BACKGROUND: People with psychoses often report fixed, delusional beliefs that are sustained even in the presence of unequivocal contrary evidence. Such delusional beliefs are the result of integrating new and old evidence inappropriately in forming a cognitive model. We propose and test a cognitive model of belief formation using experimental data from an interactive ‘Rock Paper Scissors’ (RPS) game. METHOD: Participants (33 controls and 27 people with schizophrenia) played a competitive, time-pressured interactive two-player game (RPS). Participants' behavior was modeled by a generative computational model using leaky integrator and temporal difference methods. This model describes how new and old evidence is integrated to form a playing strategy to beat the opponent and to provide a mechanism for reporting confidence in one’s playing strategy to win against the opponent. RESULTS: People with schizophrenia fail to appropriately model their opponent’s play despite consistent (rather than random) patterns that can be exploited in the simulated opponent’s play. This is manifest as a failure to weigh existing evidence appropriately against new evidence. Furthermore, participants with schizophrenia show a ‘jumping to conclusions’ (JTC) bias, reporting successful discovery of a winning strategy with insufficient evidence. CONCLUSIONS: The model presented suggests two tentative mechanisms in delusional belief formation: (i) one for modeling patterns in other’s behavior, where people with schizophrenia fail to use old evidence appropriately, and (ii) a metacognitive mechanism for ‘confidence’ in such beliefs, where people with schizophrenia overweight recent reward history in deciding on the value of beliefs about the opponent.