Market selection when markets are incomplete

In the first period agents trade Arrow securities in zero supply. The set of available Arrow securities is of a specific form, but it can be complete or incomplete. In the second period one out of many possible states of nature is realized. I show that agents with more accurate beliefs (in the sense of higher market entropy) will accumulate more wealth and therefore dominate the economy. This holds regardless of agents' preferences over risk and in both complete and incomplete market economies. These results indicate that belief accuracy rather than preferences over risk is the critical factor determining survival. However, the exact sense in which agents with more accurate beliefs become wealthier is stronger in complete market economies than in incomplete market economies.