A core premise of complexity theory is that global patterns in complex systems emerge out of the synchronization between the states of elements on the local level. Whereas the terms synchronization or desynchronization are generic to any type of system when we are dealing with elements that have agency, that is to say, some form of choice over their actions, we may refer to this as cooperation and competition. As agents now have some choice as to whether they synchronize their state with other agents locally – what we may call cooperation – or inversely, they may choose to adopt an asynchronous state with respect to other agents – what we will call competition. Cooperation and competition between agents do not occur randomly, they are the product of both local and global forces. The incentives for an agent to choose one of either are often built into the context of the situation they are engaged in. In order to illustrate this, we will look at what is called a zero-sum game.
In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant’s gain or loss is exactly balanced by the losses or gains of the other participants. If the total gains of the participants are added up and the total losses are subtracted, they will sum to zero. Cutting a cake, where taking a larger piece reduces the amount of cake available for others, is an example of this. A zero-sum game is also called a strictly competitive game, as the pie cannot be enlarged by good negotiation and cooperation. There is no incentive for cooperation between agents in these situations but in fact a strong attractor state toward competition. War is another example of a zero sum situation. In these games, what the other loses you gain, thus keeping track and comparing your state to that of your opponent makes sense. Zero-sum games are linear and additive. The whole system is simply a summation of its constituent elements. Thus, they are essentially simple or non-complex.
Mix Strategy Games
Complexity arises when we have a dynamic between competition and cooperation. Situations where participants are interdependent, being able to all gain or suffer together, are referred to as non-zero-sum. For example, all trade is by definition positive sum, because when two parties agree to an exchange, each party must consider the goods it is receiving to be more valuable than the goods it is delivering. This type of positive-sum game is a strong driver towards cooperation, as the pie gets bigger and everyone gets higher payoffs by simply interacting. There are many scenarios like this where the cost of coordination is relatively low and the payoff is relatively high. Everyone driving on the correct side of the road is an example of this. There is little incentive not to do so and very high incentives to coordinate, thus making cooperation a very strong attractor state. However, not all scenarios are as simple as this. Non-zero-sum games often involve an interplay between competition and cooperation. As an example of this, we might think about a game of doubles tennis where you have a zero-sum game of competition with your opposition, but a positive sum game with your team member. Problems in the real world are typically non-zero-sum, where there is no single optimal strategy that is preferable to all others, nor is there a predictable outcome. Players engaged in a non-zero sum conflict have both some complementary interests and some interests that are opposed.
Variables To Cooperation
There are a number of variables that can be altered to adjust whether a game will on balance favor cooperation or competition between agents. Ongoing interactions between agents over a prolonged period of time, as well as dense interactions, allows for trust building. Within many traditional societies, there is some required resource placed at the heart of the community, such as a water well, or mill in order to promote interaction. This interaction between agents helps to develop reputation systems and identification so that people can cooperate with those they know to be trustworthy, owing to their cooperation in the past. Bringing people together, giving them information and channels for communication are the basic ingredients for social cooperation and self-organization. Research on lobster fishing off of Maine New England showed that small communities on islands are better able to cooperate in order to maintain their commons than those on the mainland.
Another key factor governing cooperation and competition within complex adaptive systems is externalities. To illustrate this, we might think about a classical example called the tragedy of the commons. Garrett Hardin in 1968 wrote a paper in Science Magazine in which he imagined a grazing pasture that was open to all, and he posited that if this was the case everyone would bring their animals on to graze the pasture more and more which would end in the over usage of the commons and its ultimate collapse. Any individual will get an immediate gain from overgrazing the pasture but the long term cost of this would be spread out over the whole population of people using the resource. And thus, the cost would be externalized from the simple cost-benefit equation that each agent is making, meaning the full cost is not subtracted from the benefits to the individual, and thus the action is in their individual interests even if it is to everyone’s detriment. The choice by an agent to overgraze the pasture is then considered a rational action, by rational we simply mean that the action is consistent with the logic of the agent’s self-preservation.
The Social Dilemma
The tragedy of the commons is an instance of the more generic social dilemma, which is a dynamic where individual rational choice leads to a situation where everyone is worse off. We might say individual rationality leads to collective irrationality. The social dilemma is behind many economic and social challenges from overfishing to traffic jams to air pollution and voting. The basic mechanics driving this system are feedback loops and externalities. As soon as we have interactions between agents within a system, what one element does affects another. But the question is, does this affect then return to the agent that created it? If it does, then the agent must account for it. I might be too lazy to carry my coat with me when I go out but if I know that this action will have an immediate negative effect on me in the very short term future when it starts raining, then I will take account of it, factoring it into the equation that governs my current actions. However, if one element does affect another, without that effect then returning to its source, then we have externalities. We call it an externality because the effect that one agent is having on its environment becomes external to the equation under which the agent is operating. If as in our first example every action of an agent feeds back to its source, then the system will be self-regulating with every cost and benefit being paid for by the agent that created it, and thus everything can be regulated by the agents locally in a distributed fashion. But with negative externalities, the cost and benefits of an agent’s actions become decoupled from the local regulatory mechanisms of the agents and there becomes a need for global governance and top-down regulation.
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