One of the common conceptions in AI is the idea of game theory. We see that in the predominance of chess and other games in the literature as metrics of AI success. We see it in the names of machine learning concepts such as generative adversarial networks. We see it in academia in that a limited number of seats in teaching and administrative structure are available. We see it in perceptions of biological history. We see it in sports and finance and geopolitical endeavors.
Is Our Current Perception Skewed?
When mathematician John von Neumann and economist Oskar Morgenstern wrote Theory of Games and Economic Behavior, it was 1943. Nazi forces were devastating Europe and Japanese forces had taken Korea and much of China. The context of games was intended to be economic, but von Neumann was also involved in the technological revolution needed to oppose these forces in an adversarial game called WWII. The idea of games changed from play to preservation of civilization.
Yet civilization, although it may rely on defensive action to counter what may or may not be destructive offense, it is more defined by collaboration for mutual benefit (Finnish win-win-tilanne). Civilization is a game of preservation and the avoidance of loss, as John Donne intoned in his famous poem when he wrote, "If a clod be washed away by the sea, Europe is the less," implying that the loss of one person is a loss for all, based on the Golden Rule (Jesus). It is this higher thinking of the objective of the game that preserves civilization, not adversarialism.
It is often the unique, original ideas that forward civilization in the area of ideas. It is often the lives and families of those who, at the time the idea arises, are not in power that change the thought collective (Ludwik Fleck). These are a few examples of those that disturbed cultural norms (including scientific ones) and led to a forward step for us all.
- Saul of Tarsus
- Hypatia of Alexandria
- Isaac Newton
- Huang Yuanyong (黃遠庸)
- Mahatma Gandhi
- Martin Luther King
- Richard Stallman
Reconciliation of Game Theory with Concepts of Civilization
Nobel laureate John Forbes Nash Jr. contributed to the mathematical idea that in economic systems real world curvature in relations, the game is not a zero sum game. This is the basis for the question.
As gaming continues to penetrate further into mobile device and Internet usage and as AI games continue to gain degrees of angle in the pie chart of most national defense spending budgets, the definition of games that are not based on the WWII model of what a game must be gains importance.
How can designers of educational, entertainment centered, economic, financial, and military games transition their thinking toward cherishing alternative thought and re-prioritizing concepts like detente, playing for fun, employee collaboration, and educational objectives that are not zero sum GPA (grade point average) games based on #2 pencil multiple guess assessments?
Mathematics Leading to Game Design Concepts
First must come a mathematical idea of value, where the value between the individual and the body of all humans is tied. The mathematics may be theoretical (and probably should be at first), but must also be applied such that no one can achieve a high score in a game without developing an increase in the velocity of achievement in class of those with low achievement velocities. This requires a curved (non-linear) system, much like occurs in nature. It is a more realistic game than where all the adversaries are killed and the champion is now alone in the game space such that, had the game application not ended, no real value was gained — only loss.
In this context, we can return to the title question.
How can a collaboration game be defined mathematically?
What kinds of value functions incentivize collaboration and frustrate the actions of those that try to trounce everyone else to get ahead? How can we characterize the curvature of the required functions such that too many individual losses block the ultimate achievements of current leaders? If the Golden Rule, mutual appreciation, and collaboration are truly the ways civilization progresses forward, how can scoring be designed to reflect this reality? What qualities, mathematically, must the model have?
The objective is to define mathematically a very specific thing indicated in the title question. That some background is give is solely to encourage out of the box thinking in responding specifically and correctly to a narrow and well defined question.