12.5 Decentralized teams, games, and nonclassical information

Witsenhausen’s classes become families of UODL declarations indexed by information shape and objective shape. Classical, partially nested, nonclassical, and nonsequential systems vary the first; teams and games vary the second. The central problem is to determine when local decision sections assemble into a global object and when the obstruction is informational rather than computational.

Crossword and Sudoku solving from Chapter 9 are finite team problems: local agents propose entries while a limit enforces global compatibility. In a game, the corresponding universal object must be paired with player-indexed observers or an equilibrium-defect object. In a nonclassical system, changing a local action may change later observations, so every counterfactual profile must be evaluated on its own induced history.