What is the name of this game?

Question

I'm hoping someone here might help me identify the name of the game below.

Is it simply a deadlock game where mutual defection is a weak nash equilibrium?

                  Player 2

                 C       D
              -----------------
           C  | 0, 0  |  0, 1 |
Player 1      -----------------
           D  | 1, 0  |  1, 1 |
              -----------------

More generally:

                  Player 2

                 C       D
              -----------------
           C  | a, a  |  a, b |
Player 1      -----------------
           D  | b, a  |  b, b |
              -----------------

Where b > a.

Answer 1

According to the Games article Names for Games: Locating 2 × 2 Games by Bryan Randolph Bruns, this game is "Double Harmony".

It's particularly boring since your "defect" just means "take the high payoff", and there's no reason for either player not to.