Rethinking Strategy: How We Understand Decisions in Uncertain Situations
The so-called “signaling games” are situations where one person (the sender), moves first and has some information that another person who observes this move (the receiver) doesn’t, and both must make decisions based on what they believe the other knows or will do. Such stylized models are widely used to analyze economic and political phenomena. Pierpaolo Battigalli of Bocconi’s Department of Decision Sciences and Emiliano Catonini of New York University Shanghai in their new article "The Epistemic Spirit of Divinity", published in the Journal of Economic Theory, investigate how these beliefs and strategies interact, offering new ways to think about how people make choices when facing incomplete information.
How Beliefs Can Transform Decisions
The Nash equilibrium approach of traditional game theory assumes that players in a game make decisions based on precise and correct expectations about how the other person thinks and behaves. Despite such strictures, traditional theory allows many equilibria and in its “refinement program” seeks ways to weed out most of them. The so-called “divine equilibrium” is one the most applied refinements of Nash equilibrium in signaling games, and yet it is hard to get a deep understanding of this concept. Battigalli and Catonini adopt the approach of so-called “epistemic game theory”, the formal study of interactive reasoning in games, to introduce a new perspective: beliefs about the other player’s moves aren’t always clear-cut, especially in situations where off-path actions—those not expected in the usual flow of the game—come into play. The main assumption that they uncover in the “divine” equilibrium concept, and explicitly express, is the following: it is transparent to both players that the sender’s conjecture about the reaction rule of the receiver is independent of the sender’s private information. This is what allows the authors to capture what they (jokingly) call the “epistemic spirit of divinity”, without accepting the most arbitrary aspects of the divinity criterion.
"Our approach allows for more flexibility by not requiring absolute certainty in how off-path moves are interpreted," the authors explain. Instead of assuming everyone sticks rigidly to a supposedly correct model of the other players, their theory embraces the uncertainty that comes with real-life decision-making. This gives players room to form different possible beliefs about what the other might do if things go off-script. It’s a more realistic approach that acknowledges how complicated human thinking can be.
A Real-Life Example: Deciding on Education and Jobs
To make their ideas clearer, the authors use a job-market example. Imagine a person deciding how much education to pursue. They could stop at a bachelor’s degree (BSc), or go further for a master’s (MSc) or even a PhD. But while a good employee (one who benefits from additional education) may continue studying to qualify for higher-paying jobs, a bad employee (whose productivity does not improve with further education) may pursue more education anyway for signaling purposes.
The employer (the receiver in the game) must decide which level of education to value more, and how much salary to offer based on whether they think a candidate is good or bad at their job. But both “good” and “bad” candidates might make the same education choices, not because it suits them, but because of how they think the employer will react. For example, a bad candidate might still go for a PhD just to appear more qualified, while a good candidate might stop at an MSc, believing that’s enough to land a better position. Battigalli and Catonini show that these choices depend heavily on what each player thinks the other is likely to do. Their framework explains why such tricky dynamics emerge and why divine equilibrium yields arbitrarily restrictive predictions when the sender has at least three possible choices.
What This Means: A New Way to Predict Behavior
Battigalli and Catonini, building on earlier work in epistemic game theory, open up new possibilities for understanding decision-making in real-world situations. By accepting that people’s beliefs about others are often imperfect and fluid, we can better predict how individuals or groups might behave when facing uncertain outcomes. Their framework isn’t just theoretical—it could influence how we think about negotiations, market behavior, and even personal relationships where information is shared unevenly. By weaving together belief systems, strategic thinking, and flexibility, Battigalli and Catonini offer a dynamic way to think about decision-making in signaling games. They challenge old assumptions and provide a more realistic approach to understanding why people make the choices they do when faced with uncertainty.
