Players and Strategies

Game Theory · Axiom Academy

Understanding the fundamental components of game theory: who plays and what choices they can make 1. Players: The Decision-Makers In game theory, players are the individuals, groups, or entities that make decisions within a game. Each player has their own objectives and can influence the outcome through their choices. A player is a decision-making agent in a game, typically denoted as i from the set of all players N = 1, 2, ..., n . Chess: Two players (White and Black) Business Competition: Competing firms in a market Voting: Citizens or legislators making decisions Poker: Multiple individuals at the table It's crucial to distinguish between strategies and actions . An action is a single move at a specific point in the game, while a strategy is a complete plan that specifies what action to take in every possible situation. Action: A single choice at one decision point Strategy: A complete contingency plan for all possible situations in the game Action: Move pawn from e2 to e4 Strategy: "If the game starts, move e4. If opponent responds with e5, then play Nf3. If opponent plays c5, then play Nf3 followed by d4..." 3. Strategy Sets: Available Choices Each player has a strategy set that contains all possible strategies they could employ. The strategy set represents the full range of choices available to a player. For player i , their strategy set S i contains all feasible strategies. A specific strategy is denoted as s i ∈ S i . Player 1's strategy set: S 1 = Cooperate, Defect

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