This paper develops a tractable model of wishful thinking that captures both the benefits and costs of optimistic biased beliefs and the behaviors they induce. Building on Bratcha and Brown (2012) and Caplin and Leahy (2019), we propose a two-stage framework in which a decision maker selects actions and belief structures under uncertainty, balancing subjective utility against the cost of departing from prior beliefs. The cost is formalized using a \(\phi \) -divergence–based belief distortion function, encompassing measures such as Kullback–Leibler, reverse Kullback-Leibler, and Pearson \(\chi ^2\) distances. Our contributions are threefold: (i) we characterize optimal beliefs, showing they twist prior probabilities toward high-utility states across a broad class of divergences; (ii) we link WT behavior to risk-seeking actions via convex risk measures; and (iii) we introduce cognitive censoring and cognitive emergence, capturing extreme beliefs. Methodologically, the model provides new insights into how optimistic beliefs reshape decision-making, extending the theoretical foundations of WT and opening avenues for future research.
