Coalition Building
- coalition games
- enforceable agreements/alliances can be made between players
- cooperative game theory
- given the possible benefits of each cooperative alliance, which alliances are robust? Which ones are “fair”?
Cooperative Game
- set of players N
- characteristic function v
- assigns a value to each (sub-)coalition
- properties
- monotonicity: larger coaltition → larger payoff
- superadditivity: any 2 coalitions combined >= both coalitions separately
Solution: The Core
- no agent wants to deviate
- slides 3 13
- may be …
- not fair
- empty
- hard to compute
- any agreement within core is stable
- no coalition or sub-agreement would brake away
Shapley Value
- award based on marginal contribution
- depends on what is already present in a coalition
- expression after minus … Opportunity Cost of the coalition if the coalition does not include you
- shapley value may be outside of core → feasible, but not stable
Politics
- contribution power only takes into account the amount to reach majority
- if only 5% is missing to >50% then only 5% are actually meaningful
- anything over 5% is just hot air
- smaller coalitions partners are more meaningful than their vote share would suggest
- smaller parties get higher share of e.g. minister spots than their share of votes