Stable sets in one-seller assignment games

We consider von Neumann -- Morgenstern stable sets in assignment games with one seller and many buyers. We prove that a set of imputations is a stable set if and only if it is the graph of a certain type of continuous and monotone function. This characterization enables us to interpret the standards of behavior encompassed by the various stable sets as possible outcomes of well-known auction procedures when groups of buyers may form bidder rings. We also show that the union of all stable sets can be described as the union of convex polytopes all of whose vertices are marginal contribution payoff vectors. Consequently, each stable set is contained in the Weber set. The Shapley value, however, typically falls outside the union of all stable sets.

Why (and When) are Preferences Convex? Threshold Effects and Uncertain Quality

It is often assumed (for analytical convenience, but also in accordance with common intuition) that consumer preferences are convex. In this paper, we consider circumstances under which such preferences are (or are not) optimal. In particular, we investigate a setting in which goods possess some hidden quality with known distribution, and the consumer chooses a bundle of goods that maximizes the probability that he receives some threshold level of this quality. We show that if the threshold is small relative to consumption levels, preferences will tend to be convex; whereas the opposite holds if the threshold is large. Our theory helps explain a broad spectrum of economic behavior (including, in particular, certain common commercial advertising strategies), suggesting that sensitivity to information about thresholds is deeply rooted in human psychology.

The Filippov-Wazewski relaxation theorem revisited

The converse statement of the Filippov-Wazewski relaxation theorem is proven, more precisely, two differential inclusions have the same closure of their solution sets if and only if the right-hand sides have the same convex hull. The idea of the proof is examining the contingent derivatives to the attainable sets.

Convex and exact games with non-transferable utility

We generalize exactness to games with non-transferable utility (NTU). A game is exact if for each coalition there is a core allocation on the boundary of its payoff set. Convex games with transferable utility are well-known to be exact. We consider ve generalizations of convexity in the NTU setting. We show that each of ordinal, coalition merge, individual merge and marginal convexity can be uni¯ed under NTU exactness. We provide an example of a cardinally convex game which is not NTU exact. Finally, we relate the classes of Π-balanced, totally Π-balanced, NTU exact, totally NTU exact, ordinally convex, cardinally convex, coalition merge convex, individual merge convex and marginal convex games to one another.

A cardinally convex game with empty core

In this note we present a cardinally convex game (Sharkey, 1981) with empty core. Sharkey assumes that V (N) is convex, we do not do so, hence we do not contradict Sharkey's result.

Designing Choice Sets to Exploit Focusing Illusion

Focusing illusion describes how, when making choices, people may put disproportionate attention on certain attributes of the options and hence, causing those options to be overvalued. For instance, in deciding whether or not to take out a loan, people may focus more on getting the loan than on its small and dispersed costs. Building on recent literature on focusing illusion in economic choice, we theoretically propose and empirically test that focusing illusion can be advantageously exploited such that attention is put back on the ignored attributes. To demonstrate this, we use hypothetical loan decisions where people choose between loans with different repayment plans to finance a purchase. We show that when adding a steeply decreasing-installments plan to the original choice set of not borrowing or borrowing under a fixed-installments plan, the preference for the fixed-installments plan is lessened. This is because preference for the fixed-installments plan shifted towards not borrowing. We discuss potential applications of our results in designing choice sets of intertemporal sequences.