Sure, here is the formal definition of a game as a kind of search problem:

1. Initial State: This is the starting point of the game. It's the configuration of the game before any moves have been made.

2. Player(s): These are the entities that make decisions in the game. In a single-player game, there is one decision-maker. In a multiplayer game, there are multiple decision-makers, and the game's outcome can depend on the decisions of any or all players.

3. Actions or Moves: These are the choices that a player can make at any point in the game. The set of possible actions can depend on the current state of the game.

4. Transition Model: This is a description of how the game changes in response to a player's action. It takes the current state and a player's action as input, and it produces a new state as output.

5. Goal Test: This is a way to determine whether the game is over. It takes a state as input and returns a boolean indicating whether that state is a goal state.

6. Path Cost: This is a way to assign a numerical value to a sequence of actions. The path cost can be used to determine the quality of different strategies.

7. Utility Function: This is a measure of the desirability of a game outcome. For a single player, it might simply be the path cost. For multiple players, it might be a vector of path costs, one for each player.

8. Adversaries: In some games, players work against each other. The adversaries' actions can affect the outcome of the game.

9. Chance: Some games include elements of randomness. The transition model might include a chance component, where the outcome is not entirely determined by the current state and the players' actions.

Question

Sure, here is the formal definition of a game as a kind of search problem:

1. Initial State: This is the starting point of the game. It's the configuration of the game before any moves have been made.

2. Player(s): These are the entities that make decisions in the game. In a single-player game, there is one decision-maker. In a multiplayer game, there are multiple decision-makers, and the game's outcome can depend on the decisions of any or all players.

3. Actions or Moves: These are the choices that a player can make at any point in the game. The set of possible actions can depend on the current state of the game.

4. Transition Model: This is a description of how the game changes in response to a player's action. It takes the current state and a player's action as input, and it produces a new state as output.

5. Goal Test: This is a way to determine whether the game is over. It takes a state as input and returns a boolean indicating whether that state is a goal state.

6. Path Cost: This is a way to assign a numerical value to a sequence of actions. The path cost can be used to determine the quality of different strategies.

7. Utility Function: This is a measure of the desirability of a game outcome. For a single player, it might simply be the path cost. For multiple players, it might be a vector of path costs, one for each player.

8. Adversaries: In some games, players work against each other. The adversaries' actions can affect the outcome of the game.

9. Chance: Some games include elements of randomness. The transition model might include a chance component, where the outcome is not entirely determined by the current state and the players' actions.

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