Game Theory Definitions Flashcards
Action or Strategy
Actions chosen by a player.
Agent
A player that can accept or reject a contract offered by a principal.
Asymmetric Information
A move by Nature occurs before any player acts, and some, but not all, players are ignorant of what Nature chose.
Best Response
A player’s optimal choice of action to a particular choice of others.
Common Knowledge
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.
Contractible
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.
Cooperative game
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.
Equilibrium and Nash Equilibrium
A set of actions chosen by all players such that given others’ choices no player wants to change his choice unilaterally.
Folk theorem
A result(s), especially in repeated games, that many held to be true, but was proved formally much later.
Incomplete Information
A move by Nature occurs before any player makes acts, and some players do not know what Nature chose.
Information Set
A collection of states, each corresponding to a different set of prior actions by all players.
Informed Player
A player that has observed Nature’s move in a game of asymmetric information.
Mixed strategies
A player’s choice of action that attaches a probability to each available action.
Move
An opportunity for a player to choose action.
Multi-stage game
A game consisting of several stages, each stage corresponding to an opportunity for one or more players to act.
Nature
An entity that makes a probabilistic move in respect of one of the elements of the game.
Non-cooperative game
A game in which players cannot make binding agreements as to their actions.
Payoff
Profits or utility to players after all players have chosen their action.
Perfect Information
Players know all that has occurred before their move.
Players
Participants in a game.
Principal
A player that can offer a contract for consideration by an agent.
Pure strategy
A player’s choice of a single action with probability 1, from among all available actions.
Sub-game
When players take turns to choose an action, a game that starts possibly after some choices have been made but other choices remain.
Sub-game Perfectness
A Nash equilibrium to a game that is also a Nash equilibrium in every sub-game.
What is game theory concerned with?
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.
Individual entities in game theory
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.
What makes game theory valuable?
Its ability to model the interaction between players.
Strategic Form of Game
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.
Game Tree
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.
What do you call a game where players move simultaneously?
Imperfect Information
Prisoners’ Dilemma
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.
Cheap Talk
Such talk that is non-binding.
Perfect Equilibrium
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.
