Information Acquisition with $α$-Divergence Costs
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913177529221120 |
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| author | Ui, Takashi |
| author_facet | Ui, Takashi |
| contents | Building on the $f$-information model of Bloedel et al. (2025), this paper introduces a one-parameter family of information acquisition models and characterizes optimal information acquisition. This family extends the mutual information model (Matějka and McKay, 2015) while preserving its analytical tractability. The information cost is derived from the $α$-divergence, which nests the KL-divergence ($α=-1$), the reverse KL-divergence ($α=1$), and the squared Hellinger distance ($α=0$), and is represented in closed form via the $α$-integration of Amari (2007). The optimal choice probabilities belong to the $q$-exponential family, which appears in nonextensive statistical mechanics (Tsallis, 1988) and in the $q$-logit model of traffic route choice (Nakayama, 2013). This family reduces to the modified logit in the mutual information case (Matějka and McKay, 2015). We also show that $α$ determines how payoff levels affect the set of actions chosen with positive probability in each state. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28026 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Information Acquisition with $α$-Divergence Costs Ui, Takashi Theoretical Economics Building on the $f$-information model of Bloedel et al. (2025), this paper introduces a one-parameter family of information acquisition models and characterizes optimal information acquisition. This family extends the mutual information model (Matějka and McKay, 2015) while preserving its analytical tractability. The information cost is derived from the $α$-divergence, which nests the KL-divergence ($α=-1$), the reverse KL-divergence ($α=1$), and the squared Hellinger distance ($α=0$), and is represented in closed form via the $α$-integration of Amari (2007). The optimal choice probabilities belong to the $q$-exponential family, which appears in nonextensive statistical mechanics (Tsallis, 1988) and in the $q$-logit model of traffic route choice (Nakayama, 2013). This family reduces to the modified logit in the mutual information case (Matějka and McKay, 2015). We also show that $α$ determines how payoff levels affect the set of actions chosen with positive probability in each state. |
| title | Information Acquisition with $α$-Divergence Costs |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2605.28026 |