Game

In adversarial search problem environment is multiagent, competitive where in the agent's goals are in conflict.

Adversarial search problems are commonly known as games.

Mathematical game theory a branch of economics views any multiagent environment as a game, provided that, impact of each agent on the others is "significant" regardless of whether the agent are co-operative or competitive.

The term game means a sort of conflict in which n individuals or groups (known as players) participate.

Game theory denotes games of strategy. John Von Neumann is acknowledged as father of game theory.

Neumann defined game theory in 1928 and established the mathematical framework for all subsequent theoretical developments.

Game theory allows decision-makers (players) to cope with other decision-maker (players) who have different purposes in mind. In other words, players determine their own strategies in terms of the strategies and goal of their opponent.

Games are integral attribute of human beings. Games engage the intellectual faculties of humans.

If computers are to mimic people they should be able to play games.

A game has at least 2 players. Solitaire is the term used for single player games of concentration and are not considered game by game theory.

Every instance of the game must end and when an instance ends, each player receives a payoff / outcome.

• A payoff is a value associated with each player's final situation.
• A zero-sum game is one, in which elements of payoff matrix sum to zero.
• In typical zero-sum game Win is X points, Draw is 0 and Loss is -X points making the sum 0.

Game is formally defined with following four components :

• The initial state, which includes the board position and identifies the player to move.
• A successor function, which returns a list of (move, state) pairs, each indicating a legal move and the resulting state.
• A terminal test, which determines when the game is over.
  • States where the game has ended are called as terminal states.
• A utility function (also called an objective function or payoff function), which gives a numeric value for the terminal states.
  • In chess, the outcome is a win, loss or draw, with values +1, 1, or 0.
  • Some game have a wider variety of possible outcomes; the payoffs in backgammon range from +192 to -192.