Definition:Game
Definition
In the context of game theory, a game is any social situation which involves more than one person.
More specifically, a game is a problem of strategy between two or more parties in which all parties involved seek (usually) to maximise their outcome.
A game $G$ can be specified by:
- its players
- the moves available to each player
- the preference relation for each player:
that is:
- $G = \sequence {N, \sequence {A_i}, \sequence {\succsim_i} }$
$G$ can also be specified by:
- its players
- the moves available to each player
- the payoff function for each player:
that is:
- $G = \sequence {N, \sequence {A_i}, \sequence {u_i} }$
Rules
A game is specified completely by its rules.
They prescribe for each player a model of rational choice:
- $(2): \quad$ A set $C$ of consequences of each of those moves
- $(3): \quad$ A consequence function $g: A \to C$ which maps a consequence to each action
- $(4): \quad$ A preference relation $\succsim$, which is a total ordering on $C$.
Player
Each of the parties involved in a game are called players.
Strategy
A strategy is a complete plan of action that defines what a player will do under all circumstances in a game.
Payoff
The payoff of a game is the reward or punishment made to a player at the end of the game as a result of combination of the various strategies employed.
Also see
- Results about games can be found here.
Sources
- 1956: Steven Vajda: The Theory of Games and Linear Programming ... (previous) ... (next): Chapter $\text{I}$: An Outline of the Theory of Games: $2$
- 1983: Morton D. Davis: Game Theory (revised ed.) ... (previous) ... (next): $\S 1$: An Overview
- 1991: Roger B. Myerson: Game Theory ... (previous) ... (next): $1.1$ Game Theory, Rationality, and Intelligence
- 1993: Richard J. Trudeau: Introduction to Graph Theory ... (previous) ... (next): $1$. Pure Mathematics: Games
- 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): $1.2$: Games and Solutions
- 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): $2.1$: Strategic Games