  Humans are universal decision makers: we reason causally to understand the
world; we act competitively to gain advantage in commerce, games, and war; and
we are able to learn to make better decisions through trial and error. In this
paper, we propose Universal Decision Model (UDM), a mathematical formalism
based on category theory. Decision objects in a UDM correspond to instances of
decision tasks, ranging from causal models and dynamical systems such as Markov
decision processes and predictive state representations, to network multiplayer
games and Witsenhausen's intrinsic models, which generalizes all these previous
formalisms. A UDM is a category of objects, which include decision objects,
observation objects, and solution objects. Bisimulation morphisms map between
decision objects that capture structure-preserving abstractions. We formulate
universal properties of UDMs, including information integration, decision
solvability, and hierarchical abstraction. We describe universal functorial
representations of UDMs, and propose an algorithm for computing the minimal
object in a UDM using algebraic topology. We sketch out an application of UDMs
to causal inference in network economics, using a complex multiplayer
producer-consumer two-sided marketplace.
