> For example of the latter, how about the observation that social
> inequality past a certain point tends to perpetuate itself and
> increase? A and B have more than C-Z, in some sort of system that
> competes for power, capitalist, feudal, bronze age empire,
> whatever--any sort of class society with significant production above
> subsistence. A-Z compete with one another but also cooperate in a
> social system which has lots of rigid rules for cooperation.
I haven't looked at the paper in question, but I recently wrote a theoretical paper on a very related topic. It's a dynamic game in continuous time. It uses the jargon BL and Doug found so hilarious. So you are duly forewarned.
In case you wonder, I don't think differential games or conventional economic theory is the nec plus ultra in the social sciences, but I don't think it's necessarily sinful either.
This is what I posted on PEN-L (slightly edited):
A while ago, on PEN-L, there was a discussion about the usefulness of game theory in economic analysis.
Well, I just finished the draft of a paper in which I use the differential-game approach to analyze the conditions that tip off an abstract two-agent (e.g. a rich and a poor country, a husband and a wife, capitalists and workers, etc.) from "cooperation" to distributional conflict.
In this simple economy, the agents can be initially endowed with different amounts of wealth. Then they decide at each instant whether to use the wealth for current consumption (which yields immediate gratification) or fund current appropriation actions (e.g. lobbying to change tax policy, buying safe boxes, or forcefully expropriating the other guy), or to produce for the next instant in time and have more wealth for future consumption. They are trying to individually maximize the total sum of their gratification over continuous time for the life of the game.
I pinned down a closed-form Markovian Nash equilibrium (believe me, this is not easy to do with a very nonlinear rule governing the growth of each player's wealth). I also analyzed its most obvious or salient features. Because of the concavity of the appropriation function, only extreme conditions of inequality (reflected in high differences in the shadow prices of wealth of each player or, equivalently in this game, high differences in the consumption rates) can induce the players to break an (implicit, non-binding, not agreed upon) commitment to "cooperate."
That surprised me. I expected that the opposite would be the case, i.e. that I'd need to impose very special conditions to prevent mildly unequal players from getting at each other's throat. Human cooperation is more robust than I thought before I began to look at this mental experiment. And that's kind of encouraging. (Although in my paper, the term "cooperation" is used in a very general sense. So it includes free voluntary exchange. I look at it as cooperation with reciprocity enforced and regulated by prices. On the other hand, direct cooperation can be viewed as "exchange" without reciprocity being enforced or prices regulating it.)
Now, this result applies to each point in time during the life of the game. So, for a given point in time, cooperation looks very probable and distributional conflict the opposite. However, this result may be reversed when looking at the whole dynamics of the game. Only in general have I looked at the dynamic properties of the game. The system of differential equations derived from the Markovian Nash equilibrium are very nonlinear. So that means that, to solve it, I'd have to use numerical simulation and stuff. Economic theorists don't quite like that as of now. The preference is for closed-form solutions with sharp implications.
At this point, it is not clear to me whether the nonlinearities will lead small inequalities at a point in time to build up over time to the point of creating the conditions that induce a distributional fight. Or, contrariwise, that the concavity of the appropriation function will act as some sort of self-correcting mechanism, so that large inequalities induce appropriation, which corrects the inequality and re-establishes harmony.
The model is deterministic. Clearly, a bit of randomness can easily induce frequent food fights.
Anyway, if any of you is curious about it, I'll be glad to send you the draft off-list. Hopefully, you'll let me know what you think.