There’s something to be said for this model… it looks rather realistic in the case where there is a large imbalance of power between trading partners. The powerful partner is likely to get everything it wants, and the powerless one may quite plausibly be worse off than if the trade never happens. I think poor little Slug isn’t going to keep that leaf for very long.
The powerful partner is likely to get everything it wants
Currently, I see no evidence for that claim (apart from the utility-equally-linear-in-every-resource case). Slug can easily have a utility that gives it two leaves, for instance.
The only constraint is that no player can lose more than they could theoretically gain. Within that constraint, there exists utilities that give Slug the maximum that he could get.
Currently, I see no evidence for that claim (apart from the utility-equally-linear-in-every-resource case). Slug can easily have a utility that gives it two leaves, for instance.
I can’t see how that works, provided the Galaxy partner has declining marginal utility in leaves. Suppose the New Republic has N leaves already (where N is a very large number). By definition of the zero-point, and scaling, New Republic has Utility(N leaves) = 0, Utility(N+1 leaves) = 1. With declining marginal utility, it must have Utility(N-1 leaves) < −1.
At most, Slug can have utility(2 leaves) = 1, in the case where its limited mind thinks one extra leaf is as good as a whole galaxy of extra leaves, but then it is still impossible for the optimal trade to be a transfer of one leaf from Galaxy to Slug. The same applies for transfer of two or more leaves. The only exception I can see is if the Slug happens to have some sort of really exotic leaf which is more valuable to Galaxy than two or more regular leaves. Then there could be an exchange. The problem is that Slug is then likely to be adapted to its exotic leaf, and can’t eat the regular ones.
The only other possible trades are: No exchange at all; Slug loses its leaf and gets nothing in return; Slug loses its leaf and gets something else in return (such as a slug pellet). Whether Slug keeps its leaf seems to depend on whether it has utility(0 leaves) < −1 that is, whether its own marginal utility declines so rapidly that its single existing leaf is more valuable than the incremental value from a whole galaxy of additional leaves! That seems a bit unlikely if it has any sort of Darwinian utility (the expected fitness gain from N leaves is truly enormous, compared to the fitness loss of its own life).
Basically, under any plausible utility functions, Slug is going to get squashed by Galaxy. Which sounds realistic, as I said.
In your example, you setup the galaxy to care more about losing a leaf than gaining one (which is fine!), hence triggering the “you can only lose as much as you can gain”.
But within these constraints, there is no reason to suspect one player will come out ahead.
There’s something to be said for this model… it looks rather realistic in the case where there is a large imbalance of power between trading partners. The powerful partner is likely to get everything it wants, and the powerless one may quite plausibly be worse off than if the trade never happens. I think poor little Slug isn’t going to keep that leaf for very long.
Currently, I see no evidence for that claim (apart from the utility-equally-linear-in-every-resource case). Slug can easily have a utility that gives it two leaves, for instance.
The only constraint is that no player can lose more than they could theoretically gain. Within that constraint, there exists utilities that give Slug the maximum that he could get.
I can’t see how that works, provided the Galaxy partner has declining marginal utility in leaves. Suppose the New Republic has N leaves already (where N is a very large number). By definition of the zero-point, and scaling, New Republic has Utility(N leaves) = 0, Utility(N+1 leaves) = 1. With declining marginal utility, it must have Utility(N-1 leaves) < −1.
At most, Slug can have utility(2 leaves) = 1, in the case where its limited mind thinks one extra leaf is as good as a whole galaxy of extra leaves, but then it is still impossible for the optimal trade to be a transfer of one leaf from Galaxy to Slug. The same applies for transfer of two or more leaves. The only exception I can see is if the Slug happens to have some sort of really exotic leaf which is more valuable to Galaxy than two or more regular leaves. Then there could be an exchange. The problem is that Slug is then likely to be adapted to its exotic leaf, and can’t eat the regular ones.
The only other possible trades are: No exchange at all; Slug loses its leaf and gets nothing in return; Slug loses its leaf and gets something else in return (such as a slug pellet). Whether Slug keeps its leaf seems to depend on whether it has utility(0 leaves) < −1 that is, whether its own marginal utility declines so rapidly that its single existing leaf is more valuable than the incremental value from a whole galaxy of additional leaves! That seems a bit unlikely if it has any sort of Darwinian utility (the expected fitness gain from N leaves is truly enormous, compared to the fitness loss of its own life).
Basically, under any plausible utility functions, Slug is going to get squashed by Galaxy. Which sounds realistic, as I said.
In your example, you setup the galaxy to care more about losing a leaf than gaining one (which is fine!), hence triggering the “you can only lose as much as you can gain”.
But within these constraints, there is no reason to suspect one player will come out ahead.