using a comprehensive modeling framework and a behavioral experiment in Papua New Guinea with ingroup/outgroup pairings, the study evaluates the conditions under which these mechanisms support cooperation and whether their interaction provides a better explanation.

Prior work suggests that uncertainty in repeated interactions can favor cooperation through reputational incentives and risk asymmetries, especially within cohesive ancestral groups (e.g., 1–3, 9–13). Competing accounts emphasize intergroup competition and cultural group selection, where cooperative groups outperform selfish groups in conflict or competition (4–7, 14–19), though critics argue that migration and within-group selection quickly erode between-group variation, weakening group selection (8). Research on continuous and repeated prisoner’s dilemmas shows many equilibria and that increasing strategic flexibility can undermine sustained cooperation (20,21,35,36). Theories of fairness and norm enforcement can transform social dilemmas into coordination games with cooperative equilibria (28–31,32). Anthropological and historical debates on ancestral warfare and group structure highlight uncertainties in the prevalence and impact of intergroup conflict (22,23,38–40). Meta-analytic work documents robust ingroup favoritism in cooperation (10,42). This literature motivates testing whether repeated interactions, intergroup competition, or their combination can explain contemporary one-shot cooperation patterns.

Modeling: The authors model a two-player sequential social dilemma with a continuous action space. In each stage game, both players have endowments. The first mover may transfer any amount to the second mover; this transfer is doubled. Conditional on the first mover’s transfer, the second mover may transfer any amount to the first mover; this transfer is also doubled. A one-shot interaction is a single stage game; repeated interactions consist of multiple stage games with fresh endowments each time. A strategy is defined by (i) an initial transfer (first interaction as first mover) and (ii) a response function mapping the partner’s most recent transfer to one’s own transfer in subsequent interactions. Scenarios: (1) Repeated interactions (RI): only ingroup play, games can be one-shot or repeated; no intergroup competition. (2) Group competition (GC): individuals play one-shot games with both ingroup and outgroup partners; intergroup competitions occur; strategies can condition on partner’s group. (3) Joint scenario: as GC, but ingroup games are repeated, outgroup games one-shot; intergroup competitions occur. Strategy-space dimensionality: Strategies vary from 2 to 4 dimensions. Two dimensions allow perfect reciprocity and monotonic escalating or de-escalating reciprocity. Three dimensions introduce ambiguous reciprocity (escalate at low partner transfers, de-escalate at high transfers). Four dimensions allow non-linear mixtures (complex response functions). Key manipulated parameters (six characteristics):

• Dimensionality of strategy space: 2, 3, or 4 dimensions.
• Cancellation effects at individual level via life cycle: decoupled (migration after game play, before ingroup reproduction) versus coupled (migration before game play), affecting relatedness/productivity links.
• Cancellation effects at group level: varied by the number of groups moving in the metapopulation each generation (Ξ). Ξ = 40 minimizes group-level cancellation; Ξ = 0 maximizes it.
• Sensitivity of group competition to between-group differences in aggregate resources (λ): larger λ increases sensitivity.
• Migration rates (m): either 8 or 16 of 24 individuals migrate per group per generation (lower vs higher relatedness respectively).
• Initial conditions: populations seeded with either perfect reciprocators (maximal initial cooperation) or unconditionally selfish individuals (minimal initial cooperation). Simulation and outcomes: Evolutionary simulations track invasion, persistence, and equilibrium of strategy types under the three scenarios across parameter combinations. Outcomes include mean surplus per individual per ingroup interaction, distribution of initial transfers, and classification of response functions (escalators, de-escalators, ambiguous, quasi-types). Extended analyses consider increased interaction lengths (n up to 1,000), stronger multipliers (quadrupling), near-zero migration, weak selection, and mistakes (behavioral noise). Behavioral experiment: Conducted among Ngenika and Perepka groups in the Western Highlands of Papua New Guinea. Implemented the same two-person sequential dilemma as a one-shot game, with treatments manipulating group affiliation to create ingroup and outgroup pairings. Measured first-mover initial transfers and second-mover response functions. Statistical analysis employed ordinal logistic regressions (standard errors clustered on subject for second-mover analyses) to test for overall reciprocity (slope) and ingroup–outgroup differences in cooperative responsiveness.

• Repeated interactions alone: Cooperative strategies invade under 2D strategy space but do not persist once ambiguous reciprocity is permitted (3D or 4D). Populations drift to escalation degrees susceptible to invasion by ambiguous strategies; cooperation collapses. Results are robust to life-cycle variants (decoupled vs coupled), migration rates (low/high), longer interaction lengths, larger multipliers, and even near-zero migration (only small cooperation gains).
• Group competition alone: Supports ingroup cooperation only under a delicate mix: coupled life cycle, maximal sensitivity of group competition to resource differences (λ = 100), and relatively low migration (m = 8/24). Otherwise, both ingroup and outgroup strategies evolve low initial transfers and de-escalation. Thus, GC is not a robust stand-alone explanation.
• Joint scenario (repeated ingroup + intergroup competition): Produces super-additive cooperation. Even when neither RI nor GC supports cooperation alone, their combination yields robust evolution of high ingroup cooperation (high initial transfers and escalating reciprocity) and uncooperative reciprocity toward outgroup partners (low initial transfers, de-escalation). Super-additivity holds across wide conditions: 3–4D strategy spaces, high migration, moderate λ well below maximum, both life cycles, and even with maximal group-level cancellation effects. Intergroup competition stabilizes the cooperative escalating equilibria against drift and ambiguous-reciprocity invasions, acting as an equilibrium selection mechanism.
• Empirical support (PNG experiment): First movers gave higher initial transfers to ingroup partners (odds ratio 6.273, t = 3.973, P = 1.76 × 10^−4). Second movers exhibited positively sloped response functions overall (OR 2.090, t = 5.698, P = 2.33 × 10^−8) and were more cooperative with ingroup than outgroup partners (OR 4.744, t = 3.518, P = 4.83 × 10^−4). Critically, second movers showed escalating reciprocity to ingroup and de-escalating reciprocity to outgroup partners, matching the joint-scenario prediction.

The findings challenge the sufficiency of both repeated interactions and intergroup competition as stand-alone evolutionary explanations for one-shot cooperation. Under repeated interactions, finite populations drift toward regions where ambiguous reciprocity invades, undermining sustained cooperation. Under intergroup competition, cooperation requires a fragile conjunction of low migration, high sensitivity of competitions to resource differences, and specific life-cycle timing; otherwise, cancellation effects and migration decouple productivity from winning, and cooperative advantages dissipate. When combined, however, intergroup competition stabilizes the cooperative equilibria that repeated interactions make possible but fragile, shifting selection toward high-payoff escalating reciprocity within groups without requiring large between-group differences. This joint mechanism explains the nuanced ingroup–outgroup reciprocity pattern—escalation for ingroup, de-escalation for outgroup—observed in the PNG experiment. The results imply that evolutionary accounts of human cooperation should emphasize interacting mechanisms rather than single-process explanations and that modest between-group variation can suffice when mechanisms complement each other.

The paper demonstrates that neither repeated interactions nor intergroup competition reliably supports the evolution of cooperation on their own. Ambiguous reciprocity destabilizes cooperative reciprocity under repeated interactions, and group competition requires a delicate configuration to favor cooperation. Their combination, however, produces robust, super-additive cooperation: cooperative escalating reciprocity within groups and uncooperative reciprocity toward outgroups. Behavioral evidence from Papua New Guinea aligns with this prediction. The study contributes a comprehensive modeling framework and empirical test showing how interacting evolutionary forces can explain one-shot cooperation. Future research should assess the prevalence of the predicted ingroup–outgroup reciprocity pattern across diverse societies, explore mechanisms (e.g., cultural transmission) that increase between-group variation and thus super-additivity, and investigate how norm psychology, inequality aversion, and other proximate mechanisms interact with these evolutionary forces.

• Uncertainty about ancestral social structures and migration patterns necessitated broad parameter sweeps; exact historical conditions remain unknown.
• Cooperative equilibria under repeated interactions are fragile in finite populations; results hinge on allowing richer (3D/4D) strategy spaces, though these require only memory of the last move.
• Group competition as a stand-alone mechanism is sensitive to a conjunction of parameters (life cycle, λ, migration); in many realistic settings it fails to support cooperation.
• Simulated between-group variation was limited (≈4–7% of total variation), potentially understating the scope for group selection; cultural transmission increasing between-group differences could amplify effects.
• Behavioral data come from a single field context (Ngenika and Perepka groups in Papua New Guinea); generalizability to other populations requires further study.
• Models primarily analyze dyadic interactions; higher-order group dynamics and network structures were not the focus.
• Although extensions with mistakes and weak selection yielded similar conclusions, other forms of noise or learning dynamics may alter outcomes and warrant exploration.