According to Anatol Rapoport, this was an instruction from an army brochure of the US-Army during World War II:
A grenade falls into a narrow trench with several soldiers in it. All soldiers will die with high probability, if not one soldier launches himself on the grenade and sacrifices his life in order to save the lives of the others. The soldiers have the choice between "dying" and "possibly surviving", with the latter option excluding the option of "voluntary sacrificing" oneself.
Urmson, J.O. (1969): Saints and Heroes; in: Moral Concepts, ed. Joel Feinberg, London: Oxford University Press.
Friends are separated in solitary cells and kept prisoners without any communication possibility. In every cell there is one switch. If the switch is flipped, the captive switching it is killed, and all the others are released. If none of the switches is operated until a specific moment in time, everybody dies. If you sacrifice yourself and operate the switch, you are a hero. Anyways, also someone else could flip the switch, in an extreme case even everyone. In this case you would die in vain and you would not claim the status of a hero as well. Therefore, for all of the prisoners, there is a big incentive to let somebody else operate the switch.
There's a blackout in a district, outside a snowstorm blusters, and the electric power plant is 3 km away by foot. If the power plant is not informed, there will be no electricity. A volunteer from the neighborhood should walk there, but he is the only one taking the cost for the whole community upon himself. Formally, this volunteer's dilemma looks as follows:
||At least one person goes there voluntarily||Everyone says, somebody else should go|
|You go there voluntarily||1||-|
|You say somebody else should go||2||0|
Experiments show that the probability of a single individual taking the initiative decreases with an increasing number of people involved in a social dilemma.
Darley, John M. / Latané, Bibb (1968): Bystander intervention in emergencies: Diffusion of responsibility. Journal of Personality and Social Psychology, 8, 377-383.
In small groups of people who are close to each other, the probability to generate voluntary cooperation is higher than in big, anonymous groups.
Olson, Mancur, Jr. (1965): The Logic of Collective Action: Public Goods and the Theory of Goods. Cambridge, MA: Harvard University Press.
Of course, communication plays a major role in this context. According to Rapoport, in the language of the natives of Tierra del Fuego there is the word "mamihlapinatapai", which can be translated as: "a look shared by two people, each wishing that the other will offer something that they both desire but are unwilling to suggest or offer themselves."
Rapoport, Anatol / Chammah, Albert M. (1965): Prisoner's Dilemma. AnnArbor: University of Michigan Press.
In ballots, a single electoral vote only has direct influence, if there is a draw between the parties one can vote for. However, in bigger political (democratic) elections, this is highly improbable. A single individual, facing the effort (costs) to go to the ballots, can therefore ask himself why he should vote, if his vote has no influence anyways. If all the people would consider this question and nobody went voting, this would be fatal for democracy and significantly "costlier" for each individual than going to the polls once.
Hence, while politicians keep bothering their heads about why only few people participate in ballots, the real interesting question is why, in the first place, some people do.
For each single deep sea fisher, it is individually "rational" to cast for fish in open (international) waters as much as possible, even if this means that the seas are being overfished. As in the voting example, the excuse could be that the single action of one fisherman does not have a big effect on fish.
Excessive showering or car washing in drought periods causes little concealment-costs to the individual, but can cause high costs due to water scarcity to the society.
Formally seen, the social state generates a social dilemma, if the level of welfare (e.g. social security) for an individual is higher than or approximately as high as the amount of money he or she would earn when having a job ("jobless trap").
Typical "Commons-situations" can emerge when employees, whose company is about to crash, form an ally to buy the company and start leading it together. If their income depends on further production, they will have a high incentive for "free-loading" (i.e. free riding). Everyone will try to get out as much as possible and to invest as little as possible. Not uncommonly, after some time such collective entrepreneurial experiments end up in hierarchic management structures again.