I'm trying to downgrade python version of anaconda via conda install python=3.3, but have following error:

~/anaconda3/bin$ ./conda install python=3.3
Fetching package metadata .........
Solving package specifications: .


UnsatisfiableError: The following specifications were found to be in conflict:
  - gevent -> python 2.6*
  - python 3.3*
Use "conda info <package>" to see the dependencies for each package.

How to resolve conflicts with the packages?

If you want to set specific version, use it like this:

WARNING: This command will overwrite the default python version system-wise

conda install python=3.6

To create environment with a specific version, you can do:

conda create -n $PYTHON36_ENV_NAME python=3.6 anaconda  # set custom env name

The anaconda at the end allows the env to use all anaconda packages

For more information refere to Anaconda documentation