Game Theory Definitions

Question 1

Action or Strategy

Answer 1

Actions chosen by a player.

Question 2

Agent

Answer 2

A player that can accept or reject a contract offered by a principal.

Question 3

Asymmetric Information

Answer 3

A move by Nature occurs before any player acts, and some, but not all, players are ignorant of what Nature chose.

Question 4

Best Response

Answer 4

A player’s optimal choice of action to a particular choice of others.

Question 5

Common Knowledge

Answer 5

A common knowledge element is something that each player knows, and further knows that others know that he knows it, and so on ad infinitum.

Question 6

Contractible

Answer 6

Some element that can be written into a contract so that the disposition/distribution of the contract is based on the exact outcome of the element, and a third party, other than the players, can help in verifying the outcome.

Question 7

Cooperative game

Answer 7

A game in which players can make binding agreements as to their actions. Thus, members of OPEC play a cooperative game when they agree to what level of production each is to maintain. In contrast, supermarkets, for example, choose pricing strategies non-cooperatively.

Question 8

Equilibrium and Nash Equilibrium

Answer 8

A set of actions chosen by all players such that given others’ choices no player wants to change his choice unilaterally.

Question 9

Folk theorem

Answer 9

A result(s), especially in repeated games, that many held to be true, but was proved formally much later.

Question 10

Incomplete Information

Answer 10

A move by Nature occurs before any player makes acts, and some players do not know what Nature chose.

Question 11

Information Set

Answer 11

A collection of states, each corresponding to a different set of prior actions by all players.

Question 12

Informed Player

Answer 12

A player that has observed Nature’s move in a game of asymmetric information.

Question 13

Mixed strategies

Answer 13

A player’s choice of action that attaches a probability to each available action.

Question 14

Move

Answer 14

An opportunity for a player to choose action.

Question 15

Multi-stage game

Answer 15

A game consisting of several stages, each stage corresponding to an opportunity for one or more players to act.

Question 16

Nature

Answer 16

An entity that makes a probabilistic move in respect of one of the elements of the game.

Question 17

Non-cooperative game

Answer 17

A game in which players cannot make binding agreements as to their actions.

Question 18

Payoff

Answer 18

Profits or utility to players after all players have chosen their action.

Question 19

Perfect Information

Answer 19

Players know all that has occurred before their move.

Question 20

Players

Answer 20

Participants in a game.

Question 21

Principal

Answer 21

A player that can offer a contract for consideration by an agent.

Question 22

Pure strategy

Answer 22

A player’s choice of a single action with probability 1, from among all available actions.

Question 23

Sub-game

Answer 23

When players take turns to choose an action, a game that starts possibly after some choices have been made but other choices remain.

Question 24

Sub-game Perfectness

Answer 24

A Nash equilibrium to a game that is also a Nash equilibrium in every sub-game.

Question 25

What is game theory concerned with?

Answer 25

How individual entities, persons or organizations, choose actions taking into account how other participants do the same.

In other words:

Specifying actions for all players ensuring that for each player his/her chosen actions are optimal given the actions of other players, implying that optimality is relative.

Question 26

Individual entities in game theory

Answer 26

These entities are called players even though the decisions that they make are in the context of situations with real-world consequences quite different from the entertainment that parlor games yield. Players are assumed to choose actions to maximize their expected utility, following the accepted model of single-person decision making. In this sense we may view game theory as a generalization of single-person decision theory to multi-person decision making.

Question 27

What makes game theory valuable?

Answer 27

Its ability to model the interaction between players.

Question 28

Strategic Form of Game

Answer 28

A game that consists of three elements:

1) Players (i when i = 1, 2, …, N )
2) An action/strategy (from a set Ai = { ai })
3) Payoff (πi)

The payoff πi is to be thought of as the utility to player i when he
chooses ai and the other players choose a-i.

Question 29

Game Tree

Answer 29

The sequence of decisions in a game like Chess, where each player has a turn to make a move by choosing an action, followed by other players each in turn.

Question 30

What do you call a game where players move simultaneously?

Answer 30

Imperfect Information

Question 31

Prisoners’ Dilemma

Answer 31

Replacing firms with prisoners, actions S and I by Deny and Confess (to a crime), and leaving the ordering of the utilities the same. In that game, Confess is a dominant strategy for both, but if they could cooperate to choose Deny they would be better off.

Question 32

Cheap Talk

Answer 32

Such talk that is non-binding.

Question 33

Perfect Equilibrium

Answer 33

One of the central ideas in dynamic programming is Bellman’s Principle of Optimality. This has force in multi-stage games in the following sense: a player’s strategy should be such that it is a best response at each information set.