Randomness And Game Theory

The theoretical supposition is that randomness and non-zero-game theory can coexist

Don’t be put off by the following: Game theory is the study of mathematical models of strategic interaction between rational decision-makers. It applies to a wide range of behavioral relations — the science of logical decision making in humans, animals and computers.

I’m not going to offer a freshman course in game theory here. Rather, as one pragmatist to another I’m going to note how game theory coexists with randomness, an inevitable reality of everything from the universe to our individual lives. To do this, I have to note that there are two versions of theory. One is the common usage of the term, meaning suppositions regarding what is unknown, not well understood or open to varying degrees of randomness. The other is the scientific version in which hypothesis is the suppositional part and theory is the resulting facts. We’re going with the former.

Randomness, of course, is self-defining. Even though we know it occurs all the time in various ways, we can’t prevent it from happening. We can anticipate it and plan for it in terms of responses, but ultimately we have limited control over how and when it occurs. So process and outcome may or may not be reliably predictable. As I’ve noted previously, odds of a million-to-one against something happening not only don’t mean it won’t happen, but also don’t mean it couldn’t happen more than once.

Game theory can incorporate or disregard randomness. The primary use of game theory is to describe and model how human populations behave. However, there is disagreement on the assumptions made by game theorists because these are often violated when applied to real-world situations. Which is to say, game theorists usually assume players act rationally even though human behavior often deviates from this. There are many varieties of game theory, but the two most commonly recognized even by non-theorists are zero-sum and non-zero-sum games.

The basic premises of these two versions is simple. In zero-sum games choices by players can neither increase nor decrease the available resources, and the total benefit to all players in the game, for every combination of strategies, always adds to zero — a player benefits only at the equal expense of others. In non-zero-sum games the outcome has net results greater or less than zero — a gain by one player does not necessarily correspond with a loss by another.

For a pragmatist, the message is obvious. The theoretical supposition is that randomness and non-zero-game theory can coexist. That is, outcomes are most likely to result in combinations of winning/losing existing for all players to varying degrees that also vary with the randomness of circumstances and details. One of the most important lessons of this is that cooperation is often superior to adversarial assumptions about winning or losing.

Winning versus losing is not random to those who believe life is all about zero-sum games. In order to be a winner, everyone else has to lose. The result is behavior and ethical choices focused solely on winning and not losing. Inevitable randomness is not accepted, forcing the zero-sum mentality to do whatever is believed necessary to ensure winning irregardless of what that might mean to others. Rules, process, honesty are ignored, this being perceived as necessary to avoid losing.

All of which is to say that randomness and game theory are not esoteric issues. Our modern globalized world is really a non-zero-sum game. It has to be because cooperation and partnership are essential for dealing with many important issues. Citizens who believe their nation can only win if others lose are utterly wrong. When we work together — locally to globally — for the greater good, all win. The ideologically driven won’t understand this, the pragmatic will.