This paper explores the interdependence between market structure and an important class of cognitive biases. Starting with a familiar bilateral monopoly framework, we characterize the endogenous emergence of preference distortions during bargaining which cause negotiators to perceive their private valuations differently than they would outside the adversarial negotiation context. Using this model, we then demonstrate how a number of external interventions in the structure and/or organization of market interactions (occurring before trade, after trade, or during negotiations themselves) can profoundly alter the nature of these dispositions. Our results demonstrate that many such interventions frequently (though not always) share qualitatively similar characteristics to market interventions that are often proposed for overcoming more conventional forms of market failure. Nevertheless, our analysis underscores the importance of understanding the precise link between cognitive failures and market structure prior to the implementation of any particular proposed reform.