Cooperative Game Theory

Shapley value, core, nucleolus, coalition formation, cost allocation, and bargaining solutions.
TUTORIALS

Cooperative Game Theory

Shapley value, core, nucleolus, coalition formation, cost allocation, and bargaining solutions.

The bankruptcy game and the Talmudic rule

cooperative-gt
bankruptcy-game
talmud
fair-division

Implement the contested garment principle and the Talmudic bankruptcy rule in R, show their connection to the nucleolus of cooperative games, and compare with proportional and constrained equal awards division methods.

May 8, 2026

Hedonic coalition formation games

cooperative-gt
coalition-formation
hedonic-games
matching

Implement hedonic coalition formation with individual and Nash stability concepts in R, applied to a roommate matching example with 6 players.

May 8, 2026

Core stability in cooperative games — unblocked allocations and the Bondareva-Shapley theorem

cooperative-gt
core
coalitional-games
linear-programming

Define the core of a cooperative game, check non-emptiness via linear programming and the Bondareva-Shapley theorem, compute core allocations for classic games, and visualize the core as a region in the simplex for three-player games.

May 8, 2026

Rubinstein’s alternating-offers bargaining game

cooperative-gt
bargaining
rubinstein
subgame-perfection

Implement Rubinstein’s infinite-horizon alternating-offers model in R, derive the unique subgame-perfect equilibrium as a function of discount factors, and visualise how patience determines bargaining power.

May 8, 2026

The Shapley-Shubik power index for weighted voting games

cooperative-gt
voting-power
shapley-value

Measure each voter’s true power in weighted voting games using the Shapley-Shubik index, and discover why voting weight and voting power are fundamentally different.

May 8, 2026

The Shapley value — fair division of cooperative surplus

cooperative-gt
shapley-value
fair-division
coalitional-games

Derive the Shapley value axiomatically, implement it for arbitrary coalitional games in R, and visualize marginal contributions and fairness properties with interactive examples.

May 8, 2026

Voting power indices — when weight does not equal power

cooperative-gt
voting-power
banzhaf
shapley-shubik

Compute the Banzhaf and Shapley-Shubik power indices for weighted voting games in R, apply them to the EU Council, UN Security Council, and US Electoral College, and visualize the divergence between voting weight and true voting power.

May 8, 2026
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