  It is increasingly possible for real-world agents, such as software-based
agents or human institutions, to view the internal programming of other such
agents that they interact with. For instance, a company can read the bylaws of
another company, or one software system can read the source code of another.
Game-theoretic equilibria between the designers of such agents are called
\emph{program equilibria}, and we call this area \emph{open-source game
theory}.
  In this work we demonstrate a series of counterintuitive results on
open-source games, which are independent of the programming language in which
agents are written. We show that certain formal institution designs that one
might expect to defect against each other will instead turn out to cooperate,
or conversely, cooperate when one might expect them to defect. The results hold
in a setting where each institution has full visibility into the other
institution's true operating procedures. We also exhibit examples and ten open
problems for better understanding these phenomena. We argue that contemporary
game theory remains ill-equipped to study program equilibria, given that even
the outcomes of single games in open-source settings remain counterintuitive
and poorly understood. Nonetheless, some of these open-source agents exhibit
desirable characteristics -- e.g., they can unexploitably create incentives for
cooperation and legibility from other agents -- such that analyzing them could
yield considerable benefits.
