StrategicLab
Learning path · 3 labs

Cooperation & Coalitions

How should the gains from cooperation be shared?

Move from choosing against an opponent to evaluating agreements and groups. First study what two players can achieve together, then compare how larger coalitions share value and how individual members affect collective decisions.

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

    Two-Player Cooperation

    Understand feasible agreements and bargaining between two players.

    Learning outcome: Map the feasible agreements of two players and choose one with transferable utility or Nash bargaining.

    Level
    Intermediate
    Time
    About 20 min per method
    Concepts
    Feasible set · Pareto frontier · Transferable utility · Nash bargaining
    A blue player and a red player shaking hands over a dark divider, with a row of yellow gold bars split between them and one bar being slid across.
  2. Step 2

    Coalitional Games

    Assign values to groups and compare stability and allocation rules.

    Learning outcome: Compare imputations, the core, the Shapley value and the nucleolus on one characteristic function.

    Level
    Advanced
    Time
    About 20 min per method
    Concepts
    Characteristic function · Core · Shapley value · Nucleolus
    A blue player and a red player shaking hands beside a small stack of yellow cubes while a yellow third player holds out one more cube to join them.
  3. Step 3

    Voting Power

    Apply coalition values to pivotal voters and distinguish votes from power.

    Learning outcome: Measure Shapley–Shubik power from pivotal voters and separate voting weight from power.

    Level
    Intermediate
    Time
    About 15 min
    Concepts
    Weighted voting · Pivotal voter · Shapley–Shubik index
    A blue voter with weight 4, a yellow voter with weight 2 and a red voter with weight 3 around a round table, with a quota card reading 5 and a gold ring around the blue and yellow weights.
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