Introduction to Game theory

(L1-L8)

LECTURE 1 

Why is game theory interesting?

Strategic games

• Evolve when your decision is influences by that of others and it influences others’

• Players interact and what is best for them depends on what others do

• Learn to use intuition to guide rational thinking and apply rational thinking to guide intuition

LECTURE 2

Some foundations of Game Theory:

—> Strategic environment

—> Rules

—> Assumptions

—> Terminology

—> Strategic environment

1. Players

2. Strategies

3. Payoffs

1. Players —> who are they?

They are everyone who has an effect on your well-being

2. Strategies —> what are they and what do they do?

=the actions available to each player, and they define a plan of action for every contingency

3. Payoffs

• numbers which reflect the players’ interests

• describe each players’ well-being under each possible outcome

• can take fairness, reputation etc. into account

• do not indicate that players are narrowly selfish

—> Rules

1. Timing of moves

2. Nature of conflict and interaction

3. Informational conditions

4. Enforceability of agreements and contracts

1. Timing of moves

SIMULTANEOUS or SEQUENTIAL

What do we mean by a ‘simultaneous move’?

We mean that opponents are not aware of each other’s decision when they make their own (even if they do not make decisions at the same point in time)

What do we mean by ‘sequential moves’?

We mean that they happen one after another.

2. Nature of conflict and interaction

What is the nature of interactions?

—> a one-shot interaction

—> a repeated interaction

3. Information conditions

FULL INFORMATION or ASYMMETRIC (IMPERFECT) INFORMATION

Two important assumptions to consider

1. Rationality

2. Common knowledge

1. Rationality

Players:

• aim to maximise their payoffs

• are perfect calculators

• are implementers of their desired strategy

What does the assumption of rationality imply?

That players can:

1. Rank all payoffs over all possible outcomes (know their interest)

2. Calculate which actions serve best to their interest

—> Can we always assume rationality though?

2. Common knowledge

Each player knows the rules of the game and everyone is aware of this

—> Can we always assume common knowledge or do we have to settle with a common understanding of the rules of the game?

Some terminology

1. Normal form

2. Extensive form

3. Equilibrium

1. Normal form

• A list of players

• A list of strategies for each player

• For each strategy a list of payoffs that players receive

2. Extensive form

• Timing of actions that players may take

• Information that players have when they take those actions

3. Equilibrium

What is the outcome of people interacting?

Stable equilibrium: once it is reached, there is no reason to move.