28 March, 2016

How the twain shall meet -- III: Dharma and Game Theory

Continuing in my series of posts about how I see synergy between Eastern and Western thought, I would like to connect one of the most beautiful mathematics of the 20th century with some of the foundations of Indian thought.

As mentioned in previous posts, if there is one concept that can encapsulate the cultural paradigm of India and parts of China, East and South-East Asia, it is the concept of "Dharma". The term is used in so many different contexts, giving it several different translations like "righteousness", "religion", "duty", "ethics" etc. all of which fail to capture its essence.

Dharma represents a state of "sustainability" or "invariance". (Here is a paper describing dharma as sustainability or a state of "equilibrium" and here is yet another paper defining Dharma as sustainability). As described by Robert Lingat in his book "The Classical Law of India" Dharma is defined as "what is firm and durable, what sustains and maintains.."

In current day approaches to systems theory, such definitions point to concepts like invariance, optimality, equilibrium and stability. The concept of Dharma is applied to human (and animal) societies, but it is derived from an even more fundamental concept called Rta, which is the postulated fundamental element of invariance across all matter and physical phenomena.

In the Western world, an important milestone in the 20th century is the emergence of the mathematics of rational choice and correlated rational choice. This pertains to modeling the dynamics of systems of rational, autonomous agents (like humans or animals) that operating in a situated environment. This field of study is popularly called Game Theory.

While Game Theory had its beginnings in the analysis of parlour games, it quickly grew in scope to encompass the analysis of any form of situated, correlated rational choice across disparate autonomous agents. Some key results like the "Nash equilibrium" are now the stuff of popular artistic imagination.

Game Theory quickly expanded beyond questions concerning situated rational choice, with the introduction of "iterated" and "evolutionary" games. In these games, agents interact with one another over several iterations, giving them the luxury of "memory". Hence, if one player betrayed another player in one iteration, future actions by the other player would likely change in order to account for the betrayal. A strategy for an iterated game needs to keep this in mind before committing an action.

Evolutionary games bring in yet another dimension by introducing the notion of "generations". In evolutionary games, over time, players may change their beliefs about other players or the system in general, and in turn, their strategies. Evolutionary games are characteristic of not just human societies, but of life in general. The dynamics of genetic coding and crossover to create offspring, are often driven by evolutionary prospects.

Hence, animals that live in cold climates tend to evolve furs and other mechanisms to protect from the cold, while animals living in topical climates tend to evolve higher sensitivity towards predators and other creatures.

In evolutionary games, occasionally there are strategic configurations that are not only very robust in their environments, but are also robust against other contending strategies. Such strategic configurations have no incentive to evolve further, as from a strategic standpoint, they are infallible.

Such configurations are called "Evolutionarily Stable Strategies" or ESS for short. They represent strategic configurations that cannot be easily "invaded" and dominated by a new (also called "mutant") incumbent strategy that was initially rare.

For instance, a business idea that is an ESS tends to prevail not only across economic or social upheavals, but also prevails when confronted with other, contending business ideas that may be more powerful. The ESS is also called the evolutionary "best response" function to the specifics of the game. In other words, regardless of how others evolve, an ESS provides the best strategic response to the challenges posed by others' choices. And when others adopt ESS, the ESS is still the best strategic prospect.

The above description of an ESS is precisely the notion of Dharma! A dharmic act is one that is robust and that which prevails across upheavals. Its significance does not get eroded when confronted with other, more powerful thoughts. And when faced with uncertainty, following the path of Dharma gives one the best strategic prospects.

While the concept of Dharma and that of ESS, is profound, there is no simple way by which we can arrive at an ESS, given any system. An ESS may be discovered after centuries of evolution, and what appears like an ESS, may give way when some fundamentals of the underlying system changes.

A well known book called "The Evolution of Cooperation" by Robert Axelrod shows how a strategy called "Tit for Tat" (or reflecting cooperation for cooperation and non-cooperation for non-cooperation) is an ESS for an evolutionary version of the Iterated Prisoners' Dilemma (IPD) game. However, later results have shown that when the game is played with imperfect information (which is a more realistic possibility), "Tit for Tat" collapses from its evolutionarily stable position.

The quest for Dharma hence is potentially unbounded in terms of depth and sophistication. The need to evolve better and more robust strategies is a never ending quest. However, as part of the quest, we may encounter ideas and worldviews that are stable enough to cater to several generations.

This has been the story of dharmic cultures over time. Dharmic cultures have explored several models and directions in their quest for social dharma. These included organizing the society (the varna system), organizing a person's life (Brahmacharya to Sanyasa), organizing spiritual quests (the marga system), etc. Many of the advocated practices were "local minima" or stable strategies for those times, but which collapsed with changing conditions.

The above kind of thinking and quest was already about 2500 years old (and in a state of disarray) at the time of the Buddha (who rejected several of the memes around that time to forge a new direction in the quest for Dharma). And such thinking still continues to persist and thrive in about a sixth of the world's population.

Modern mathematics like Game Theory, Synergetics, Optimization and Prospect Theory are some of the best possible tools for the Western mind to understand and interpret Eastern thought..