Business Economics Chapter 1

WHAT: What each player can do? STRATEGY SET

It is a set of strategies (choices or options) from which a player can choose.

Another example for you to practice: New York Times vs. Washington Post over Cover Story: Each one has two stories to choose to publish: either President Clinton's Scandal or Economic Crisis. We assume:

(1) NYT and Washington Post equally match with each other in the market, so they will equally share the readers when they publish the same story. (2) There are 100m readers for Scandal story and 40m readers for Crisis story. The payoff matrix is as follows.

Definition of a Dominant Strategy:

A dominant strategy for a player is a strategy that is always the best for the player, regardless of the other players' strategies.

Definition of a Dominated Strategy:

A dominated strategy for a player is a strategy that is always inferior to another strategy for the player, regardless of the other players' strategies.

Smart

They all know how to choose in order to maximize their self interests

If one confesses but the other one chooses not to confess, the confessing one will be awarded with immediate release and freedom,

but the other one will serve 10 years in jail for his refusal to confession.

Each one's strategy set has two elements:

either to confess or not to confess. This is {Confess, Not Confess}.

Finally our solution should be (Scandal, Crisis),

i.e., NYT chooses scandal and POST chooses crisis.

In the first case when Jerry confesses, Tom's best choice

is to confess (confess -5>not -10).

If neither confesses

then each will only serve 0.5 year in jail for the minor offense of possession of illegal substance.

Actually our second method of dominated strategy is more general than the first method of dominant strategy

whenever you can find the solution by using the first one, you can find the same solution by applying the second one.

WHO

who are the players in the game? PLAYERS

In summary, the method of elimination of dominated strategy goes as follows. Find a dominated strategy for a player, and then start with this player.

First eliminate this player's dominated strategy, in turn eliminate the other player's dominated strategy. We continue this process till we eliminate all dominated strategies of every player, whatever is left should be our solution.

Therefore, regardless of Jerry's choices, "confess" is always the best strategic choice for Tom

Following the above logic, you will find the same conclusion for Jerry. So eventually both Tom and Jerry will choose to confess. This analysis shows us the idea of a dominant strategy for a player.

This second method does not depend on which player to start with, as long as the player has a dominated strategy.

For example, you can try our prisoners' dilemma case by eliminating either Tom's dominated strategy or Jerry's. Eventually you will have the same solution.

Payoff: Payoff is how much you can get as a result of everyone's choice of strategy.

It shows all the possible outcomes of the game for everyone. Below we will use the PAYOFF MATRIX to show it.

Now it is turn for POST to eliminate its dominated strategy.

Now POST should eliminate Scandal, because Scandal is inferior to Crisis (35<40).

Our first method of dominant strategy is like a direct way, which straightforwardly identifies the optimal solution.

Our Second method of elimination of dominated strategy is like an indirect way, which finds the solution by getting rid of all bad choices.

In a word, rationality is common knowledge among all players.

Our new method of elimination of dominated strategy is based on this crucial assumption.

For Jerry, let us take out Jerry's payoff numbers

Since Jerry is the second player, we compare columns. The first column (-5, 0) is always better than the second column (-10, -0.5). So Confess (the first column) is the dominant strategy for Tom.

For example, let us take out Tom's payoff numbers

Since Tom is the first player, we compare rows. The first row (-5, 0) is always better than the second row (- 10, -0.5). So Confess (the first row) is the dominant strategy for Tom.

Obviously here they are playing a simultaneous game

Since they are in separate rooms, none of them knows the other one's strategic choice when he is making his own.

Solving the game by using the dominant strategy:

So if a player has a dominant strategy, he will choose it. If we can find for each player a dominant strategy, then we can solve the game by predicting that they all will choose their respective dominant strategies.

We see both NYT and Post have "scandal" as their respective dominant strategies.

So the game can be solved by using the dominant strategy method, and both will choose "scandal" in the end

The first player has no dominant strategy, but a dominated strategy, M. The second player has neither dominant strategy nor dominated strategy.

So we should start from the first player and eliminate M first.

common knowledge of rationality.

That is, everyone is not only rational, but also knows that the others are rational and understands that the others know he is rational.

Simultaneous Game: Players seem to move at the same moment.

The key is: when a player is choosing his strategy, he cannot observe what strategies are chosen by the other players

Sequential Game: Players seem to move in a sequence.

The key is: when some later player is choosing his strategy, he already observes what strategies are chosen by some previous players.

Our new method of elimination of dominated strategy is based on this crucial assumption.

Then in the eyes of both NYT and POST, Crisis should never be chosen. Instead it should be eliminated from the game.

Selfish

They care only their own payoff and nothing about the other players

In the second case of Jerry's refusal to confession

Tom's best choice is still to confess (confess 0> not - 0.5)

How to find a dominant strategy for a player?

Two steps: For the first (second) player, first pick all his payoffs from each cell, and remember it should be the first (second) number in each cell. Then you compare different rows (columns), to see which row (column) always gives you the biggest one. That one should be your choice.

Use my comparison method Comparing the first player NYT's two rows

Use my comparison method Comparing the first player NYT's two rows, we find the first row, scandal (50, 100), is always better than the second row, crisis (40, 20).

We put Tom as the first player and Jerry as the second player. There are two important rules:

We put Tom as the first player and Jerry as the second player. There are two important rules:

HOW: How the players should play the game? RULE OF GAME

We study two kinds of rules in this class: simultaneous game (before midterm) and sequential game (after midterm).

If both confess

then each will serve 5 years in jail for the major crime of drug trafficking.

Comparing the second player POST's two columns,

we find the first column, scandal (50, 100), is always better than the second column, crisis (40, 20).

The logic behind this method is similar to the famous saying of the celebrated detective Sherlock Holmes,

"Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth."

All players are RATIONAL

(selfish and smart)