Vedic Astrology

A game in a game theory is any interaction between n multiple people in which each player’s playoff is affected by the decision of other.

The principles of Game Theory:-

1. A game needs to include multiple players (>=2)
2. Players need to interact with each other
3. There needs to be a reward
4. Players act rationally
5. Players act according to their personal self interest

There are two terms to distinguish the kind of strategies followed by the players:

Dominant Strategy

A Dominant Strategy is a strategy that is the best choice for a player, regardless of the strategies chosen by other players. If a player has a dominant strategy, they will always prefer it, as it yields a higher payoff than any other strategy available.

Nash Equilibrium

A Nash Equilibrium is a concept within game theory where no player can benefit by unilaterally changing their strategy, given the strategies of the other players. In other words, each player’s strategy is optimal, taking into account the strategies of others. This means that if all players are at a Nash Equilibrium, they have no incentive to deviate from their chosen strategy because it will not result in a better outcome for them.

Nash Equilibrium and Dominant Strategy in the Prisoner’s Dilemma

The Prisoner’s Dilemma is a classic example in game theory that illustrates the concepts of Nash Equilibrium and Dominant Strategy.

Scenario

Two criminals are arrested and interrogated separately. They cannot communicate with each other. Each prisoner has two options:

• Cooperate with the other prisoner by remaining silent.
• Betray the other prisoner by confessing.

Payoff Matrix

Game Theory Matrix	Prisoner B: Cooperate	Prisoner B: Betray
Prisoner A: Cooperate	(1 year, 1 year)	(3 years, 0 years)
Prisoner A: Betray	(0 years, 3 years)	(2 years, 2 years)

• If both prisoners cooperate, they each get 1 year in prison.
• If one cooperates and the other betrays, the betrayer goes free and the cooperator gets 3 years.
• If both betray, they each get 2 years.

Dominant Strategy

A Dominant Strategy is the best strategy for a player, regardless of what the other player does. In the Prisoner’s Dilemma:

• Betraying is the dominant strategy for both prisoners.
• If Prisoner A thinks Prisoner B will cooperate, betraying gives A 0 years (better than 1 year).
• If Prisoner A thinks Prisoner B will betray, betraying gives A 2 years (better than 3 years).

Since betraying is better in both scenarios, it is the dominant strategy for both prisoners.

Nash Equilibrium

A Nash Equilibrium occurs when no player can benefit by changing their strategy, given the other player’s strategy. In the Prisoner’s Dilemma:

• Both prisoners choosing to betray each other is the Nash Equilibrium.
• Given that Prisoner B betrays, Prisoner A cannot do better than betraying (2 years instead of 3 years).
• Given that Prisoner A betrays, Prisoner B cannot do better than betraying (2 years instead of 3 years).

Therefore, both prisoners betraying is the Nash Equilibrium because neither can improve their outcome by changing their strategy unilaterally.

Summary

• Dominant Strategy: Betraying is the best strategy for each prisoner, no matter what the other does.
• Nash Equilibrium: Both prisoners betraying is a stable state where neither has an incentive to deviate.

The Prisoner’s Dilemma highlights the conflict between individual rationality (betraying) and collective rationality (cooperating), showing how players acting in their own self-interest can lead to suboptimal outcomes for both.

Check: Game Theory: The Pinnacle of Decision Making (YouTube)