A theory of interaction between rational agents.

  • Institutional Design is the field in public policy & PPE that makes sure game theory & agent incentives are taken into account
  • It’s part of economics because it’s about rational agents interacting


def. Game. Assuming players:

  • : Strategy space of player
  • : which strategy combination happened.
  • : associated cost of happening for each player

Types of Games

  • Timing:
    • Static (=Simultaneous)
    • Dynamic (=Sequential Move)
  • Strategy Formulation:
    • Pure Strategy: deterministic mapping from information set to action set
    • Mixed Strategy: probabilistic mapping that depends on a Random Variable
  • Information availability:
    • Complete Information
    • Incomplete Information
  • Repetition:
    • One-off,
    • Finite-Repetition,
    • Infinite-Repetition
  • Payoff structure:
    • Zero-sum: each strategy tuple sums to zero
    • Positive/Negative Sum

Equilibria Types

→ See Equilibria in Game Theory

  • Static, Pure, One-off→ Nash Equilibrium
  • Dynamic, Pure → Subgame Perfect Nash Equilibirum
  • Static, Incomplete, (Pure or Mixed) → Baysian Nash Equilbilibrium (BNE)
  • Dynamic, Incomplete, (Pure or Mixed) → Subgame Perfect Baysian Nash Equilibirum (PBE)

Games Modeled by Game Theory

(DevonThink) Game Theory List of Games for many types of simultaneous game's payoff matricies.


  • Strategy Tuple of player is denoted
  • Payoff to player given strategy by , by player , etc. ⇒ is denoted
    • Alternatively, Cost is given as:
  • Nash Equilibria are Tuples:
    • In a simultaneous game, all player’s strategy should be specified
    • In a sequential game, the second player (=follower)’s strategy should include the response for all of the first player (=leader)’s moves.
      • Notation:

Branches of Game Theory

  1. Experimental game theory
  2. Evolutionary game theory—using game theory to explain strategies that affect natural selection
  3. Applied game theory