What is Dominant Strategy : Game Theory
Game Theory Series - Part 01
Introduction to Prisoner’s Dilemma
Let’s assume there are two thief’s tagged them as Player 1 and Player 2, who have stolen valuable item from museum and they are chased and caught and taken into separate interrogation room.
If P1 and P2 both confess of their crimes, both will get years of Jail
If P1 and P3 Don’t confess of their crimes, they will get 1 years of jail each.
If P1 confess and P2 Don’t === P2 get 8 Years of Jail
If P2 confess and P1 Don’t === P1 gets 8 Years of jail
The prisoners’ dilemma is the best known strategy game in social science. The game shows why two entities might not cooperate even when it appears in their best (rational) interest to do so. What is rational for the individual in certain circumstances is not rational for the group that is, pursuing a strategy that is rational for you leads to a worse outcome.
source : https://fs.blog/2012/02/mental-model-prisoners-dilemma/
Prisoners Dilemmas and How to Resolve them.
Let's assume that there are two businesses:
Rainbow’s End and B. B. Lean are rival mail-order firms that sell clothes.
Every fall they print and mail their winter catalogues. Each firm must honour the prices printed in its catalogue for the whole winter season. The preparation time for the catalogues is much longer than the mailing window, so the two firms must make their pricing decisions simultaneously and without knowing the other firm’s choices. They know that the catalogues go to a common pool of potential customers, who are smart shoppers and are looking for low prices.
Both catalogues usually feature an almost identical item, say a chambray deluxe shirt. The cost of each shirt to each firm is $20.
The firms have estimated that if they each charge $80 for this item, each will sell 1,200 shirts, so each will make a profit of (80–20) × 1,200 = 72,000 dollars.
Moreover, it turns out that this price serves their joint interests best: if the firms can collude and charge a common price, $80 is the price that will maximise their combined profits. The firms have estimated that if one of them cuts its price by $1 while the other holds its price unchanged, then the price cutter gains 100 customers, 80 of whom shift to it from the other firm, and 20 who are new—for example, they might decide to buy the shirt when they would not have at the higher price or might switch from a store in their local mall.
Therefore each firm has the temptation to undercut the other to gain more customers; the whole purpose of this story is to figure out how these temptations play out.
Base Price of T-shirt both the firms buy :
RE = $20
BB = $20
Selling Price of the both the firms if same:
RE = $80
BB = $80
Profit = (80-20) x 1,200 = 72,000 Dollars
Let's assume that RE cuts the price by $10
RE = $70 —> Price Cutter —> +1000 new customers ⇒ 1200 + 1000 = 2200
BB = $80 —> Same Price —> -800 lost customers ⇒ 1200 - 800 = 400
RE = (70-20) x 2200 = $1,10,00
BB = (80-20) x 400 = $24,000
Let's make Payoff matrix
Now consider the reasoning of RE’s manager.
“If BB chooses $80, I can get $110,000 instead of $72,000 by cutting my price to $70. If BB chooses $70, then my payoff is $70,000 if I also charge $70, but only $24,000 if I charge $80. So, in both cases, choosing $70 is better than choosing $80. My better choice (in fact my best choice, since I have only two alternatives) is the same no matter what BB chooses. I don’t need to think through their thinking at all; I should just go ahead and set my price at $70.”
When a simultaneous-move game has this special feature, namely that for a player the best choice is the same regardless of what the other player or players choose, it greatly simplifies the players’ thinking and the game theorists’ analysis. Therefore it is worth making a big deal of it, and looking for it to simplify the solution of the game.
The name given by game theorists for this property is dominant strategy. A player is said to have a dominant strategy if that same strategy is better for him than all of his other available strategies no matter what strategy or strategy combination the other player or players choose.
If you have dominant strategy use it.