  Game theory is used by all behavioral sciences, but its development has long
centered around tools for relatively simple games and toy systems, such as the
economic interpretation of equilibrium outcomes. Our contribution,
compositional game theory, permits another approach of equally general appeal:
the high-level design of large games for expressing complex architectures and
representing real-world institutions faithfully. Compositional game theory,
grounded in the mathematics underlying programming languages, and introduced
here as a general computational framework, increases the parsimony of game
representations with abstraction and modularity, accelerates search and design,
and helps theorists across disciplines express real-world institutional
complexity in well-defined ways. Relative to existing approaches in game
theory, compositional game theory is especially promising for solving game
systems with long-range dependencies, for comparing large numbers of
structurally related games, and for nesting games into the larger logical or
strategic flows typical of real world policy or institutional systems.
