Two people agree to meet, but each has their own things to do. One hesitates: what if the other doesn't come? And decides not to go. The other thinks the same. The meeting doesn't happen. That's the simple mechanism the authors dissect: a joint endeavor requires everyone to invest time, but the payoff depends on whether the partner participates.
In the model, each person keeps a to-do list ordered by importance. A joint activity gets a spot in this list not by chance but by choice: the value of the joint endeavor minus the estimated risk that the partner won't show. As long as both are confident enough in each other, the pair stays in the 'coupled' phase — things are done together. But once doubts cross a threshold, the system slides into the solitary phase, where everyone is busy only with themselves. The transition is sharp, like a light switch, and going back is hard: you need to 'keep the door open' alone for a long time, spending time without any guarantee of a response.
If there are many people connected in a network, each person's attention is divided among contacts according to the rule 'one divided by the number of connections plus a constant.' This gives rise to a critical number of connections: if a person has too many acquaintances, they can't sustain joint activity with anyone. The solitary phase spreads through the network like an attack on the most sociable, but without a malicious actor, just from attention overload. For a group of several people, the critical number of participants drops even faster: there's a limit to the size of a company beyond which a joint endeavor won't hold.
This explains two things long seen in data on correspondence and calls: people have a limited capacity for maintaining active ties, and ties decay if the rhythm of communication is interrupted. The model shows the cause isn't laziness or forgetfulness but the very structure of choice: when everyone assesses the risk of being abandoned, a joint endeavor lives only under mutual confidence.
as written by the authors arXiv:2608.14398v1
What decides whether people do things together or separately? Many activities cannot be carried out alone, and an individual must rank them against the private tasks competing for the same time. We address this within the priority-queue description of human activity by letting each agent choose the priority of a shared task rather than drawing it from a fixed distribution: the value of the joint activity, discounted by the estimated risk that the partner will not take part. Participation becomes strategic, and the model acquires a phase transition. A coupled phase, in which joint activity is sustained, is separated from an absorbing solitary phase by a saddle-node bifurcation that we obtain in closed form. The transition is discontinuous and the solitary phase is absorbing, so collapse is irreversible unless an agent persists unilaterally for of order one memory time, a cost we also compute. The heavy-tailed interevent statistics that motivate queueing models of human dynamics survive only in a narrow window at the transition, and there the exponent is fixed by the fraction of time spent coupled rather than by queue length: the universality classes of the non-strategic model do not survive the introduction of choice. On a network, attention divides as $$1/(k+a)$$ and fixes a critical degree beyond which no coupled state exists, so the solitary phase percolates according to the Molloy--Reed criterion with the second moment truncated at that degree --- formally an attack on hubs, with no attacker. For group activities the critical degree falls as the $$(m-1)$$th root, implying a maximum group size. The transition organises two quantities already measured in communication records: a finite capacity for keeping ties active, and the decay of ties whose rhythm is interrupted.
In the model, the solitary phase 'absorbs': if a pair breaks up, returning to the previous rhythm costs long one-sided effort — roughly like hand-cranking a stalled flywheel.