🤖 AI Summary
This work proposes a cost model for information acquisition that balances analytical tractability with modeling flexibility. Building on the f-information framework, the authors introduce an α-divergence–driven cost function and derive its closed-form expression using Amari’s α-integral. By generalizing mutual information into a unified parametric family—encompassing the Kullback–Leibler divergence, reverse KL divergence, and Hellinger distance—they characterize the optimal information acquisition strategy, whose choice probabilities belong to the q-exponential family. This approach not only explicitly identifies the optimal information structure but also recovers classical corrected logit models as special cases, thereby offering a computationally tractable and flexible new paradigm for information design problems.
📝 Abstract
Building on the $f$-information model of Bloedel et al. (2025), this paper introduces a one-parameter family of information acquisition models that extends the mutual information model (Matějka and McKay, 2015) while preserving its analytical tractability, and characterizes optimal information acquisition. The information cost is derived from the $α$-divergence and represented in closed form via the $α$-integration of Amari (2007), nesting the KL-divergence ($α=-1$), the reverse KL-divergence ($α=1$), and the squared Hellinger distance ($α=0$). The optimal choice probabilities belong to the $q$-exponential family, which arises in nonextensive statistical mechanics (Tsallis, 1988) and in the $q$-logit model of traffic route choice (Nakayama, 2013). In the KL-divergence special case, this family reduces to the modified logit of Matějka and McKay (2015).