The Nature and Structure of a Game

Question 1

What does Game Theory examine?

Answer 1

Strategic decision making in situations where people’s actions are mutually interdependent.

Question 2

What are examples of mutually interdependent situations?

Answer 2

Interaction between goalkeeper and penalty taker / chess / Business

Question 3

When is strategic interaction absent?

Answer 3

Isolated individual or in perfect competition situations

Question 4

Define: A Game

Answer 4

a situation in which the actions of one person noticeably affect the welfare of another, and vice versa.

Question 5

Define: Rational Individual

Answer 5

A rational individual will try to predict and anticipate the actions of the other player and then make their decision to maximise their own utility based on those predictions

Question 6

What is the other term for the notion of rationality?

Answer 6

Instrumental rationality

Question 7

Define: Static Games

Answer 7

When players determine their actions simultaneously or when players choose their strategies in isolation.

Question 8

Define: Sequential move Games

Answer 8

Players move in a sequence, taking turns to act. Players who move later have the chance to observe their opponent’s actions before they decide how to act. Their may be a first or second mover advantage.

Question 9

Define: Zero-sum Games

Answer 9

When players’ interest are in conflict so that one player gains at the expense/ pay off other player.

Question 10

What are examples of Zero Sum Games?

Answer 10

Dividing funding people different sectors, or sharing a fixed pot of money between children.

Question 11

Define: Non-Zero-sum or variable sum games

Answer 11

When Players have at least some interest in common. trade for instance shows that at least some benefits can be accrued by all from taking part.
How advantageous a game is for both players will depend on how many times the game is played.

Question 12

Define: One Shot Games

Answer 12

The are played just once. Players can play without consideration to the reputation of the players in later interaction.

Question 13

Define: Repeated Games

Answer 13

They are played more than once, so a reputation can be built up.

Question 14

Define: Cooperative Games

Answer 14

Not of interest to game theorist because there is a binding agreement (third party) which can force players to act within the confines of their agreement even when they might not want to.

Question 15

Define: Non-Cooperative Games

Answer 15

Any agreements made will be adhered to only if it is in their individual interests of each player to do so.

Question 16

Outline the Prisoners’ Dilemma game

Answer 16

1. Police has two suspects, they require at least one of them to confess to convict them given their lack of evidence.
2. The prisoners are in different cells but they both know:

A) if no one confesses, they are charged under a minor offence - 1 year prison sentence.
B) If both confess - 6 year prison sentence.
C) If one confesses - that prisoner will be released and the other will serve a 9 year prison sentence.

Question 17

Define: Strategy

Answer 17

a complete plan of action that specifies how a player should act in response to all the various situations that might confront him/her in the course of playing a game

Question 18

What are the key features of the PD game?

Answer 18

1. players’ strategies are identical to the actions that are open to them in static games. Only play once and they don’t know what the other has chosen.
2. players have complete information (they know the pay offs, the number of players, and the strategies available to them)

Question 19

Define: common knowledge

Answer 19

if everyone knows that fact, and if everyone knows that everyone knows it, and everyone knows that everyone knows that everyone knows it, and so on, ad infinitum.

Question 20

Define: Dominance

Answer 20

When solving a game involves an attempt to rule out strategies that a rational person would never play. You can only play this if you assume common knowledge.

Question 21

Define: Strict Dominance

Answer 21

A strategy that always yields a lower payoff than other feasible strategy. Rational players will not pick this.

Question 22

What is the strictly dominated strategy for player 1 and 2 in a PD game?

Answer 22

Don’t confess always yields a lower pay off irrespective of what the other player does. So both players will choose to confess.

Question 23

Define: Pareto efficiency

Answer 23

An outcome is efficient if its impossible to move to a outcome that at least one person is made better off without making someone else worse off. If it was possible the outcome would be Pareto inefficient.

Question 24

How would you describe the outcome of PD game?

Answer 24

The outcome is Pareto inefficient. this is because there is a conflict between individual and collective rationality. The individual irrational action lead to a collectively sub-optimal Pareto inefficient outcome.

Question 25

Would communication help the outcome of a PD Game?

Answer 25

According to economic instrumental rational, a promise that both player would not confess lacks credibility. This is because it is in neither of the player interest (pay off would not be maximised) to choose not to confess. Given this theory support that rational actors would never act this way, a promise would not change the outcome given the incentives faced by the players.

Question 26

Define: Iterated strict dominance

Answer 26

The notion of strict dominance being applied successively to rule out the strategies of different players in a game. This is linked to the notion of common knowledge.

Question 27

When is a game Dominance Solvable?

Answer 27

If application of (iterated) strict dominance yields a unique prediction of how rational players will play a game