Loosely and non-rigorously, x/0 is infinite, and so all games with W=Z are extreme forms of the corner games (unless X=W=Z or Y=W=Z).
X~Y>W=Z gets you an anti-coordination game and W=Z>X~Y gets you a pure or relatively pure coordination game (Let’s Party).
Y>W=Z>X and X>W=Z>Y are interesting, because they equate games as different as the PD (or Too Many Cooks) and Abundant Commons. I would describe this game as more similar to the Abundant Commons than the PD, as Flitz/Flitz is a perfectly acceptable equilibrium. The value transfer here is neither hyperefficient nor inefficient, but merely efficient.
The triple equalities here are equivalent under name change, so, WLOG, let’s take X=W=Z. Then, there are two games: Y>X and Y<X. Looking at the diagram, X=W=Z>Y should resemble Studying for a Test, while Y>X=W=Z should resemble the Farmer’s Dilemma.
The former game has a primary theme of avoiding Y, and so, while Flitz/Flitz is an equilibrium, I would expect to see more Krump/Krump, as it is never beneficial to play Flitz when there’s any risk of Krump.
The latter game is more complex, but the equilibrium you actually see is Flitz/Flitz, because the only way to get Y is if you play Flitz.
Finally, with all four equal, there is no longer much of a game. All strategies are equilibria, the payoff is identical in each case. This is the trivial game.
Expanding on the Y>W=Z>X and X>W=Z>Y, I would split Abundant Commons at Y=Z, into Abundant Commons above the line and Deadlock below it. Then, the games equated are Deadlock and the PD, and those form a natural continuum.
Loosely and non-rigorously, x/0 is infinite, and so all games with W=Z are extreme forms of the corner games (unless X=W=Z or Y=W=Z). X~Y>W=Z gets you an anti-coordination game and W=Z>X~Y gets you a pure or relatively pure coordination game (Let’s Party).
Y>W=Z>X and X>W=Z>Y are interesting, because they equate games as different as the PD (or Too Many Cooks) and Abundant Commons. I would describe this game as more similar to the Abundant Commons than the PD, as Flitz/Flitz is a perfectly acceptable equilibrium. The value transfer here is neither hyperefficient nor inefficient, but merely efficient.
The triple equalities here are equivalent under name change, so, WLOG, let’s take X=W=Z. Then, there are two games: Y>X and Y<X. Looking at the diagram, X=W=Z>Y should resemble Studying for a Test, while Y>X=W=Z should resemble the Farmer’s Dilemma.
The former game has a primary theme of avoiding Y, and so, while Flitz/Flitz is an equilibrium, I would expect to see more Krump/Krump, as it is never beneficial to play Flitz when there’s any risk of Krump.
The latter game is more complex, but the equilibrium you actually see is Flitz/Flitz, because the only way to get Y is if you play Flitz.
Finally, with all four equal, there is no longer much of a game. All strategies are equilibria, the payoff is identical in each case. This is the trivial game.
Expanding on the Y>W=Z>X and X>W=Z>Y, I would split Abundant Commons at Y=Z, into Abundant Commons above the line and Deadlock below it. Then, the games equated are Deadlock and the PD, and those form a natural continuum.