  Following our recent development of a compositional model checking algorithm
for Markov decision processes, we present a compositional framework for solving
mean payoff games (MPGs). The framework is derived from category theory,
specifically that of monoidal categories: MPGs (extended with open ends) get
composed in so-called string diagrams and thus organized in a monoidal
category; their solution is then expressed as a functor, whose preservation
properties embody compositionality. As usual, the key question to
compositionality is how to enrich the semantic domain; the categorical
framework gives an informed guidance in solving the question by singling out
the algebraic structure required in the extended semantic domain. We
implemented our compositional solution in Haskell; depending on benchmarks, it
can outperform an existing algorithm by an order of magnitude.
