Game Theoretic Explanation of Religion

Objective: Understand the motives of religious principles using game theoretic explanation.

Religion is defined as a set of cultural practices, beliefs and principles observed among human societies that presumes the idea of God and afterlife.

Religion has been explained using two principles

1. Truthfulness of God’s Existence: God exists. Hence religion.
2. Utility of religion: Religion and God are useful (evolutionary and social cohesion/cooperation) ideas and hence religion emerged and survived.

In this article, I will try to use a mathematical concept mostly used by economists known as Game Theory to explain the survival and utility of religion from the perspective of social cohesion, i.e. religion creates social cooperation and hence it is useful. So religion survived.

Conjecture:  Religion (Eastern or Judeo-Christian) creates a set of rules (different ones but still) so that members of a society cooperate rather than cheat.

What is a Game?

Game is a situation of strategic interaction among players having their own strategies to achieve their own goals. An example of cooperation vs. cheat game is well known among economists as prisoner’s dilemma as a non-repeated game. The game can be represented in following form (this is a slightly different version of the original game).

Table 1: Prisoner’s Dilemma: Cooperate or Cheat

		Player B
		Cooperate	Cheat
Player A	Cooperate	(4,4)	(0,6)
	Cheat	(6,0)	(1,1)

If this game is played only once, each player will try to cheat because cheating for a player is better for all possible strategies by its opponents. The solution (cheat,cheat) is called Nash equilibrium; so called after the Nobel Laureate Professor John Nash. Note that Nash equilibrium is not Pareto efficient. In other words, there are other possible outcomes where both players would benefit. In this game, the players can cooperate and settle on the strategy combination (cooperate,cooperate) which gives them the highest possible total payoff of 8. But, in the hope of scooping 6, each player will end up cheating and fall into the Nash equilibrium trap where there total payoff is just 2. In this game cooperation seems to be the need of the time. But they will keep on cheating due to

1. lack of enough communication between the players before the game starts
2. lack of trust among the players regarding the opponent’s actual strategy.

 

A Repeated Game

Now suppose the game is played repeatedly n (finite number) times. What strategies will the players end up with in the nth game? Knowing that the nth game is the final game, they will most probably try to cheat for the same two reasons outlined above. Once each player realize that cheating is the best possible option for them separately in the nth game, they will cheat in the (n-1)th game as well. So the players will again fall into the trap of Nash equilibrium which is Pareto inefficient.

If life is a finitely repeated game, everyone is likely to cheat rather than cooperate and hence the chaos of conflicts, cut-throat competition and strategic cheating.

 

Ensuring cooperation

How can we change the rule of the game or the payoff so that the players automatically settle on Pareto efficient combination of (cooperation,cooperation) even without trust and enough communication before the game (without satisfying the above two conditions). Religion proposes two solutions

1. Judeo-Christian game: Ensuring that the nth game (at heaven or hell) is played fairly (tit-for-tat). If you cheat/cooperate now, you will be paid back later proportionately (fair game). If the nth game is ensured to end in (cooperation,cooperation), there is no incentive for players to cheat to begin with in the very first game.
2. Eastern religion’s game: The game will be repeated infinitely many times (reincarnation). When players know that there are infinitely many games to be played after the first game, players will know that the tit-for-tat will be applied to them. If they cheat, they will be cheated in the next life. If they cooperate, they will be cooperated accordingly in the next life. Learning this and seeing the higher pay offs resulting from (cooperation, cooperation), the players will likely cooperate indefinitely starting from the first game.

Both religious principles have tried to enforce cooperation. How successful they became can be seen in history books.

Finally, I propose a change in payoffs of the game so that there is no need of religious game to enforce cooperation among the players.

Table 2: Cooperate without the fear of hell or reincarnation

		Player B
		Cooperate	Cheat
Player A	Cooperate	(4,4)	(2,3)
	Cheat	(3,2)	(1,1)

In this game, (cooperate,cooperate) is the NASH equilibrium as well as Pareto efficient. Players will automatically cooperate as it pays higher irrespective of what other players will choose to do. Maybe evolution set the payoffs so that Nash equilibrium coincides with Pareto equilibrium, i.e. cooperation is the best possible option for players in the game of survival and reproduction irrespective of the other players’ strategies.