Normal form games are a fundamental concept in game theory, representing simultaneous-move scenarios where players make decisions without knowing others' choices. These games consist of players, strategies, and payoffs, which are organized into payoff matrices for analysis.
Strategic interdependence is a crucial aspect of game theory, where outcomes depend on all players' decisions. This concept distinguishes game theory from decision theory, as players must anticipate and respond to others' actions, making it essential in various real-world scenarios.
- Normal form games represent simultaneous-move games where players make decisions without knowing the other players' choices
- Players are the decision-makers in the game (firms, individuals, countries)
- Strategies are the actions available to each player (pricing, quantity, investment levels)
- Payoffs are the outcomes for each player based on the combination of strategies chosen (profits, market share, utility)
Construction of payoff matrices
- Payoff matrices represent the outcomes of a normal form game in a tabular format
- Rows represent the strategies of one player (Firm A's pricing options)
- Columns represent the strategies of the other player (Firm B's pricing options)
- Each cell contains the payoffs for both players given the corresponding strategy combination (Firm A's profit, Firm B's profit)
- To construct a payoff matrix:
- Identify the players and their available strategies
- List the strategies of one player along the rows and the other player along the columns
- Fill in the payoffs for each player in each cell based on the corresponding strategy combination
Elements of game structure
- To analyze a normal form game, identify its key components
- Players are the decision-makers in the game (consumers, producers, governments)
- Strategies can be pure (choosing a single action) or mixed (a probability distribution over actions)
- Payoffs are the outcomes for each player based on the combination of strategies chosen
- Payoffs can be represented as numerical values (profits in dollars), rankings (1st, 2nd, 3rd), or verbal descriptions (high, medium, low)
Strategic Interdependence
Strategic interdependence in games
- Strategic interdependence is a key feature of game theory where the outcome depends on the decisions of all players involved
- Each player's optimal strategy depends on their beliefs about the other players' strategies (best response)
- Players must anticipate and respond to the actions of others (strategic thinking)
- The presence of strategic interdependence distinguishes game theory from decision theory, which focuses on individual decision-making without strategic interactions
- Examples of strategic interdependence include pricing decisions by competing firms (Coke vs Pepsi), arms races between nations (US vs USSR), and negotiations and bargaining situations (labor unions vs management)