An outside individual option increases optimism and facilitates collaboration when groups form flexibly

The study investigates how voluntary participation—via an outside individual option—affects the initiation and success of collaborative endeavors modeled as threshold public goods. Traditional models often assume fixed group boundaries and mandatory participation, emphasizing free riding and mechanisms to mitigate it (e.g., norms, punishment, reciprocity). However, many real-world collaborations have flexible memberships where people can opt in or out and may have attractive individual alternatives. The central questions are whether and how an individual outside option facilitates collaboration when groups form voluntarily, and how to reconcile this with prior findings that individual options can undermine public goods provision when group boundaries are fixed. The authors propose that voluntariness can raise optimism about others’ cooperativeness, filtering out pessimistic defectors and potentially inducing belief updates that increase cooperation, with effects contingent on the externality that loners impose on collective outcomes.

Prior work on public goods has focused on mitigating free riding through social preferences, norms, peer punishment, and reciprocity in repeated interactions. Optional public goods games showed that exit options can change dynamics, sometimes leading to coexistence of cooperators, defectors, and loners. Conversely, research on collective risk dilemmas and self-reliance reported that individual solutions can crowd out group cooperation and reduce efficiency when group boundaries are fixed, making loners equivalent to defectors for group outcomes. The present study integrates these strands by emphasizing loners’ externality: with fixed groups (high externality), individual options harm cooperation; with flexible group formation (low externality), individual options can facilitate cooperation. The work also connects to studies on exit options in dyadic or repeated settings, partner choice, and reputation, while highlighting a distinct mechanism here: intrinsic belief updating about others’ cooperativeness in one-shot, voluntary group formation contexts.

The authors develop and test a voluntary threshold public goods game (TPGG) with an outside individual option. Model: Players have an initial endowment of 10 points. They first decide to opt into group collaboration or take an outside individual option ("leave") yielding a certain 10-point bonus (total 20 with endowment). If they opt in, they are randomly assigned to groups of 5. In groups, each member chooses to cooperate (contribute the 10-point endowment) or defect (keep it). If at least q group members cooperate (q∈{2,4,5}), all group members receive 30 extra points; otherwise, contributions are lost and no group bonus is created. Mandatory participation corresponds to no outside option; voluntary participation includes the outside option. Players are assumed to hold subjective beliefs y∈[0,1] about others’ cooperativeness. Expected payoffs: E[π|C]=30·Γ−1; E[π|D]=10+30·Γ; E[π|L]=20, where Γ is the binomial probability that at least k of the other 4 members cooperate given belief y and threshold q. Best responses and population cooperation rate are derived as functions of y and its population distribution φ(y) (modeled with Beta distributions in analyses). Theoretical predictions: (i) voluntary participation induces self-selection, with pessimistic defectors opting out and optimists opting in, raising within-group cooperation; (ii) with q=5, defection is dominated by leaving; (iii) belief updating may further increase cooperation under voluntary participation; and (iv) the impact of outside options depends on loners’ externality p (or ρ), ranging from 1 (loners equivalent to defectors in fixed groups) to 0 (no externality with flexible group formation). Experiment (main): Preregistered within-subject 2×3 factorial design manipulating participation (mandatory vs voluntary) and threshold (q=2,4,5). N=191 participants (recruited at University of Tokyo and Meiji Gakuin University) completed six one-shot conditions in pseudo-randomized order without feedback. In each condition, participants first estimated the distribution of others’ actions (cooperate/defect/leave) and then chose their own action. Both estimates and choices were incentivized; payoffs were based on points from the TPGG and estimation accuracy. Group size was 5; if the number of opt-ins was not a multiple of 5, remaining were assigned to the individual option. Additional experiment: To test the externality mechanism, a between-condition manipulation varied loners’ externality at ρ∈{0,0.5,1} (q=4), using the same protocol as the voluntary condition; N=182. Statistical analysis: Primary inference via participant-level bootstrap (1,000 iterations) to obtain 95% CIs for cooperation rates, group success rates, and normalized efficiency (average payoff relative to optimal threshold-matching contribution). Mixed-effects logistic regressions with random intercepts assessed relationships between beliefs and actions (defection/leaving), action shifts between conditions, and belief changes; ROC-AUC compared predictive power of raw expectations vs pivotal probabilities.

• Voluntary participation increased within-group cooperation across thresholds relative to mandatory participation: Δp_coop (voluntary − mandatory) q=2: +0.16 (95% CI [0.06, 0.25]); q=4: +0.22 (95% CI [0.14, 0.31]); q=5: +0.21 (95% CI [0.16, 0.27]).
• Group success rates were substantially higher under voluntary participation, approaching 1 across thresholds; differences (voluntary − mandatory): q=2: +0.12 (95% CI [0.05, 0.20]); q=4: +0.41 (95% CI [0.27, 0.56]); q=5: +0.70 (95% CI [0.57, 0.80]).
• Efficiency (normalized average payoff) within groups was higher in voluntary vs mandatory: q=2: +0.06 (95% CI [0.02, 0.10]); q=4: +0.32 (95% CI [0.20, 0.43]); q=5: +0.63 (95% CI [0.52, 0.71]). At the population level (including loners), efficiency was higher under voluntary except at q=2: q=2: −0.07 (95% CI [−0.11, 0.01]); q=4: +0.18 (95% CI [0.07, 0.28]); q=5: +0.53 (95% CI [0.43, 0.60]).
• Mechanism 1 (self-selection): Lower beliefs about others’ cooperativeness predicted defection under mandatory and leaving under voluntary participation (mixed-effects logistic regressions; defection: z=−3.92, p<0.001; leaving: z=−4.45, p<0.001). Those who defected under mandatory were more likely to leave when voluntary (z=4.86, p<0.001), indicating filtering of pessimistic defectors out of groups.
• Mechanism 2 (belief updating): Among non-loners (stayed in groups across conditions), cooperation rates were higher under voluntary (q=4: +0.09, 95% CI [0.01, 0.18]; q=5: +0.14, 95% CI [0.09, 0.20]; q=2: +0.08, 95% CI [−0.02, 0.19]). Cooperative action shifts were associated with increased optimism about others’ cooperation (mixed-effects regression: z=9.12, β=0.82, p<0.001).
• Fear vs greed: Defection rates decreased monotonically with higher expectations about others’ cooperation, and raw expectations outpredicted pivotal probabilities for action choices, highlighting fear (low expected cooperation) rather than greed as the primary driver of defection.
• Reconciling prior findings via loners’ externality: With full externality (p=1), introducing an individual option lowers group success (as in fixed group settings). With low/no externality (p≈0), individual options enhance collaboration (as in flexible voluntary groups). Additional experiment manipulating ρ (q=4) showed effective cooperation and group success highest at ρ=0 and declining with higher ρ; loners increased from 28.6% (ρ=0) to 65.9% (ρ=0.5). Beliefs were more optimistic at lower ρ (z=16.24, β=−3.55, p<0.001).

Findings show that when collaboration features flexible group formation, an outside individual option can improve within-group cooperation, group success, and efficiency. Voluntariness works through two pathways: it filters out pessimistic defectors (reducing fear-driven defection) and induces some remaining participants to update beliefs optimistically and cooperate. The study reconciles prior reports of negative effects of individual options by introducing the loners’ externality parameter: with fixed group boundaries (high externality), loners function like defectors and harm collective outcomes; with flexible membership (low externality), loners exert little to no negative impact, and the option facilitates collaboration. The results emphasize fear as the dominant deterrent to cooperation at initiation stages and suggest that designing collaborative contexts to reduce pessimistic expectations and to minimize loners’ externality can substantially improve outcomes.

The paper demonstrates theoretically and experimentally that an outside individual option, when coupled with flexible group formation, increases optimism and cooperation, raising group success and efficiency. Two mechanisms—self-selection of optimists and belief updating toward optimism among non-loners—underpin these benefits. By formalizing loners’ externality, the study integrates conflicting literatures, showing when individual options hinder vs help collaboration. Future work should endogenize belief formation, test repeated-interaction settings to examine maintenance (not just initiation) of cooperation, and generalize across broader parameter ranges (group size, benefits, loner payoffs) and motivational factors (e.g., competence, confidence, non-payoff motives).

• Belief formation was not endogenized; analyses considered fixed beliefs and equilibrium convergence without modeling heterogeneous depths of reasoning or perceived decision noise.
• One-shot design focuses on initiation of cooperation; dynamics in repeated interactions may differ as beliefs converge via feedback.
• Parameter scope was limited (group size 5; specific payoffs and thresholds); while extensions suggest robustness, broader parameter exploration is needed.
• Self-selection may be influenced by factors beyond expectations (e.g., competence, confidence, fairness or efficiency concerns), which were not the main focus; exploratory analyses suggest limited role for fairness in the main data.