Questions and Answers
What is adversarial search in the context of artificial intelligence?
Adversarial search involves planning ahead in a world where other agents are planning against us.
Which of the following is a characteristic of a two-player zero-sum game?
In chess, the outcome is a win (1), loss (0), or draw (____).
1/2
Perfect information is synonymous with partially observable information.
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What does the minimax value represent in game theory?
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Match the following types of games with their examples:
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What does the term 'ply' refer to in game theory?
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Study Notes
Introduction to Adversarial Search and Games
- Adversarial search examines planning in environments where multiple agents may strategize against each other.
- Games serve as models for adversarial scenarios in AI, akin to grand prix racing in automobile design.
Key Concepts of Games in AI
- A game is defined as a search problem characterized by:
- Initial state (S0): The starting configuration of the game.
- Players (To-Move): The current player making the decision.
- Actions (ACTIONS): The available legal moves in the current state.
- Result (RESULT): The outcome of a chosen action.
- Terminal-Test (TERMINAL-TEST): Indicates whether the game has concluded.
- Utility (UTILITY): A function defining the final payoff for a player when reaching a terminal state.
Types of Games
- Two-player zero-sum games are commonly studied, including chess and Go.
- Characteristics of zero-sum games:
- Deterministic: Outcomes depend solely on players' actions, with no randomness.
- Turn-taking: Players alternate turns.
- Perfect information: All players are aware of all aspects and states of the game.
- Zero-sum: Gain for one player equals loss for the other, implying no mutual benefits.
Game Classification
- Deterministic, Perfect Information Games: Examples - chess, Go, checkers.
- Deterministic, Imperfect Information Games: Examples - Battleship, blind tic-tac-toe.
- Chance Games: Examples - Backgammon, Monopoly, Poker (features randomness).
Game Trees
- Defined as a representation where:
- Vertices are game states.
- Edges represent possible moves between states.
- A complete game tree encompasses every possible sequence of moves until a terminal state.
- Game trees may be infinite, particularly with unbounded state spaces or repetitive game positions.
Minimax Search for Optimal Strategies
- Minimax search aims to optimize decision-making by selecting moves that maximize the minimum gain.
- Ply denotes one move made by one player within the game tree.
- The objective is to achieve the highest minimax value, signifying the best possible outcome assuming optimal play from both opponents.
Minimax Algorithm Overview
- The Minimax algorithm is structured to evaluate game states and determine the best action:
- MINIMAX-DECISION: Returns the action that maximizes the minimum value.
- MAX-VALUE function: Computes the utility value of a given game state.
Real-Time and Stochastic Games
- Despite ideal conditions for games (perfect play), real-world scenarios often involve elements of uncertainty and time constraints.
- Decisions in imperfect real-time situations or stochastic games require approximation and strategic assumptions.
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Description
Explore the intricacies of adversarial search in artificial intelligence through Chapter 5. This chapter delves into strategies like minimax decisions and α–β pruning. Understand the challenges of planning in competitive environments and the various types of games involved in AI decision-making.
