1. The basic structure is described of a game theory model of the distribution of a wintering shorebird, the oystercatcher Haematopus ostralegus, foraging on 12 mussel Mytilus edulis beds whose quality as feeding areas for the birds differed. Model parameters were derived from field studies made over 15 years. A companion paper tests model predictions and illustrates how the model can be used to derive survival curves and predict estuary carrying capacity. 2. Mussel-bed quality was measured as the intake rate achieved by an oystercatcher of average competance foraging at random over the bed, and varied threefold across beds. Each individual in the model was given its own foraging efficiency, drawn at random from a normal distribution whose mean and variance depended on the bird's age and feeding method. Its susceptibility to interference from other foraging birds was calculated from its local dominance score, the percentage of wins it had over the other individuals currently on the same bed. A bird's local dominance score on a particular mussel bed was calculated from the proportion of birds on that bed having a lower global dominance rank, a measure of a bird's competitive ability relative to those of all other birds on the estuary. Across individuals, foraging efficiency and susceptibility to interference were unrelated. 3. In every iteration, the model calculated a bird's putative intake rate on each bed by subtracting the reduction in intake rate due to interference from the intake rate the bird could achieve there in the absence of interference. Each individual could then move to the mussel bed which, at that time, gave it the highest intake rate, provided the differences were sufficiently large (3%) for it to discriminate. 4. The main model limitations were the absence of: (i) a real-time base, so time-lags due to learning were not included; (ii) the energy costs associated with moving between beds; (iii) the opportunity for birds to increase their dominance score or foraging efficiency through familiarity with a mussel bed; (iv) the opportunity for individuals to control the amount of competition to which they are exposed by selecting particular times in the tidal cycle at which to feed; and (v) factors known to affect bed attractiveness to oystercatchers, such as the consistency of the substrate. None the less, the model was regarded as a suitable starting point for exploring how the proportion failing to acquire enough food, and either emigrating or starving, is affected by population size