Smith (1985) Inuit foraging groups

Smith EA (1985) Inuit foraging groups: Some simple models incorporating conflicts of interest, relatedness, and central-place sharing. Ethology and Sociobiology 6: 27-47. 

From the abstract: 
Several simple models of optimal foraging group size are developed to explore the effect of the following factors: (1) conflicts of interest between group members and perspective joiners; (2) genealogical relatedness and kin-directed altruism; and (3) the scope of the sharing rule governing division of the harvest.

Abstract results:
Where the alternative is low-return solitary foraging, "joiners" are shown to prefer group sizes that are often suboptimal (in per capita efficiency) for "members." Predicted group sizes are also above per-capita optima where kin-directed altruism is important and/or where groups and individuals pool their catch at a central place.
Predictions from the models are tests quantitatively with data on Inuit foraging groups. Some models offer an improvement in accounting for variation in foraging group size, but others do not; empirical and theoretical gaps in our understanding are revealed that call for further research.

The basic model: 
For any foraging group, the per capita return is the sum over all members of the energy acquired minus the energy expended, divided evenly by the group size and the time duration of the foraging period.

Conflict of interest between members and joiners.
Consider a solitary hunter considering whether or not to join a group of size n – 1. Let R(n) be the per-capita payoff for a group of size n. 
Joiner's rule: A solitary hunter should want to join as long as R(n) > R(1).
Member's rule: A group member should favor an additional forager as long as R(n) > R(n – 1).
A conflict of interest therefore occurs whenever R(n – 1) > R(n) > R(1). Under the assumptions of the model, such conflicts should be common, especially when the expected payoffs from solitary foraging are low.

Social foraging and inclusive fitness
This section extends the previous model to incorporate inclusive fitness considerations. Here, an individual deciding whether to become the nth member of a foraging group, at least some of whose members are close kin, should prefer to join if the sum of his share plus the share of the n  – 1 members (devalued by r, the mean coefficient of relatedness between the joiner and the members) would exceed the sum of his harvest from solitary foraging plus the harvest the same group of foragers would obtain without him (again devalued by r).

The larger r becomes (all else equal), the more important the effect on members' shares of joining becomes to the joiner, and hence the less likely a joiner is to act selfishly in joining a group and depressing the per capita return rates simply because the joiner's share will be higher that way.

From the member's perspective, the situation is more complex. Here, the inclusive fitness calculation must account for the effects of (1) the decision maker, (2) the joiner, (3) the other members, as well as the other members' shares if the prospective joiner is excluded, and (5) the joiner's expected return from solitary foraging -- al devalued by the appropriate coefficients of relatedness. The model predicts that the higher the coefficient of relatedness, the more likely members will be to prefer to admit another member, even if this reduces all members' shares somewhat but markedly increases the share of the joiner.

Communal sharing at the settlement level
The previous models assumed that members of a foraging group share their catch equally among group members, but only among group members. Here, he analyzes a model in which all foragers co-reside in a camp that shares resources. Specifically, each day foragers leave camp and forage singly or in one or more groups, returning their catch to the camp, where it is pooled and then divided into equal shares for each resident. For simplicity, ignore differences between individuals in foraging effort and success, and consider only the case in which a single foraging group forms. The decision thus concerns how large this group will be, and hence how many individuals will forage alone on any day.

An individual should therefore weigh joining the group against remaining solo, and should do this whenever the following condition is met:
n R(n) > (n – 1) R(n – 1) + R(1),
where n is the number in the foraging group.

One interesting implication is that the optimal group size under the band-sharing rule will always be greater than or equal to the size that maximizes the per capita harvest of the foraging group, and less than or equal to the maximum size allowed by the joiner's preference rule.