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 -divergence–based belief distortion function, encompassing measures such as Kullback–Leibler, reverse Kullback-Leibler, and Pearson  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.

We present a model that elucidates wishful thinking by incorporating both the costs and benefits of biased beliefs. We show that wishful thinking can be characterized as equivalent to superquantile-utility maximization within the class of threshold belief-distortion cost functions. This equivalence implies that wishful thinking leads decision-makers to prefer options with greater skewness and higher risk. Finally, we demonstrate how our framework enables the analysis of optimistic stochastic choice and optimistic risk aversion.

Motivated reasoning plays a critical role in competitive, high-stakes environments such as job applications. This paper develops a game-theoretic framework in which workers, influenced by motivated reasoning, make an application decision, while a strategic firm determines hiring standards. Motivated reasoning distorts subjective beliefs, shaping worker confidence and application behavior. A comparison of equilibria under statistical discrimination and blind hiring shows that firms have a profit incentive to relax testing standards for less confident groups to counteract self-selection and encourage applications. 

This note presents a simple model of motivated reasoning

where decision-makers combine observational evidence with psychologically manufactured evidence. By adopting a revealed-preference approach, I derive bounds on the psychological desires that can rationalize data without making restrictive assumptions about observational evidence acquisition. This facilitates testing for the presence and direction of agents’ psychological desires using choice data, providing a practical tool for identifying motivated reasoning through observed choices.

I present a model of stochastic choice in which an additive perturbation term penalizes deviations from an anchoring choice vector. This framework generalizes logit choice while capturing richer substitution patterns, including the endogenous formation of choice sets. I extend the model to environments with uncertainty, introducing a novel approach to information acquisition that I term risky learning. Risky learning is an intrapersonal equilibrium where acquiring information enables agents to take risks that would otherwise be untenable. The framework admits Shannon-entropy-based rational inattention as a special case, but extends well beyond it, allowing state-dependent choice sets, novel aggregation properties, and insightful violations of IIA.

We consider decision makers who evaluate actions according to beliefs distorted at a cost from some posited probabilistic model: pessimists, whose preferences generalize the multiplier preferences of Hansen and Sargent (2001, 2008); and optimists, whose preferences generalize the wishful thinking described in Caplin and Leahy (2019). An action is justifiable if it is a best-reply to some model in the distorted-beliefs problem. We show that, for pessimists, greater pessimism and, for optimists, less optimism both expand the set of justifiable actions.

In a recent note, Strzalecki [2024] discusses a model of belief updating denoted as variational Bayes. We extend  Strzalecki’s framework by using the class of statistical distances known as ϕ-divergences, generating a broader and more versatile class of non-Bayesian updating rules. Our approach enables belief updating rules that censor unlikely state realizations, diminishing the influence of highly improbable observations. From a behavioral perspective, we show that this new class includes updating rules that are both more conservative, retaining beliefs closer to priors, and more exploratory, allowing for significant updates in response to meaningful signals, compared to traditional Bayesian updating.

Through advertising, firms transmit messages to consumers, influencing how they view a product. The content of these messages can be simple or quite complex, and firms must decide what type of content to use. Complex messaging motivates the development of a novel notion of obfuscation in advertising content. I show that obfuscating content is preferable for complex products, and comparative statics for the optimal advertising level are provided. A comparison is drawn between this obfuscating content view of advertising and Nelson's standard “advertising to signal quality” view. I show they have many similarities, but that obfuscating content explains, separate from a higher willingness to pay, investing more in advertising to consumers who view the good as high quality.

Here, you can find a link to slides that overview our contributions in the papers Wishful Thinking is Risky Thinking and Wishful Thinking and Censored Beliefs.