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A representation theorem for events within lattice structures of state-spaces

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  • Alex A. T. Rathke

Abstract

For the standard lattice model of information structures, we derive a reduced poset representation which provides the same informational content as the complete lattice structure which derives it. Rational agents can recover the complete lattice of events by means of the reduced poset alone. We find that both structures provide isomorphic models under mild conditions.

Suggested Citation

  • Alex A. T. Rathke, 2025. "A representation theorem for events within lattice structures of state-spaces," Papers 2505.18615, arXiv.org, revised Jul 2025.
    • Handle: RePEc:arx:papers:2505.18615
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    References listed on IDEAS

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    1. Tirole, Jean, 1982. "On the Possibility of Speculation under Rational Expectations," Econometrica, Econometric Society, vol. 50(5), pages 1163-1181, September.
    2. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    3. Fukuda, Satoshi, 2024. "On the axiomatization of an unawareness structure from knowing-whether operators," Journal of Mathematical Economics, Elsevier, vol. 115(C).
    4. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
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