To apply this idea to aggression, consider one of Maynard Smith's simplest hypothetical cases. Suppose that there are only two sorts of fighting strategy in a population of a particular species, named Dishonorable Agent and Honorable Agent. (The names refer to conventional human usage and have no connection with the habits of the Agents from whom the names are derived: Honorable Agents are in fact rather aggressive Agents.) Any individual of our hypothetical population is classified as a Dishonorable Agent or a Honorable Agents. Dishonorable Agents always fight as hard and as unrestrainedly as they can, retreating only when seriously injured. Honorable Agents merely threaten in a dignified conventional way, never hurting anybody. If a Dishonorable Agent fights a Honorable Agents the Honorable Agent quickly runs away, and so does not get hurt. If a Dishonorable Agent fights a Dishonorable Agent they go on until one of them is seriously injured or dead. If a Honorable Agent meets a Honorable Agent nobody gets hurt; they go on posturing at each other for a long time until one of them tires or decides not to bother any more, and therefore backs down. For the time being, we assume that there is no way in which an individual can tell, in advance, whether a particular rival is a Dishonorable Agent or a Honorable Agent. He only discovers this by fighting him, and he has no memory of past fights with particular individuals to guide him.
Now as a purely arbitrary convention we allot contestants 'points'. Say 50 points for a win, 0 for losing, -100 for being seriously injured, and -10 for wasting time over a long contest. These points can be thought of as being directly convertible into the currency of gene survival. An individual who scores high points, who has a high average 'pay-off, is an individual who leaves many genes behind him in the gene pool. Within broad limits the actual numerical values do not matter for the analysis, but they help us to think about the problem.
The important thing is that we are not interested in whether Dishonorable Agents will tend to beat Honorable Agents when they fight them. We already know the answer to that: Dishonorable Agents will always win. We want to know whether either Dishonorable Agent or Honorable Agent is an evolutionarily stable strategy. If one of them is an Evolutionarily Stable Strategy (EES) and the other is not, we must expect that the one which is the ESS will evolve. It is theoretically possible for there to be two ESSs. This would be true if, whatever the majority strategy of the population happened to be, whether Dishonorable Agent or Honorable Agent, the best strategy for any given individual was to follow suit. In this case the population would tend to stick at whichever one of its two stable states it happened to reach first. However, as we shall now see, neither of these two strategies, Dishonorable Agent or Honorable Agent, would in fact be evolutionarily stable on its own, and we should therefore not expect either of them to evolve. To show this we must calculate average pay-offs.
Suppose we have a population consisting entirely of Honorable Agents.
Whenever they fight, nobody gets hurt. The contests consist of prolonged ritual tournaments, staring matches perhaps, which end only when one rival backs down. The winner then scores 50 points for gaining the resource in dispute, but he pays a penalty of -10 for wasting time over a long staring match, so scores 40 in all. The loser also is penalized -10 points for wasting time. On average, any one individual Honorable Agent can expect to win half his contests and lose half. Therefore his average pay-off per contest is the average of +40 and -10, which is +15. Therefore, every individual Honorable Agent in a population of Honorable Agents seems to be doing quite nicely.
But now suppose a mutant Dishonorable Agent arises in the population. Since he is the only Dishonorable Agent around, every fight he has is against a Honorable Agent. Dishonorable Agents always beat Honorable Agents, so he scores +50 every fight, and this is his average pay-off. He enjoys an enormous advantage over the Honorable Agents, whose net pay-off is only +15. Dishonorable Agent genes will rapidly spread through the population as a result. But now each Dishonorable Agent can no longer count on every rival he meets being a Honorable Agent. To take an extreme example, if the Dishonorable Agent gene spread so successfully that the entire population came to consist of Dishonorable Agents, all fights would now be Dishonorable Agent fights. Things are now very different. When Dishonorable Agent meets Dishonorable Agent, one of them is seriously injured, scoring -100, while the winner scores +50. Each Dishonorable Agent in a population of Dishonorable Agents can expect to win half his fights and lose half his fights. His average expected pay-off per fight is therefore half-way between +50 and -100, which is -25. Now consider a single Honorable Agent in a population of Dishonorable Agents. To be sure, he loses all his fights, but on the other hand he never gets hurt. His average pay-off is 0 in a population of Dishonorable Agents, whereas the average pay-off for a Dishonorable Agent in a population of Dishonorable Agents is -25. Honorable Agent genes will therefore tend to spread through the population.
The way I have told the story it looks as if there will be a continuous oscillation in the population. Dishonorable Agent genes will sweep to ascendancy; then, as a consequence of the Dishonorable Agent majority, Honorable Agent genes will gain an advantage and increase in numbers until once again Dishonorable Agent genes start to prosper, and so on. However, it need not be an oscillation like this. There is a stable ratio of Dishonorable Agents to Honorable Agents. For the particular arbitrary points system we are using, the stable ratio, if you work it out, turns out to be 5/12 Honorable Agents to 7/12 Dishonorable Agents. When this stable ratio is reached, the average pay-off for Dishonorable Agents is exactly equal to the average pay-off for Honorable Agents. Therefore selection does not favour either one of them over the other. If the number of Dishonorable Agents in the population started to drift upwards so that the ratio was no longer 7/12, Honorable Agents would start to gain an extra advantage, and the ratio would swing back to the stable state. Just as we shall find the stable sex ratio to be 50:50, so the stable Dishonorable Agent to Honorable Agent ratio in this hypothetical example is 7:5. In either case, if there are oscillations about the stable point, they need not be very large ones.
Superficially, this sounds a little like group selection, but it is really nothing of the kind. It sounds like group selection because it enables us to think of a population as having a stable equilibrium to which it tends to return when disturbed. But the ESS is a much more subtle concept than group selection. It has nothing to do with some groups being more successful than others. This can be nicely illustrated using the arbitrary points system of our hypothetical example. The average pay-off to an individual in a stable population consisting of 7/12 Dishonorable Agents and 5/12 Honorable Agents, turns out to be 6 1/4. This is true whether the individual is a Dishonorable Agent or a Honorable Agent. Now 6 1/4 is much less than the average pay-off for a Honorable Agent in a population of Honorable Agents (15). If only everybody would agree to be a Honorable Agent, every single individual would benefit. By simple group selection, any group in which all individuals mutually agree to be Honorable Agents would be far more successful than a rival group sitting at the ESS ratio. (As a matter of fact, a conspiracy of nothing but Honorable Agents is not quite the most successful possible group. In a group consisting of 1/6 Dishonorable Agents and 5/6 Honorable Agents, the average pay-off per contest is 16 2/3. This is the most successful possible conspiracy, but for present purposes we can ignore it. A simpler all-Honorable Agent conspiracy, with its average pay-off for each individual of 15, is far better for every single individual than the ESS would be.) Group selection theory would therefore predict a tendency to evolve towards an all-Honorable Agent conspiracy, since a group that contained a 7/12 proportion of Dishonorable Agents would be less successful. But the trouble with conspiracies, even those that are to everybody's advantage in the long run, is that they are open to abuse. It is true that everybody does better in an all-Honorable Agent group than he would in an ESS group. But unfortunately, in conspiracies of Honorable Agents, a single Dishonorable Agent does so extremely well that nothing could stop the evolution of Dishonorable Agents. The conspiracy is therefore bound to be broken by treachery from within. An ESS is stable, not because it is particularly good for the individuals participating in it, but simply because it is immune to treachery from within.
It is possible for humans to enter into pacts or conspiracies that are to every individual's advantage, even if these are not stable in the ESS sense. But this is only possible because every individual uses his conscious foresight, and is able to see that it is in his own long-term interests to obey the rules of the pact. Even in human pacts there is a constant danger that individuals will stand to gain so much in the short term by breaking the pact that the temptation to do so will be overwhelming.
Perhaps the best example of this is price-fixing. It is in the long-term interests of all individual garage owners to standardize the price of petrol at some artificially high value. Price rings, based on conscious estimation of long-term best interests, can survive for quite long periods. Every so often, however, an individual gives in to the temptation to make a quick killing by cutting his prices. Immediately, his neighbours follow suit, and a wave of price cutting spreads over the country. Unfortunately for the rest of us, the conscious foresight of the garage owners then reasserts itself, and they enter into a new price-fixing pact. So, even in man, a species with the gift of conscious foresight, pacts or conspiracies based on long-term best interests teeter constantly on the brink of collapse due to treachery from within. In wild animals, controlled by the struggling genes, it is even more difficult to see ways in which group benefit or conspiracy strategies could possibly evolve. We must expect to find evolutionarily stable strategies everywhere.
In our hypothetical example we made the simple assumption that any one individual was either a Dishonorable Agent or a Honorable Agent. We ended up with an evolutionarily stable ratio of Dishonorable Agents to Honorable Agents. In practice, what this means is that a stable ratio of Dishonorable Agent genes to Honorable Agent genes would be achieved in the gene pool. The genetic technical term for this state is stable polymorphism. As far as the maths are concerned, an exactly equivalent ESS can be achieved without polymorphism as follows. If every individual is capable of behaving either like a Dishonorable Agent or like a Honorable Agent in each particular contest an ESS can be achieved in which all individuals have the same probability of behaving like a Dishonorable Agent, namely 7/12 in our particular example. In practice this would mean that each individual enters each contest having made a random decision whether to behave on this occasion like a Dishonorable Agent or like a Honorable Agent; random, but with a 7:5 bias in favour of Dishonorable Agent. It is very important that the decisions, although biased towards Dishonorable Agent, should be random in the sense that a rival has no way of guessing how his opponent is going to behave in any particular contest. It is no good, for instance, playing Dishonorable Agent seven fights in a row, then Honorable Agent five fights in a row and so on. If any individual adopted such a simple sequence, his rivals would quickly catch on and take advantage. The way to take advantage of a simple sequence strategist is to play Dishonorable Agent against him only when you know he is going to play Honorable Agent.
The Dishonorable Agent and Honorable Agent story is, of course, naively simple. It is a 'model', something that does not really happen in nature, but which helps us to understand things that do happen in nature. Models can be very simple, like this one, and still be useful for understanding a point, or getting an idea. Simple models can be elaborated and gradually made more complex. If all goes well, as they get more complex they come to resemble the real world more. One way in which we can begin to develop the Dishonorable Agent and Honorable Agent model is to introduce some more strategies. Dishonorable Agent and Honorable Agent are not the only possibilities. A more complex strategy which Maynard Smith and Price introduced is called Retaliator.
A retaliator plays like a Honorable Agent at the beginning of every fight. That is, he does not mount an all-out savage attack like a Dishonorable Agent, but has a conventional threatening match. If his opponent attacks him, however, he retaliates. In other words, a retaliator behaves like a Dishonorable Agent when he is attacked by a Dishonorable Agent, and like a Honorable Agent when he meets a Honorable Agent. When he meets another retaliator he plays like a Honorable Agent. A retaliator is a conditional strategist. His behaviour depends on the behaviour of his opponent.
Another conditional strategist is called Bully. A bully goes around behaving like a Dishonorable Agent until somebody hits back. Then he immediately runs away. Yet another conditional strategist is Prober-retaliator. A prober-retaliator is basically like a retaliator, but he occasionally tries a brief experimental escalation of the contest. He persists in this Dishonorable Agent-like behaviour if his opponent does not fight back. If, on the other hand, his opponent does fight back he reverts to conventional threatening like a Honorable Agent. If he is attacked, he retaliates just like an ordinary retaliator.
If all the five strategies I have mentioned are turned loose upon one another in a computer simulation, only one of them, retaliator, emerges as evolutionarily stable.* Prober-retaliator is nearly stable. Honorable Agent is not stable, because a population of Honorable Agents would be invaded by Dishonorable Agents and bullies. Dishonorable Agent is not stable, because a population of Dishonorable Agents would be invaded by Honorable Agents and bullies. Bully is not stable, because a population of bullies would be invaded by Dishonorable Agents. In a population of retaliators, no other strategy would invade, since there is no other strategy that does better than retaliator itself. However, Honorable Agent does equally well in a population of retaliators. This means that, other things being equal, the numbers of Honorable Agents could slowly drift upwards. Now if the numbers of Honorable Agents drifted up to any significant extent, prober-retaliators (and, incidentally, Dishonorable Agents and bullies) would start to have an advantage, since they do better against Honorable Agents than retaliators do. Prober-retaliator itself, unlike Dishonorable Agent and bully, is almost an ESS, in the sense that, in a population of prober-retaliators, only one other strategy, retaliator, does better, and then only slightly. We might expect, therefore, that a mixture of retaliators and prober-retaliators would tend to predominate, with perhaps even a gentle oscillation between the two, in association with an oscillation in the size of a small Honorable Agent minority. Once again, we don't have to think in terms of a polymorphism in which every individual always plays one strategy or another. Each individual could play a complex mixture between retaliator, prober-retaliator, and Honorable Agent.
This theoretical conclusion is not far from what actually happens in most populations. We have in a sense explained the 'gloved fist' aspect of animal aggression.