What is cooperative game theory economics?
Cooperative game theory deals with how coalitions, or cooperative groups, interact when only the payoffs are known. It is a game between coalitions of players rather than between individuals, and it questions how groups form and how they allocate the payoff among players.
What is a convex game?
In game theory, a convex game is one in which the incentives for joining a coalition increase as the coalition grows. This paper shows that the core of such a game — the set of outcomes that cannot be improved on by any coalition of players — is quite large and has an especially regular structure.
What is cooperative and non cooperative game theory?
Definition. Cooperative game theory focuses on how much players can appropriate given the value each coalition of player can create, while non-cooperative game theory focuses on which moves players should rationally make.
How do you prove a game is convex?
A coalition form game (N,v) with side payments is a convex game if for all coalitions S and T, v(S) + v(T) ≤ v(S ∩ T) + v(S ∪ T). This condition arises when each player provides some number of units of a homogeneous input and production displays increasing returns to scale.
What is a non-cooperative game in game theory?
In game theory, a non-cooperative game is a game with competition between individual players, as opposed to cooperative games, and in which alliances can only operate if self-enforcing (e.g. through credible threats). Negative-sum game and Zero-sum game are both types of non-cooperative games.
Do all games have Nash equilibrium?
While Nash proved that every finite game has a Nash equilibrium, not all have pure strategy Nash equilibria. For an example of a game that does not have a Nash equilibrium in pure strategies, see Matching pennies.
What is a superadditive game?
Superadditive Games •A game G = (N, v) is superadditive if for all S; T ⊂N, if S ∩ T = ∅, then v(S ∪T) ≥ v(S) + v(T). •Superadditivity is justified when coalitions can always work without interfering with one another
What is game theory in economics?
of anticipation and excitement, especially moving into the 1980s and early 1990s. Game theory is now a standard tool in economics. Contributions to game theory. are made by economists across the spectrum of fields and interests, and economists. regularly combine work in game theory with work in other areas.
What is superadditivity and when is it justified?
•Superadditivity is justified when coalitions can always work without interfering with one another •The value of two coalitions will be no less than the sum of their individual values. •Implies that the grand coalition has the highest payoff •How should the coalition divide its payoff? •in order to be fair •in order to be stable
What is game theory of entry deterrence?
Game Theory: A game of entry deterrence. If a new firm enters the market then the payoff will depend on whether the incumbent fights or accepts. If the incumbent fights they both get 0. If it does not fight then the incumbent gets 1 and the entrant gets 2. Therefore the equilibrium is for the new firm to enter and the incumbent to accept.