Intro to Nash Equilibrium
in the context of cooperating for Peace by signalling in all honesty for wanting peace ☮️ →“We are here for something bigger than you and me. Let’s work together for a better world.”
Nash Equilibrium, named after John Nash, is defined as a decision making strategy in a non-cooperative game with 2 or more players where each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one’s own strategy. — https://en.wikipedia.org/wiki/Nash_equilibrium
The beautiful idea of “doing what is best for one self + group in order to yield the best outcome” has inspired cooperation and worthy pursuits of win-win games. I hope this trend continues to reach a wider audience especially at the intersection of science and religion.
“Science deals mainly with facts; religion deals mainly with values. The two are not rivals. They are complementary.” — Reverend Dr. Martin Luther King Jr. (1963). Strength to Love.
Let’s take a look at an example of the Peace and War dilemma which is on top of mind.
In this Peace War payoff matrix, if both A and B were to give Peace a chance that would give 2 points to A and 2 points to B or (2, 2) which is a good payoff for both A and B … yet the Nash equilibrium = (War, War) or (1, 1) with lower points. How is that? 🤔
It’s too risky for A to move for Peace. If B moves to War then A would lose everything and vice versa. In this scenario, every move to War would secure at least 1 point. Warmongers are incentivized with point/s (e.g., 3 or 1) regardless of the opponent’s move, hence the default is (War, War) or (1,1). As an exercise, try modifying the points in the payoff matrix with other incentives.
In general, to find the Nash Equilibrium you would evaluate the “dominant strategy” for each player and then identify the cell or (A, B, ..) in the payoff matrix that contains all the “dominant strategies”. The “dominant strategy” is defined as serving the self-interest of each player regardless of the other players’ possible moves.
In the real world, there are no winners in War. We are here for the long time horizon where Peace is the intelligent choice and must be earned. Winning with Peace requires being able to trust your opponent will want Peace too … if not now, maybe at some point in the future.
What if you can’t trust your opponent?
In the Ancient Greek language, there is a word called agape which is the highest form of love that transcends eros and philia. “Love is the only creative redemptive power in the universe” — Reverend Dr. Martin Luther King Jr.
Cooperation can happen with Peace (2, 2) or War (1, 1) … so why not choose Peace? Intentionally moving towards Peace for all have the greatest rewards. It is hard work. Peace may not happen in the first round. If at first you don’t succeed then try, try again in an honest and intentional way that may involve using strategies like tit-for-tat which has been proven to work well in A.I. computer simulations.
In the documentary Nice Guys Finish First, Richard Dawkins make a convincing argument for tit-for-tat and how evolution often favor cooperation over selfish behavior.
The main takeaway is by signalling a desire for Peace, that initiation can ultimately lead to cooperation for Peace. Basically, if there are some genuine signals sent to your opponent that you want to cooperate for Peace to enjoy the fruits of education, respect, inclusion, elevated conversations, engagement in civil rules of advanced societies … then there’s HOPE.
The truth is often simple and beautiful. That’s the beauty of math — You take something complicated from the real world and make it abstract into clean basic symbols that makes the world easier to understand in order to influence positive changes.
This was a brief introduction to Nash Equilibrium and an application to advocate for Peace. To learn more about Nash Equilibrium, check out additional examples with different goals and try out your own scenarios.
With ❤️ Math ☕️ Peace ☮️ Hope 🙏 and Understanding
