The key step in planning is to define a roadmap to get to target state over a period of say 3 to 5 years. Now pedants have often corrected me here to call it a Route Map, which actually defines a path from current to target. Now the questions is can we define the Route Map a priori or a posteriori? Your concept of Game Theory applies here, because as you say: “crucially Game Theory analyses the strategy in the context of other competitors and their strategies, the implication being that an strategy is only as good as the strategies of your competitors – if their strategy is better you are going to lose.”
Interactions in the market with competitors guided by their own strategies, are going to determine how the CEO and CxO respond to opportunities and risks to value creation. So in planning I have been working on how to scope and prioritise tactical projects which come forward with the money to deliver.

A Game Theoretic Model of planning for business change will or should identify the optimum decision in each prioritisation round. It should be able to establish synergies between tactical and strategic solutions to what comes from the left field (i.e. the resource competitive field of markets and supply chains).

It would be good if we got together to exchange notes, and take it further.

Great original thinking stuff.