Olson's theory explores the market failures where individual consumer rationality and firms' profit-seeking do not lead to efficient provision of the public goods, i.e. where another level of provision would provide a higher utility at a lower cost.
Note, however, that the theory is not necessarily a challenge to the invisible hand principle of Adam Smith. It only limits the domain in which that principle applies: for purely private goods in ideal competitive markets, the pursuit of self-interest is still efficient.
Besides economics, the theory has found many applications in political science, sociology, anthropology and environmentalism.
It can be shown that the provision of the public good increases when tied to the private good, as long as the private good is provided by a monopoly (otherwise the private good would be provided by competitors without the link to the public good).
If the costs of the exclusion mechanism are not higher than the gain from the collaboration, clubs can emerge. James M. Buchanan showed in his seminal paper that clubs can be an efficient alternative to government interventions.
A nation can be seen as a club whose members are its citizens. Government would then be the manager of this club. This is further studied in the Theory of the State.
Wikipedia is another example, where collaboration is fostered at the level of individual pages; this involves fewer participants than collaboration on the encyclopedia as a whole. Collaboration on wikibooks is more difficult for the same reason.
Over the past twenty years or so analytic philosophers have been exploring the nature of collective action in the sense of acting together, as when people paint a house together, go for a walk together, or together execute a pass play. These particular examples have been central for three of the philosophers who have made well known contributions to this literature:Michael Bratman, Margaret Gilbert, and John Searle, respectively.
In Gilbert (1989) and subsequent articles and book chapters including Gilbert (2006, chapter 7) Gilbert argues for an account of collective action according to which this rests on a special kind of interpersonal commitment, what Gilbert calls a "joint commitment". A joint commitment in Gilbert's sense is not a matter of a set of personal commitments independently created by each of the participants, as when each makes a personal decision to do something. Rather, it is a single commitment to whose creation each participant makes a contribution. Thus suppose that one person says "Shall we go for a walk?" and the other says "Yes, let's". Gilbert proposes that as a result of this exchange the parties are jointly committed to go for a walk, and thereby obligated to one another to act as if they were parts of a single person taking a walk. Joint commitments can be created less explicitly and through processes that are more extended in time. One merit of a joint commitment account of collective action, in Gilbert's view, is that it explains the fact that those who are out on a walk together, for instance, understand that each of them is in a position to demand corrective action of the other if he or she acts in ways that affect negatively the completion of their walk. In Gilbert (2005) she discusses the pertinence of joint commitment to collective actions in the sense of the theory of rational choice.
In Searle (1990) Searle argues that what lies at the heart of a collective action is the presence in the mind of each participant of a "we-intention". Searle does not give an account of we-intentions or, as he also puts it, "collective intentionality", but insists that they are distinct from the "I-intentions" that animate the actions of persons acting alone.
In Bratman (1993) Bratman proposed that, roughly, two people "share an intention" to paint a house together when each intends that the house is painted by virtue of the activity of each, and also intends that it is so painted by virtue of the intention of each that it is so painted. That these conditions obtain must also be "common knowledge" between the participants.
Discussion in this area continues to expand, and has influenced discussions in other disciplines including anthropology, developmental psychology, and economics. One general question is whether it is necessary to think in terms that go beyond the personal intentions of individual human beings properly to characterize what it is to act together. Bratman's account does not go beyond such personal intentions. Gilbert's account, with its invocation of joint commitment, does go beyond them. Searle's account does also, with its invocation of collective intentionality. The question of whether and how one must account for the existence of mutual obligations when there is a collective intention is another of the issues in this area of inquiry.