They remember a limited stretch of the past, the last m turns of the game. At each step, each player independently samples s of those turns from its memory and uses that to guess the probability that other players will make various moves. It then selects the "best reply" move, the one which maximizes its expected pay-off, conditional on that distribution of other players' moves. (It needn't know anything about others' utility functions to do this, but in general must know its own.) Since considerations other than immediate selfish utility (altruism, stubbornness, self-hatred, drugs, stupidity) play a role in decision-making, there is some small probability that actors will not play the best-reply, but make some other move. Young considers both a fixed probability of perversity (not his word), and situations where moves are more likely the closer they approach the best reply; the general picture is similar in both cases.
It's worth a moment to appreciate the virtues of these agents, as theoretical devices. They are adaptive, but not too adaptive --- conversely, they are dumb, but not too dumb. Only a limited amount of information is available to them, and they don't always use all of that. They are self-interested, but occasionally perverse. They are, in short, trying to do the best they can for themselves with limited means, and sometimes shoot themselves in the foot. What, then, can they achieve?
In essence, what they accomplish is the formation of customary institutions. Young defines a convention as a situation where everyone has been making the same move for as long as anyone can remember (i.e. at least m turns), and moreover where it is in nobody's interest to be the only player making an unconventional move. (Conventions are Nash equilibria.) The effect of his "adaptive play" dynamics is that, independent of the starting moves, the game spends most of its time in conventions, and especially in those conventions which are, in a well-defined sense, easy to reach and hard to leave, where breaking out of the convention requires considerable and sustained perversity. More generally, if fixed conventions do not exist, adaptive play will lead to what he calls "curb sets," sets of strategies which are best replies to each other, and again concentrate on curb sets which are stable in the defined sense. All this assumes that m is fixed and finite, that s is reasonably small compared to m, and that the players are not too perverse --- not unreasonable assumptions. These results are very robust to variations in the learning process, heterogeneity in utility functions, etc.
The results are even robust to imposing a spatial structure on the game, and requiring that people play with their neighbors, and know just what their neighbors have done. So long as there is some probability of their playing with distant agents, the nature of the stable states doesn't change in any important respect; what does change, and does depend on the precise social geometry of the game, is how long different states last, how quickly transitions between them happen, and just how likely it is that different conventions are in force in different but connected parts of the world. (This is only proved in detail for certain kinds of games, but it seems likely that it will prove to be true quite generally.) As Young notes, this leads to math like that used in statistical mechanics.
Having shown all this, in his last two chapters Young applies his results to bargaining over the division of a fixed pie, and to two-party contractual division more generally. The basic result is that adaptive play fixes on conventions which maximize the product of the gains to agreement of the two sides, giving more weight to the better informed side. (If players sometimes exchange roles --- "a natural consequence of mobility between classes" --- then the stable division tends to 50-50.) Now, it's a readily observable fact that, even when there is some class mobility, most contracts (e.g. between landlord and tenant, or capitalist and worker) are not fair, that gross inequity is not only the historical norm, but usually enshrined by custom. But remember that Young's results are about the division of everything over and above the disagreement payoff. For one party the disagreement payoff may be letting a field lie fallow, or a marginal reduction in production, whereas for the other it's destitution, a blow to the head, or being chopped down by an armored man on horseback. Young does not make this point, but I felt much better about the results after it occurred to me.
Young closes with a summary (useful) and some half-hearted reflections on the possible implications for government (which strikes me as naïve about what policy can do and has done, even when opposed by custom).
The word "evolutionary" in Young's subtitle is misleading, at least if evolution is taken to mean anything more specific than "forming gradually." In particular, nothing in his models corresponds to selection via differential reproductive success. (He makes a curious mistake in this connection in sec. 2.1, arguing that selection only works for "genetically programmed" behavior. This objection loses all force if we make the replicators not people but their rules of behavior --- as is done by some of the authors he cites!) What he has shown is that groups made up of one type of adaptive (but still pretty dumb), selfish (but sometimes perverse) agent can develop customary institutions which are better than a blow to the head --- not perfectly reliably, but still with high probability. Moreover he is, so far as I know, the first to have shown this with mathematical rigor, and no hand-waving. (No prior knowledge of game theory or economics is needed to follow him, but considerable mathematical maturity is.) There are three obvious and important directions in which to go from here. (Mathematical elaboration is obvious, but not necessarily important.) First: seeing how much will change if we use some other kind of learning than adaptive play, even (to be radical) mechanisms with psychological evidence behind them --- Young claims that little would need fixing, but this isn't self-evident. Second: Comparing the predictions of this kind of model, as far as can be done, with the real world. (Young has already started on the later task, in other publications.) Third: Incorporating the effects of policy, of some agents being in a position to re-cast the rules of the game. As it stands, we have here a book of very great interest to economists, to other social scientists not averse to abstract models, and to those designing autonomous agents.