This chapter discusses a model of cognitive learning that is based on the idea of ‘schemas’, and shows how it can be formalized and brought to bear on learning in strategic situations. Hypothesis testing offers a very different perspective on the learning process than does standard Bayesian learning. The latter seeks to identify prior beliefs that capture the correct strategies right from the beginning. Under hypothesis testing, by contrast, beliefs emerge endogenously as the players thread their way through an immense space of possible strategies, testing and rejecting alternative ideas of what is going on. This approach can be made to work with mild restrictions on the nature of the tests and the way in which new hypotheses are formed, and with no restrictions at all on the structure of the payoffs. Although hypothesis testing is by no means the only way of achieving probabilistic forms of convergence to Nash equilibrium, it is a particularly natural way of achieving this aim while preserving certain key aspects of rational decision making, including the weighing of beliefs against evidence and the adoption of more or less optimal behaviour given one’s current beliefs.
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