This paper proposes a perfectly competitive model of a market with adverse selection. Prices are determined by zero‐profit conditions, and the set of traded contracts is determined by free entry. Crucially for applications, contract characteristics are endogenously determined, consumers may have multiple dimensions of private information, and an equilibrium always exists. Equilibrium corresponds to the limit of a differentiated products Bertrand game. We apply the model to establish theoretical results on the equilibrium effects of mandates. Mandates can increase efficiency but have unintended consequences. With adverse selection, an insurance mandate reduces the price of low‐coverage policies, which necessarily has indirect effects such as increasing adverse selection on the intensive margin and causing some consumers to purchase less coverage.

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Experimentally naive mice matched the proportions of their temporal investments (visit durations) in two feeding hoppers to the proportions of the food income (pellets per unit session time) derived from them in three experiments that varied the coupling between the behavioral investment and food income, from no coupling to strict coupling. Matching was observed from the outset; it did not improve with training. When the numbers of pellets received were proportional to time invested, investment was unstable, swinging abruptly from sustained, almost complete investment in one hopper, to sustained, almost complete investment in the other-in the absence of appropriate local fluctuations in returns (pellets obtained per time invested). The abruptness of the swings strongly constrains possible models. We suggest that matching reflects an innate (unconditioned) program that matches the ratio of expected visit durations to the ratio between the current estimates of expected incomes. A model that processes the income stream looking for changes in the income and generates discontinuous income estimates when a change is detected is shown to account for salient features of the data.

Acquisition of conditioned responding is thought to be determined by the number of pairings of a conditioned stimulus (CS) and an unconditioned stimulus (US). However, it is possible that acquisition is primarily determined not by the number of trials but rather by quantities that often correlate with the number of trials, such as cumulative intertrial interval (ITI) and the number of sessions. Four experiments examined whether the number of trials has an effect on acquisition of conditioned responding, once cumulative ITI and number of sessions are equated. Results of the experiments with rats and mice favor the hypothesis that over an eightfold range, variation in number of CS-US pairings has little effect. It is suggested that learning curves might more accurately be plotted across cumulative ITI or number of sessions, and not across number of trials. Results pose a challenge to trial-centered accounts of conditioning, as demonstrated by simulations of the Rescorla-Wagner model, a simplified version of Wagner's standard operating procedure model (SOP), and Stout & Miller's sometimes competing retrieval model (SOCR). A time-centered account, rate estimation theory (RET), predicts the main finding but has trouble with other aspects of the learning process more easily accommodated by trial-centered models.

Contemporary time accumulation models make the unique prediction that acquisition of a conditioned response will be equally rapid with partial and continuous reinforcement, if the time between conditioned stimuli is held constant. To investigate this, acquisition of conditioned responding was examined in pigeon autoshaping under conditions of 100% and 25% reinforcement, holding intertrial interval constant. Contrary to what was predicted, evidence for slowed acquisition in partially reinforced animals was observed with several response measures. However, asymptotic performance was superior with 25% reinforcement. A switching of reinforcement contingencies after initial acquisition did not immediately affect responding. After further sessions, partial reinforcement augmented responding, whereas continuous reinforcement did not, irrespective of an animal's reinforcement history. Subsequent training with a novel stimulus maintained the response patterns. These acquisition results generally support associative, rather than time accumulation, accounts of conditioning.