Visibility influences strategic behavior and coordination outcomes
Visibility Design and Strategic Reasoning
Computer Science and Game Theory
Summary
How much information people see about others affects how they make decisions in groups or games. The paper shows that when people can see opponents who think like them, it changes the overall actions of the group in predictable ways. Less visibility can sometimes increase effort in competitive settings but reduce coordination. The authors also find that hiding information can hurt the smartest thinkers and that showing only noisy rankings can change how people behave. This highlights that who you see matters just as much as how smart you are in strategic situations.
What this means in practice
- •For game designers: Design game interfaces showing selective opponent information to influence player strategies and overall game dynamics.
- •For online platform managers: Shape visibility settings of leaderboards and feeds to manage user behavior in competitive or cooperative online environments.
Tested on simulated data.
Authors
Raman Ebrahimi, Sepehr Ilami, Babak Heydari, Isabel Trevino, Massimo Franceschetti
Abstract
Dashboards, feeds, and leaderboards determine whom agents believe they are playing against. We study how such information architectures shape strategic behavior, and how a designer who controls them can use visibility as a lever. We propose a behavioral model in which a transparency parameter governs how selectively agents are exposed to opponents of nearby reasoning depth, and embed it in a Cognitive Hierarchy environment, which provides a tractable language for tying agents' beliefs about the sophistication of others to what they see. We show that because the exposure operator is an exponential tilt of the type distribution, the effect of transparency on aggregate behavior has a closed form: the derivative of the aggregate action with respect to $p$ is proportional to the population-average variance of perceived sophistication. This identity signs the effect in games of strategic complements (opacity raises aggregate effort) and in coordination environments (opacity lowers the mean action), and an ordinal version holds for any response rule that is monotone in the belief. Notably, under a Poisson prior, opacity acts as a sophistication multiplier: every reasoner plays as if the population were $\mathrm{Poisson}(τ/p)$. We use this structure to characterize the disagreement-versus-level tradeoff faced by a coordination-minded designer, to identify the reasoning depths that respond most to visibility, and to show that opacity imposes a ``sophistication tax'' under which the deepest reasoners can lose to moderate ones. Simulations in which agents see only a noisy leaderboard of published actions reproduce both the reversal and the tax. Together, our findings highlight that who an agent sees, and not only how deeply it reasons, shapes strategic behavior, and point to visibility as a design lever.