Cooperative game theory Flashcards
Classify the different types of game theory
Non-cooperative game theory - self interested agents
Cooperative game theory - agents form coalitions
Behavioral games - discrepancy between theory and reality in game theory
Evolutionary game theory - agents and populations evolve
Explain what we mean by cooperative game theory, especially in relation to non- cooperative game theory
Cooperative game theory strives to answer to questions
1 Which coalition will be formed by self-interested, rational agents
2 How is the utility divided among members of this coalition
Cooperative game is a game in which players negotiate their contracts so that they can make joint strategies while non cooperative games don’t form coalitions.
Describe and explain the formal description of a cooperative game
Given a set of agents Ag={1,2,n} that can form coalitions c1,c2…cM
a cooperative game is a pair G = where Ag is the agent-set and v is the characteristic function (expected utility)
What is the core?
The core is a set of outcomes for a coalition that no other coalition objects to,
if the core is non-empty then we have a solution
In relation to cooperative games, what is the Shapley value?
The Shapley value is a measurement for distributing utility among agents. It’s based on the idea that agents should get the average marginal contribution it makes, estimated over all possible positions that it would enter the coalition.
Satisfies 3 fairness axioms:
- Symmetry - Agents that make the same contribution to the coalition should get the same utility.
- Dummy player - Agents that don’t contribute to a coalition should only recieve what they could earn on their own.
- Additivity - Agents that play two games get the sum of two games. The agents does not benefit from playing the game more than once.
Explain marginal contribution net
A marginal contribution net is an extension of the induced subgraph and is an easy representation of Shapley values without doing a lot of calculations.
What are simple games?
Simple games are games with coalition values of either yes/no, winning/loosing etc
What are weighted voting games?
Weighted voting games are natural extension of simple games possibly reducing the number of players in these games.
Weighted voting game are a more concise way of representing many simple games, f.ex. instead of representing 100 senators explicitly we represent the different blocks of voters in parties.
What is coalitional structure formation?
Central forming of coalitions
1 All nodes are owned by a single designer
2 Maximize social welfare
Try to maximize total output of all agents/voters
Try to find optimal cooperation solution
