Centralized markets reduce search for buyers and sellers. Their “thickness” increases the chance of order execution at nearly competitive prices. In spite of the incentives to consolidate, some markets, securities markets and on‐line advertising being the most notable, are fragmented into multiple trading venues. We argue that fragmentation is an inevitable feature of any centralized market except in special circumstances.

Consider a weather forecaster predicting a probability of rain for the next day. We consider tests that, given a finite sequence of forecast predictions and outcomes, will either pass or fail the forecaster. Sandroni showed that any test which passes a forecaster who knows the distribution of nature can also be probabilistically passed by a forecaster with no knowledge of future events. We look at the computational complexity of such forecasters and exhibit a linear-time test and distribution of nature such that any forecaster without knowledge of the future who can fool the test must be able to solve computationally difficult problems. Thus, unlike Sandroni's work, a computationally efficient forecaster cannot always fool this test independently of nature.

This paper presents conditions under which a person's beliefs about the occurrence of uncertain events are quantified by a capacity measure, i.e., a nonadditive probability. Additivity of probability is violated in a large number of applications where probabilities are vague or ambiguous due to lack of information.The key feature of the theory presented in this paper is a separation of the derivation of capacities for events from a specific choice model. This is akin to eliciting a probability distribution for a random variable without committing to a specific decision model. Conditions are given under which Choquet expected utility, the Machina-Schmeidler probabilistically sophisticated model, and subjective expected utility can be derived as special cases of our general model.

This paper provides an extension of Savage's subjective expected utility theory for decisions under uncertainty. It includes in the set of events both unambiguous events for which probabilities are additive as well as ambiguous events for which probabilities are permitted to be nonadditive. The main axiom is cumulative dominance which adapts stochastic dominance to decision making under uncertainty. We derive a Choquet expected utility representation and show that a modification of cumulative dominance leads to the classical expected utility representation. The relationship of our approach with that of Schmeidler who uses a two-stage formulation to derive Choquet expected utility is also explored.

The property of an allocation rule to be implementable in dominant strategies by a unique payment scheme is called revenue equivalence. We give a characterization of revenue equivalence based on a graph theoretic interpretation of the incentive compatibility constraints. The characterization holds for any (possibly infinite) outcome space and many of the known results are immediate consequences. Moreover, revenue equivalence can be identified in cases where existing theorems are silent.