How interesting! I guess the reason we intuitively want to allocate according to probability is because of prospect theory. In this example the “obvious” zero point is the start of the game, and you can never get worse than that. So the piece of the value function that can arise is concave starting at zero, i.e. it looks qualitatively like the log-curve for someone with no prior wealth.
How interesting! I guess the reason we intuitively want to allocate according to probability is because of prospect theory. In this example the “obvious” zero point is the start of the game, and you can never get worse than that. So the piece of the value function that can arise is concave starting at zero, i.e. it looks qualitatively like the log-curve for someone with no prior wealth.