StrategicLab
Learning path · 6 labs

Strategic Games

How should I decide when others also choose?

Study how choices depend on the other player's strategy. Start with zero-sum guarantees, then compare separate player objectives and sequential decisions. Poker and stochastic games extend these ideas to private information and changing states.

A suggested learning path

Follow the sequence, or jump directly to the question that interests you. Each lab opens in Guided Learning; switch to Sandbox at any time to experiment freely.

  1. Step 1

    Zero-Sum Matrix Games

    Understand mixed strategies, best responses and minimax guarantees.

    Learning outcome: Find the value and optimal mixed strategies of a zero-sum game, then reach them through linear programming, pivoting and fictitious play.

    Level
    Intermediate
    Time
    About 20 min per method
    Concepts
    Saddle point · Mixed strategy · Minimax theorem · Linear programming
    A three by three payoff matrix with a blue row player on the left and a red column player on the top.
  2. Step 2

    General-Sum Games

    Give each player a separate payoff and study Nash equilibrium.

    Learning outcome: Find the Nash equilibria of a two-player game and compare them with safety levels and dominance.

    Level
    Intermediate
    Time
    About 20 min per method
    Concepts
    Nash equilibrium · Best response · Safety level · Dominance
    Two players facing a two by two payoff table with a payoff pair in each cell.
  3. Step 3

    Game Trees

    Represent the order of decisions and what each player knows.

    Learning outcome: Build a game tree, read its information sets and solve perfect-information games by backward induction.

    Level
    Intermediate
    Time
    About 20 min per method
    Concepts
    Information sets · Backward induction · Behavioral strategies
    A blue player on a yellow path that forks while a red player stands on one of the branches.
  4. Step 4

    Poker Endgame

    Use a small hidden-card game to understand betting and bluffing.

    Learning outcome: Find a bluffing rate and a calling rate from indifference conditions.

    Level
    Intermediate
    Time
    About 15 min
    Concepts
    Hidden information · Bluffing · Indifference
    A sweating, anxious faceless blue player holding a card and a chip while a red devil whispers bluff and a yellow angel whispers call.
  5. Step 5

    Continuous Poker

    Extend private hand strengths to a continuous interval and derive thresholds.

    Learning outcome: Derive betting and calling thresholds when private hands range over an interval.

    Level
    Advanced
    Time
    About 20 min
    Concepts
    Threshold strategy · Bluffing · Indifference
    A blue player and a red player holding cards at a round blue table with a pile of chips between them.
  6. Step 6

    Stochastic Game

    Study decisions across states with probabilistic transitions.

    Learning outcome: Compute state values with Shapley iteration and evaluate stationary policies.

    Level
    Advanced
    Time
    About 25 min
    Concepts
    State value · Shapley iteration · Stationary policy
    A red player and a blue player paddling a yellow canoe together through rolling blue waves.
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