AGT: cooperative game theory

Can there be cooperation in non-cooperative game theory?

• Yes

• No

How can cooperation be achieved in non-cooperative games?

• Through repeated games

• By including punishments and/or rewards

• By aligning individual utilities with those of all players

• By removing non-cooperative players

What is the focus of cooperative game theory?

• Actions

• Payoffs

• Preferences

• Coalitions

Which of the following coalitions are valid in cooperative game theory?

• Coalitions including no players

• Coalitions including one player

• Coalitions including several players

• Coalitions including all players in a game

Which of the following are types of cooperative games?

• Transferable utility games

• Non-transferable utility games

• Prisoner's dilemma

• Coordination game

What is a core?

• The Nash equilibrium of a cooperative game

• The Bayesian information maximising equilibrium in a cooperative game

• Solution to a cooperative game, where players cannot improve their payoffs by breaking off

• Solution to a cooperative game, where players can improve their payoffs by breaking off

Consider the following cooperative game: N = {1, 2, 3,4} and

v({1}) = v({2}) = 2, v({3}) = v({4}) = 4

v({1,2}) = v({1,3}) = v({1,4}) = 6, v({2,3}) = 9, v({3,4}) = 10,

v({1,2,3}) = v({1,2,4}) = v({2,3,4}) = 13,

v({1,2,3,4}) = 18

Which of the following solutions are in the core?

• (4, 4, 5, 5)

• (2, 4, 6, 6)

• (4, 5, 5, 4)

• None of the other options

What is a Shapley value?

• Efficient and symmetric way to distribute the payoff of the coalition to the coalition members

• A synonym for core solution

• A subset of outcomes satisfying conditions of pivotal players

Consider the following cooperative game: N = {1, 2, 3} and v({1}) = 2, v({2}) = 4, v({3}) = 6

v({1,2}) =6, v({1,3}) = 8, v({2,3}) = 12

v({1,2,3}) = 14

What is the Shapley value?

• (2, 5, 7)

• (4, 5, 7)

• (2, 4, 9)

• (3, 4, 6)