Arnis Vilks

• We analyse the assumption of rationality, as it is used in mainstream microeconomics and game theory, focussing on the distinction between rationality of choice and rationality of reasoning. Specifically, we argue that rationality of choice makes sense even when the agents’ beliefs or reasoning may be mistaken, but that the substitutivity principle of standard mathematical logic makes it ill-suited for an analysis of mistaken reasoning. We therefore consider the modal logic approach to knowledge and rationality, which has been taken up recently by game theorists, and seems to be a more adequate framework for an explicit analysis of rational decision-making. In order to make precise the assumptions on agents’ rationality which logically warrant the – typically informal – conclusion that the optimal action will be taken, we formulate an axiomatic theory for a very simple specific decision problem. This framework allows us to disentangle various assumptions ‘behind’ the seemingly obvious prediction. However, we show that as soon as our theory allows us to prove formally what the agent will choose, the agent’s ‘decision problem’, as it is typically interpreted, becomes illusory. We argue that this conclusion cannot be avoided unless it is recognized that the process of solving a decision problem changes the agent’s knowledge.