Information Acquisition with $α$-Divergence Costs

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).