Monotone Games: 

This monograph offers a unified account of interdependent incentives and outcomes in environments where each individual’s choice shapes the well-being of others in distinct, structured ways—whether codirectional, contradirectional, or a combination of both. Games with strategic complements embody codirectional incentives: each player is motivated to move in the same direction as others. Games with strategic substitutes, by contrast, generate contradirectional incentives: each player is pushed toward choices that diverge directionally from those of others. Monotone games encompass the broader spectrum, admitting players whose incentives align with their peers and others whose incentives run counter to them.

The general incentive patterns and outcome structures that characterize monotone games emerge across a striking range of disciplines, including anthropology, biology, business, computer science, economics, mathematics, medicine, philosophy, physics, political science, psychology, and sociology, among many others.

In this work, the author traces the unifying threads that connect these diverse cases, clarifying how recent developments parallel or depart from earlier results, and demonstrating how a broad array of seemingly disparate findings can be understood under the single, coherent framework of monotone games. This is the first publication to offer such a comprehensive unification, and it introduces numerous new theorems alongside this synthesis. The exposition is mathematically rigorous throughout. The book marks a significant milestone in our understanding of large classes of interdependent social and strategic interactions, poised to guide researchers and students for years to come.

Portions of the material were presented by the author in his Berkeley Lectures on Monotone Games, a series of invited talks delivered at the University of California, Berkeley, in Spring 2022.