definition
admitted
Strategic Game
A strategic game (or normal-form game) is a tuple \((I, (S_i)_{i \in I}, (u_i)_{i \in I})\) where \(I\) is a set of players, \(S_i\) is the strategy set of player \(i\), and \(u_i \colon \prod_{j \in I} S_j \to U\) is the payoff function of player \(i\).
In the Lean formalization, this is a structure with fields strategy : N → Type* and
payoff : Profile → N → U, where Profile = ∀ i, strategy i.
References
- [MSZ, Chapter 2] Maschler, Solan, and Zamir, Game Theory. Definition of strategic-form game.
Used by
- Normal Form Reduction
- Repeated Game
- Standard Repeated Game
- Stochastic Game
- Bayesian Game
- Convex Game
- Quasi-Concave Game
- Smooth Game
- Supermodular Game
- Mixed Strategy
- Symmetric Game
- Dominated Strategy
- Population Game
- Potential Game
- Reny Solution
- Strategy Profile
- External Regret
- Zero-Sum Game
- Direct Mechanism Interface
- Induced Strategic Game