KRIPKE SEMANTICS, COMMON KNOWLEDGE, BOUNDED RATIONALITY AND AUMANN’S AGREEMENT THEOREM

Abstract

The first model with k-level thinking with Gaussian noise shows that small deviations for common knowledge led to “almost” common knowledge equilibria. The second model demonstrated the semantic economy idea: as agents exchange and adapt beliefs, they create shared informational value by reaching a consensus that reflects network-wide insights rather than mere individual optimization. Higher reasoning depth does not change Nash equilibria but shifts up Kantian beliefs. The shift up in Kantian beliefs suggests a greater alignment toward strategies that maximize collective welfare, rather than purely individualistic or competitive outcomes. This doesn't alter the Nash equilibrium, where players still act independently, but it emphasizes a higher baseline of cooperative or altruistic expectations among players due to more profound belief hierarchies in the reasoning process. In the third model: networked economic context where agents interact in an economic network where competitive advantage depends on the informational value generated across the network, results differ from the second example: Nash beliefs adjust based on others' best responses (shift up), while Kantian beliefs account for mutual benefit, dampening large shifts. Nash and Kantian equilibria differ when only three agents exist versus network economy.