This week’s (i.e., week 6)’s lecture aims to continue on with what was previous mentioned in class about game theory.

We ended last week’s class by playing a sort of game that has to do with game theory, but we didn’t actually go into the theory itself. This lecture introduces some new terms as they pertain to game theory.

5.1 Prisoner’s Dilemma

The Prisoner’s Dilemma is a situation in which two individuals, who are arrested for a crime and cannot communicate with each other, must decide whether to cooperate with each other or betray each other to the authorities.

Here’s the catch: If both prisoners stay silent (cooperate), they both get a relatively mild sentence. However, if one prisoner betrays the other (doesn’t cooperate) while the other stays silent, the betrayer goes free, and the one who stayed silent gets a harsh sentence. If both prisoners betray each other, they both receive moderate sentences.

The dilemma is that each prisoner must decide whether to trust the other and cooperate, which would lead to the best overall outcome, or betray the other in self-interest. It illustrates a conflict between individual rationality and the best collective outcome, often highlighting the challenges of cooperation in real-life situations.

That said, a game is just a situation with three things: a payoff structure, strategies, and players (i.e., see below graphics for example).

5.1.1 Payoff Structure

Figure 5.1: Axelrod’s Payoff Structures

Some guy called Axelrod proposed that the payoff matrix from this prisoner’s dilemma is beneficial in the following order. If you defect, the reward is the best, followed by the socially optimum solution (i.e., SOS), the nash equilibrium, and the payoff you get from losing.

Figure 5.2: Payoffs in the Prisoner’s Dilemma

In the case of the coin activity that we did last week, the nash equilibrium happens when no player can improve their situation (i.e., improve the amount of coins that they receive). The upper left quadrant is the nash equilibrium. On the contrary, that bottom right corner is known as the socially optimum solution - the best outcome for both parties.

5.1.2 Backward Induction

Figure 5.3: Example of Backwards Induction

It is actually possible to deduce the sequence in which game will be played. This is called **backwards induction* and basically involves you starting from the end of a game to its beginning.

5.1.3 Variants

Figure 5.4: Payoff for N-Person Prisoner’s Dilemmas

The prisoner’s dilemma can also be played with more than one people.

5.2 Public Goods

Figure 5.5: Types of Goods in Economics

A public good is a good that is non-rivalrous and non-excludable. A free market usually cannot make enough of these goods to go around.

Something is non-excludable if its use cannot prohibit others from using it - like a national park for instance.

Something is non-rivalrous if its use doesn’t necessarily limits somebody else’s use of it.

## Topic 5 Social Dilemmas

This week’s (i.e., week 6)’s lecture aims to continue on with what was previous mentioned in class about game theory.

We ended last week’s class by playing a sort of game that has to do with game theory, but we didn’t actually go into the theory itself. This lecture introduces some new terms as they pertain to game theory.

## 5.1 Prisoner’s Dilemma

The

Prisoner’s Dilemmais a situation in which two individuals, who are arrested for a crime and cannot communicate with each other, must decide whether to cooperate with each other or betray each other to the authorities.Here’s the catch: If both prisoners stay silent (cooperate), they both get a relatively mild sentence. However, if one prisoner betrays the other (doesn’t cooperate) while the other stays silent, the betrayer goes free, and the one who stayed silent gets a harsh sentence. If both prisoners betray each other, they both receive moderate sentences.

The dilemma is that each prisoner must decide whether to trust the other and cooperate, which would lead to the best overall outcome, or betray the other in self-interest. It illustrates a conflict between individual rationality and the best collective outcome, often highlighting the challenges of cooperation in real-life situations.

That said, a

gameis just a situation with three things: a payoff structure, strategies, and players (i.e., see below graphics for example).## 5.1.1 Payoff Structure

Figure 5.1: Axelrod’s Payoff Structures

Some guy called Axelrod proposed that the payoff matrix from this prisoner’s dilemma is beneficial in the following order. If you defect, the reward is the best, followed by the

socially optimum solution (i.e., SOS), thenash equilibrium, and the payoff you get from losing.Figure 5.2: Payoffs in the Prisoner’s Dilemma

In the case of the coin activity that we did last week, the

nash equilibriumhappens when no player can improve their situation (i.e., improve the amount of coins that they receive). The upper left quadrant is the nash equilibrium. On the contrary, that bottom right corner is known as thesocially optimum solution- the best outcome for both parties.## 5.1.2 Backward Induction

Figure 5.3: Example of Backwards Induction

It is actually possible to deduce the sequence in which game will be played. This is called **backwards induction* and basically involves you starting from the end of a game to its beginning.

## 5.1.3 Variants

Figure 5.4: Payoff for N-Person Prisoner’s Dilemmas

The prisoner’s dilemma can also be played with more than one people.

## 5.2 Public Goods

Figure 5.5: Types of Goods in Economics

A

public goodis a good that is non-rivalrous and non-excludable. A free market usually cannot make enough of these goods to go around.Something is

non-excludableif its use cannot prohibit others from using it - like a national park for instance.Something is

non-rivalrousif its use doesn’t necessarily limits somebody else’s use of it.