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arXiv · 1803.10131

The algebra of predicting agents

Joe Bolt·Jules Hedges·Viktor Winschel
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Abstract

The category of open games, which provides a strongly compositional foundation of economic game theory, is intermediate between symmetric monoidal and compact closed. More precisely it has counits with no corresponding units, and a partially defined duality. There exist open games with the same types as unit maps, given by agents with the strategic goal of predicting a future value. Such agents appear in earlier work on selection functions. We explore the algebraic properties of these agents via the symmetric monoidal bicategory whose 2-cells are morphisms between open games, and show how the resulting structure approximates a compact closed category with a family of lax commutative bialgebras.

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Joe Bolt, Jules Hedges, Viktor Winschel. 2018-03-27. The algebra of predicting agents. https://arxiv.org/abs/1803.10131

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