Game Theory - An introduction
Week 1 Concepts of Game Theory
Static games of complete information
A static game is similar to the very simple decision problems in which a player makes a once-and-for-
all decision, after which outcomes are realized. In a static game, a set of players independently
choose once-and-for-all actions, which in turn cause the realization of an outcome. Thus a static
game can be thought of as having two distinct steps:
1. Each player simultaneously and independently chooses an action.
This means that players must take their actions without observing what actions their
counterparts take and without interacting with other players to coordinate their actions.
2. Conditional on the players’ choices of actions, payoffs are distributed to each player.
The players have preferences over the outcomes of the game given by some payoff function
over outcomes.
Step 1 and 2 settle what we mean by static. The meaning of complete information is that all players
understand the environment they are in – that is, the game they are playing – in every way.
A game of complete information requires that the following four components be common
knowledge among all the players of the game:
1. All the possible actions of all the players
2. All the possible outcomes
3. How each combination of actions of all players affects which outcome will materialize
4. The preferences of each and every player over outcomes
An event E is common knowledge if everyone knows E and everyone knows that everyone knows E,
and so on.
Normal-Form Games with Pure Strategies
A strategy is defined as a plan of action intended to accomplish a specific goal.
A pure strategy for player i is a deterministic plan of action. The set of all pure strategies for player i
is denoted Si.
A normal-form game includes three components as follows:
1. A finite set of players, N = {1, 2, …, n}
2. A collection of sets of pure strategies, {S1, S2, …, Sn}
3. A set of payoff functions, {v1, v2, …, vn), each assigning a payoff value to each combination of
chosen strategies, that is, a set of functions
Two-Player Finite Game
A finite game is a game with a finite number of players, in which the number of strategies in Si is
finite for all players i Є N.
Any two-player finite game can be represented by a matrix.
Solution Concepts
A solution concept is a method of analysing games with the objective of restricting the set of all
possible outcomes to those that are more reasonable than others.
We will use the term equilibrium for any one of the strategy profiles that emerges as one of the
solution concept’s predictions. It can be seen as the likely predictions.
Week 1 Concepts of Game Theory
Static games of complete information
A static game is similar to the very simple decision problems in which a player makes a once-and-for-
all decision, after which outcomes are realized. In a static game, a set of players independently
choose once-and-for-all actions, which in turn cause the realization of an outcome. Thus a static
game can be thought of as having two distinct steps:
1. Each player simultaneously and independently chooses an action.
This means that players must take their actions without observing what actions their
counterparts take and without interacting with other players to coordinate their actions.
2. Conditional on the players’ choices of actions, payoffs are distributed to each player.
The players have preferences over the outcomes of the game given by some payoff function
over outcomes.
Step 1 and 2 settle what we mean by static. The meaning of complete information is that all players
understand the environment they are in – that is, the game they are playing – in every way.
A game of complete information requires that the following four components be common
knowledge among all the players of the game:
1. All the possible actions of all the players
2. All the possible outcomes
3. How each combination of actions of all players affects which outcome will materialize
4. The preferences of each and every player over outcomes
An event E is common knowledge if everyone knows E and everyone knows that everyone knows E,
and so on.
Normal-Form Games with Pure Strategies
A strategy is defined as a plan of action intended to accomplish a specific goal.
A pure strategy for player i is a deterministic plan of action. The set of all pure strategies for player i
is denoted Si.
A normal-form game includes three components as follows:
1. A finite set of players, N = {1, 2, …, n}
2. A collection of sets of pure strategies, {S1, S2, …, Sn}
3. A set of payoff functions, {v1, v2, …, vn), each assigning a payoff value to each combination of
chosen strategies, that is, a set of functions
Two-Player Finite Game
A finite game is a game with a finite number of players, in which the number of strategies in Si is
finite for all players i Є N.
Any two-player finite game can be represented by a matrix.
Solution Concepts
A solution concept is a method of analysing games with the objective of restricting the set of all
possible outcomes to those that are more reasonable than others.
We will use the term equilibrium for any one of the strategy profiles that emerges as one of the
solution concept’s predictions. It can be seen as the likely predictions.
