I’m reminded of this paper, which discusses a smaller set of two-player games. What you call “Cake Eating” they call the “Harmony Game”. They also use the more suggestive variable names—which I believe come from existing literature—R (reward), S (sucker’s payoff), T (temptation), P (punishment) instead of (W, X, Y, Z). Note that in addition to R > P (W > Z) they also added the restrictions T > P (Y > Z) and R > S (W > X) so that the two options could be meaningfully labeled “cooperate” and “defect” instead of “Krump” and “Flitz” (the cooperate option is always better for the other player, regardless of whether it’s better or worse for you). (I’m ignoring cases of things being equal, just like you are.)
(Of course, the paper isn’t actually about classifying games, it’s an empirical study of how people actually play these games! But I remember it for being the first place I saw such a classification...)
With these additional restrictions, there are only four games: Harmony Game (Cake Eating), Chicken (Hawk-Dove/Snowdrift/Farmer’s Dilemma), Stag Hunt, and Prisoner’s Dilemma (Too Many Cooks).
I’d basically been using that as my way of thinking about two-player games, but this broader set might be useful. Thanks for taking the time to do this and assign names to these.
I do have to wonder about that result that Zack_M_Davis mentions… as you mentioned, where’s the Harmony Game in it? Also, isn’t Battle of the Sexes more like Chicken than like Stag Hunt? I would expect to see Chicken and Stag Hunt, not Battle of the Sexes and Chicken, which sounds like the same thing twice and seems to leave out Stag Hunt. But maybe Battle of the Sexes is actually equivalent, in the sense described, to Stag Hunt rather than Chicken? That would be surprising, but I didn’t set down to check whether the definition is satsified or not...
I’m reminded of this paper, which discusses a smaller set of two-player games. What you call “Cake Eating” they call the “Harmony Game”. They also use the more suggestive variable names—which I believe come from existing literature—R (reward), S (sucker’s payoff), T (temptation), P (punishment) instead of (W, X, Y, Z). Note that in addition to R > P (W > Z) they also added the restrictions T > P (Y > Z) and R > S (W > X) so that the two options could be meaningfully labeled “cooperate” and “defect” instead of “Krump” and “Flitz” (the cooperate option is always better for the other player, regardless of whether it’s better or worse for you). (I’m ignoring cases of things being equal, just like you are.)
(Of course, the paper isn’t actually about classifying games, it’s an empirical study of how people actually play these games! But I remember it for being the first place I saw such a classification...)
With these additional restrictions, there are only four games: Harmony Game (Cake Eating), Chicken (Hawk-Dove/Snowdrift/Farmer’s Dilemma), Stag Hunt, and Prisoner’s Dilemma (Too Many Cooks).
I’d basically been using that as my way of thinking about two-player games, but this broader set might be useful. Thanks for taking the time to do this and assign names to these.
I do have to wonder about that result that Zack_M_Davis mentions… as you mentioned, where’s the Harmony Game in it? Also, isn’t Battle of the Sexes more like Chicken than like Stag Hunt? I would expect to see Chicken and Stag Hunt, not Battle of the Sexes and Chicken, which sounds like the same thing twice and seems to leave out Stag Hunt. But maybe Battle of the Sexes is actually equivalent, in the sense described, to Stag Hunt rather than Chicken? That would be surprising, but I didn’t set down to check whether the definition is satsified or not...