What is Game Theory?
Explore the definition, scope, and purpose of game theory as a tool for analyzing strategic interactions.
Strategic Thinking
Decision Making
Interactions
Game theory is the mathematical study of strategic decision-making among rational agents. It provides a framework for understanding situations where the outcome for each participant depends not only on their own decisions but also on the decisions of others.
# Game Theory Definition Framework
game_theory = {
"definition": "Mathematical study of strategic interactions",
"key_elements": {
"players": "Decision makers in the game",
"strategies": "Available choices for each player",
"payoffs": "Outcomes resulting from strategy combinations",
"information": "What players know about the game"
},
"characteristics": {
"interdependence": "Each player's payoff depends on others' choices",
"rationality": "Players seek to maximize their own payoffs",
"strategic_thinking": "Players consider others' likely actions",
"equilibrium": "Stable outcomes where no player wants to change"
},
"applications": {
"economics": ["Market competition", "Auctions", "Bargaining"],
"politics": ["Voting", "International relations", "Coalition formation"],
"business": ["Pricing", "Product development", "Strategic alliances"],
"biology": ["Evolution", "Animal behavior", "Resource competition"]
}
}
Strategic Interactions
Understand what makes a situation strategic and how it differs from individual decision-making.
Strategic Situation Characteristics:
• Multiple decision-makers (players)
• Interdependent payoffs
• Each player aware of the interaction
• Players choose strategies simultaneously or sequentially
Strategic vs Individual Decisions:
In individual decisions, outcomes depend only on your choice and external factors. In strategic situations, outcomes depend critically on what others choose to do.
# Strategic Interaction Examples
strategic_situations = {
"market_competition": {
"players": ["Firms in same industry"],
"strategies": ["Pricing", "Product quality", "Advertising"],
"interdependence": "Firm A's profit depends on Firm B's pricing",
"example": "If competitor lowers price, should I match or differentiate?"
},
"auction": {
"players": ["Bidders"],
"strategies": ["Bid amount"],
"interdependence": "Winning depends on others' bids",
"example": "How much to bid knowing others are bidding too?"
},
"arms_race": {
"players": ["Countries"],
"strategies": ["Military spending level"],
"interdependence": "Security depends on relative military power",
"example": "More spending increases security but wastes resources"
},
"coordination": {
"players": ["Team members", "Drivers", "Technology adopters"],
"strategies": ["Which standard/method to use"],
"interdependence": "Benefit from choosing same as others",
"example": "Which side of road to drive on"
}
}
Players, Strategies, and Payoffs
Learn the basic building blocks that define any game-theoretic model.
Game Components:
• Players: The decision-makers (can be individuals, firms, countries)
• Strategy set: All possible actions available to each player
• Payoff function: Maps strategy combinations to outcomes for each player
• Information structure: What each player knows when making decisions
Payoff Interpretation:
Payoffs represent players' preferences over outcomes. They can be monetary (profits, costs) or represent utility, happiness, or any measure of success the player cares about.
# Game Structure Definition
game_structure = {
"players": {
"definition": "Set of decision-makers",
"notation": "N = {1, 2, ..., n}",
"examples": ["Firms", "Countries", "Individuals", "Political parties"],
"assumptions": ["Rational", "Self-interested", "Strategic"]
},
"strategies": {
"definition": "Available actions for each player",
"notation": "Si = strategy set for player i",
"types": ["Pure strategies", "Mixed strategies"],
"examples": {
"price_competition": ["High price", "Low price"],
"auction": ["Bid $0 to $100"],
"