01
Players
The decision-makers whose outcomes are being modeled. A player can represent a person, firm, state, organism, algorithm, coalition, or other strategic agent.
Players · strategies · incentives · information · equilibrium
Game Theory
Game theory studies decisions whose consequences depend on other decision-makers. It formalizes players, strategies, information, timing, and payoffs so strategic incentives can be analyzed instead of guessed from isolated choices.
Anatomy of a game
The same actions can imply different strategies when incentives, timing, or information change.
Before solving a game, specify who acts, what they can choose, what each player values, what they know, and when they move. Equilibrium concepts only make sense relative to that model.
02
Strategies
The actions or contingent plans available to each player. A strategy can be a single move or a rule for acting after many possible histories.
03
Payoffs
Numbers that encode each player's ranking of outcomes. Their scale matters less than the preference structure they represent.
04
Information
What each player knows when acting: previous moves, private types, probabilities, signals, rules, or the choices available to others.
05
Timing
Whether choices are simultaneous, sequential, repeated, observed, hidden, or made under commitments changes the strategic structure.
Payoff matrix explorer
A strategy profile is stable only if nobody benefits by deviating alone.
Choose one strategy for each player in a classic Prisoner's Dilemma. The matrix shows the outcome, then checks what each player would gain or lose by changing only their own move while the other player stays fixed.
Selected profile
Mutual defection
Nash equilibrium
3, 3
Mutual cooperation
0, 5
Player 2 exploits
5, 0
Player 1 exploits
1, 1
Mutual defection
Each ordered pair is (Player 1 payoff, Player 2 payoff). The numbers encode preferences for this example; they are not money or universal units.
Unilateral deviation test
Player 1 deviation
-1
would reduce payoff
Player 2 deviation
-1
would reduce payoff
Best-response logic
Neither player can improve their own payoff by changing strategies alone. That makes this profile a Nash equilibrium, even though mutual cooperation gives both players a higher payoff.
Equilibrium ≠ collective optimum
The Prisoner's Dilemma is famous precisely because individually stable incentives can lead to an outcome both players prefer less than mutual cooperation.
Solution ideas
Equilibrium describes strategic stability, not moral goodness or collective perfection.
Best response
A strategy that gives a player the highest payoff among their available choices, given what the other players are doing.
Dominant strategy
A strategy that is a best response regardless of the other players' strategies. Many games do not have one.
Nash equilibrium
A strategy profile in which no player can improve their payoff by changing only their own strategy.
Efficiency
An equilibrium can be strategically stable without maximizing total welfare or making every player as well off as another feasible outcome.