In dynamic games, what each player knows — the information structure — determines what strategies are available and which equilibria exist. Classical game theory typically assumes either complete information (everyone sees everything) or a fixed partial-information pattern (each player sees only their own state). Real strategic interactions are messier: player A observes player B's actions but not C's, while player C observes both A and B but with a one-step delay. The information structure is interleaved — different players see different subsets of the game at different times.
The paper represents these interleaved structures as Mathematical Program Networks, where the topology of the network captures who-knows-what-when. Each node is a decision point; edges encode informational dependencies. The network structure is not decorative — it is the constraint that shapes the equilibrium. Two games with identical payoffs but different information topologies can have qualitatively different Nash equilibria.
For the linear-quadratic case — where dynamics are linear and costs are quadratic — the framework yields Riccati-like equations for the equilibrium strategies. The classical Riccati equation for optimal control assumes a single decision-maker with full state observation. Here, the equation structure depends on the information network: which terms appear in each player's Riccati equation reflects which states they can observe.
The structural point: information in dynamic games is not a scalar quantity (more or less). It has topology — who sees whom, when, and with what delay. This topology is as load-bearing as the payoff structure in determining what equilibria are possible.
(arXiv:2603.18407)