Call it revenge of the nerds if you like, but many high-school chess club presidents are landing the most coveted strategic-planning positions at major corporations. Chess players realize that good strategic decisions require you to take into account the likely moves and countermoves of other players. They study their competitors’ approaches to the game and identify the likely sequence of moves that will follow any particular move they make. By looking forward and reasoning backward, they drive the game toward a checkmate victory.

This ability to look forward and reason backward is enormously valuable to strategic-decision makers. When a company builds a new chemical plant or paper mill, its profitability will often turn on whether or not competitors add capacity as well. Similarly, the success of new marketing or pricing strategies depends on whether competitors replicate them. In oligopoly markets, it is hard to identify a strategic decision that isn’t influenced by the retaliatory countermoves it sets off. The best business strategists must be skilled at predicting future rounds of competitive conduct.

Yet this is easier said than done. Uncertainty often surrounds competitive conduct, and many managers either expect the companies they compete against to engage in the kind...