We model overwinter fattening strategies of dominants and subordinates as a stochastic dynamic game, basing our model on data pertaining to willow tits in Sweden. In the model the birds have two foraging habitats, one (outer branches) relatively rich in resources but also high in predation risk, the other (inner branches) less productive and less risky. The dominant is able to exclude the subordinate from the habitat it is currently using. Fluctuations in weather result in variable daily metabolic costs. The model predicts that in certain circumstances subordinates maintain a higher level of fat reserves than dominants, thereby hedging against uncertain future metabolic costs and restricted foraging opportunities. Acquiring larger fat reserves exposes the subordinate to higher levels of predation risk, reducing its probability of surviving the winter, relative to the dominant. The model's predictions are in agreement with observations and experiments, and lend support to the hypothesis that winter fattening strategies are complex adaptations to specific environmental, spatial, and social conditions.