Cooperative Game Theory Flashcards
What are the two core questions we want to answer using game theory?
1) Which coalition will form?
2) How should that coalition divide its payoffs among its members?
Which coalition usually (but not always) forms?
The grand coalition
What is the focus in a cooperative game?
On payoffs and coalitions and not on strategies
What is the implicit assumption in cooperative games?
That players can make binding agreements
What are three main solutions to solving how the worth (savings) of a coalition should be distributed?
1) The core
2) The shapley value
3) The nucleolus
How does the core describe payoff/savings distributions?
It consists of those payoff distributions that cannot be improved upon by any smaller coalition
What are common issues with the core?
It can be empty or contain a large set of payoff distributions
How does the shapley value describe payoff/savings distributions?
It consists of one point (vector) where each player receives his average contribution to the worth (savings) of coalitions
What are common issues with the shapley value?
It can be instable, even when stable outcomes exist (it exists outside of the core)
What is the strength of the nucleolus as an alternative to the core and shapley value?
It is unique and always stable as long as the core is non-empty
How does the nucleolus describe payoff/savings distributions?
The nucleolus assigns a unique payoff distribution to a game within the core, provided that the core is nonempty.
What is the general idea behind the nucleolus?
To make the largest dissatisfaction as small as possible. If there is more than one possibility to do this, then we also make the second largest dissatisfaction as small as possible, and so on.
