Chapter 4 Flashcards
Best response, beliefs, Nash equilibrium
How does solving a multi-player game differ from solving a single-agent problem?
In multi-player games, the solution depends on the strategies of other players, whereas in single-agent problems, the solution is found directly once the setup is known.
What is a best response in game theory?
A best response is a strategy that maximizes a player’s payoff given the strategies chosen by other players.
What is a Nash equilibrium?
A Nash equilibrium is a set of strategies where each player is choosing their best response to the strategies of others, and no player has an incentive to deviate.
How can you identify a Nash equilibrium in a game?
Nash equilibria can be identified by checking if each player’s strategy is the best response to the strategies of others, often using brute force or focusing on best responses.
How does a Nash equilibrium relate to strictly dominated strategies?
A strictly dominated strategy cannot be a best response and therefore cannot be part of a Nash equilibrium.
What is the difference between Nash equilibrium and Pareto efficiency?
Nash equilibrium focuses on individual incentives with no unilateral gains, while Pareto efficiency ensures that no one can improve without making someone else worse off.
What is the price of anarchy in game theory?
The price of anarchy is the ratio of the social cost of the worst Nash equilibrium to the social cost of the best Pareto efficient outcome.
What is the role of beliefs in determining a player’s strategy?
A player’s belief is an assumption about the strategies of other players, which guides the choice of a best response.
Why should weakly dominated strategies not always be eliminated?
Eliminating weakly dominated strategies can sometimes remove the only Nash equilibrium, as seen in certain extended games.
