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The objective of this paper is to present a tournament scheme where the winner is determined as a function of pairwise competition between the players. We show that this tournament can be described by a time homogeneous discrete absorbing Markov chain, and derive the appropriate expressions for the probabilities and expectations of the tournament progression.
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Diffusion processes (e.g., Wiener process, Ornstein–Uhlenbeck process) are powerful approaches to model human information processes in a variety of psychological tasks. Lack of mathematical tractability, however, has prevented broad applications of these models to empirical data. This tutorial explains step by step, using a matrix approach, how to construct these models, how to implement them on a computer, and how to calculate the predictions made by these models. In particular, we present models for binaries choices for unidimensional and multiattribute choice alternatives; for simple reaction time tasks; and for three alternatives choice problems.