Causal Discourse in a Game of Incomplete Information

Notions of cause and effect are fundamental to economic explanation. Despite the immediate intuitive content of price effects, income effects, and the like, rigorous foundations justifying well-posed discussions of cause and effect in the wide range of settings relevant to economics are still lacking. We illustrate the need for these foundations using the familiar context of an N bidder private-value auction, posing a variety of relevant causal questions that cannot be formally addressed within existing causal frameworks. We extend the causal frameworks of Pearl (2000) and White and Chalak (2009) to introduce topological settable systems, a causal framework capable of delivering the missing answers. In particular, our framework can accommodate choices that are elements of general function spaces. Our analysis suggests how topological settable systems can be applied to support causal discourse in more general games and in other areas of economic inquiry.