This paper suggests that decision-making under uncertainty is, at least partly, case-based. We propose a model in which cases are primitive, and provide a simple axiomatization of a decision rule that chooses a “best” act based on its past performance in similar cases. Each act is evaluated by the sum of the utility levels that resulted from using this act in past cases, each weighted by the similarity of that past case to the problem at hand. The formal model of case-based decision theory naturally gives rise to the notions of satisficing decisions and aspiration levels.

The paper deals with a measure theoretic model of a pure exchange economy. There are two kinds of traders: big traders, represented by atoms of the measure space, and small traders, represented by the atomless part of the measure space. The restriction of an allocation to the atomless sector is called competitive if there exists a price vector such that the consumption of every small trader is a maximal element (in terms of his preference) in the budget set defined by that price vector and by his initial endowment. We consider the set of allocations that are not blocked by any atomless coalition, or by the complement of any atomless coalition, and call it the 6~T2-core. The main results of the paper consist in defining sufficient conditions under which allocations in the Y'-core have a competitive restriction to the atomless sector, and vice versa. The economic implications and significance of the results are briefly discussed.