UNIT 6: INTERACTION AND SOCIAL PREFERENCES
1. INTRODUCTION
Social interactions could include altruism, trust, reciprocity, and anything that links you with another person
under social preferences.
We will now cover situations involving interactions rather than purely individual decisions.
We will start by looking at the foundations of game theory to build the appropriate foundations as it is a unified
and standardized way to model interactions between people. At the end, when two people or more interact, you
can frame it as a game, Game theory presents a unified and highly coherent view of behaviour in strategic
interactions between people.
Then we will look at some applications including social interaction.
2. INTRODUCTION TO GAME THEORY
2.1 ELEMENTS OF A NORMAL FORM GAME
Games are about situations in which decision makers interact; we will mostly focus on two-player games. We will
look at some models that predict equilibrium outcomes (best decision) in strategic interactions between players.
A normal or strategic form game is described by three elements:
1) The players of the game. The players of the games are the decision makers; they could be individuals, firms,
or even governments.
2) A set of actions or strategies for each player. Actions or strategies constitute the choice set of a player; a
player could have finitely many actions, or infinitely many.
3) Payoff functions (preferences) for each action profile. Meaning that if I play this and the other person play
the other strategy what should I get? Payoff functions assign a given payoff to each player for each
combination of strategies of the different players.
2.2 BEST RESPONSE FUNCTIONS
Checking each strategy set for potential equilibrium qualities is tedious, especially when games get larger. So, in
this way, we would look to the best response functions which are an easier way of finding equilibria. They are
also much better for larger games.
The idea is very simple: find the best strategy for player i, conditional on the strategies of the other players.
2.3 REPRESENTATION OF A NORMAL GAME
The crucial point about a static game is that players move at the same time (or moves are revealed at the same
time)
Normal form games have a convenient graphical representation for 2 players, where the whole game is described
in a matrix:
, THE PRISONER’S DILEMMA
The prisoner's dilemma is a standard example of a game analysed in game theory that shows why two
completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so.
This game describes the situation in which you have two suspects for a crime that are held in separate cells and
can confess or keep quiet. The different outcomes:
1) If nobody confesses, both walk after short detention (2 years).
2) If one confesses and the other does not, the confessing party walks or gets a very short sentence (1 year), while
the other party faces a long sentence (8 years).
3) If both confess, both get long jail sentences (5 years).
The prisoner’s dilemma is an important game inasmuch as it models many important processes (public goods,
arms race). The outcome of both parties is different depending on if they contribute or they do not contribute.
We are interested in equilibria of the game
What is the optimal strategy for each suspect?
Optimal strategies for suspect 1:
1. INTRODUCTION
Social interactions could include altruism, trust, reciprocity, and anything that links you with another person
under social preferences.
We will now cover situations involving interactions rather than purely individual decisions.
We will start by looking at the foundations of game theory to build the appropriate foundations as it is a unified
and standardized way to model interactions between people. At the end, when two people or more interact, you
can frame it as a game, Game theory presents a unified and highly coherent view of behaviour in strategic
interactions between people.
Then we will look at some applications including social interaction.
2. INTRODUCTION TO GAME THEORY
2.1 ELEMENTS OF A NORMAL FORM GAME
Games are about situations in which decision makers interact; we will mostly focus on two-player games. We will
look at some models that predict equilibrium outcomes (best decision) in strategic interactions between players.
A normal or strategic form game is described by three elements:
1) The players of the game. The players of the games are the decision makers; they could be individuals, firms,
or even governments.
2) A set of actions or strategies for each player. Actions or strategies constitute the choice set of a player; a
player could have finitely many actions, or infinitely many.
3) Payoff functions (preferences) for each action profile. Meaning that if I play this and the other person play
the other strategy what should I get? Payoff functions assign a given payoff to each player for each
combination of strategies of the different players.
2.2 BEST RESPONSE FUNCTIONS
Checking each strategy set for potential equilibrium qualities is tedious, especially when games get larger. So, in
this way, we would look to the best response functions which are an easier way of finding equilibria. They are
also much better for larger games.
The idea is very simple: find the best strategy for player i, conditional on the strategies of the other players.
2.3 REPRESENTATION OF A NORMAL GAME
The crucial point about a static game is that players move at the same time (or moves are revealed at the same
time)
Normal form games have a convenient graphical representation for 2 players, where the whole game is described
in a matrix:
, THE PRISONER’S DILEMMA
The prisoner's dilemma is a standard example of a game analysed in game theory that shows why two
completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so.
This game describes the situation in which you have two suspects for a crime that are held in separate cells and
can confess or keep quiet. The different outcomes:
1) If nobody confesses, both walk after short detention (2 years).
2) If one confesses and the other does not, the confessing party walks or gets a very short sentence (1 year), while
the other party faces a long sentence (8 years).
3) If both confess, both get long jail sentences (5 years).
The prisoner’s dilemma is an important game inasmuch as it models many important processes (public goods,
arms race). The outcome of both parties is different depending on if they contribute or they do not contribute.
We are interested in equilibria of the game
What is the optimal strategy for each suspect?
Optimal strategies for suspect 1:
