Strong Nash equilibrium
Encyclopedia
A strong Nash equilibrium is a Nash equilibrium
in which no coalition, taking the actions of its complements as given, can cooperatively deviate in a way that benefits all of its members
. While the Nash concept of stability defines equilibrium only in terms of unilateral deviations, strong Nash equilibrium allows for deviations by every conceivable coalition .
The strong Nash concept is criticized as too "strong" in that the environment allows for unlimited private communication. In fact, strong Nash equilibrium has to be Pareto-efficient
. As a result of these requirements, Strong Nash almost never exists.
A relatively weaker yet refined Nash stability concept is called coalition-proof Nash equilibrium
(CPNE) in which the equilibria are immune to multilateral deviations that are self-enforcing. Every correlated strategy supported by iterated strict dominance
and on the Pareto frontier is a CPNE. Further, it is possible for a game to have a Nash equilibrium that is resilient against coalitions less than a specified size k. CPNE is related to the theory of the core
.
Nash equilibrium
In game theory, Nash equilibrium is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally...
in which no coalition, taking the actions of its complements as given, can cooperatively deviate in a way that benefits all of its members
. While the Nash concept of stability defines equilibrium only in terms of unilateral deviations, strong Nash equilibrium allows for deviations by every conceivable coalition .
The strong Nash concept is criticized as too "strong" in that the environment allows for unlimited private communication. In fact, strong Nash equilibrium has to be Pareto-efficient
Pareto efficiency
Pareto efficiency, or Pareto optimality, is a concept in economics with applications in engineering and social sciences. The term is named after Vilfredo Pareto, an Italian economist who used the concept in his studies of economic efficiency and income distribution.Given an initial allocation of...
. As a result of these requirements, Strong Nash almost never exists.
A relatively weaker yet refined Nash stability concept is called coalition-proof Nash equilibrium
Coalition-Proof Nash Equilibrium
The concept of coalition-proof Nash equilibrium applies to certain "noncooperative" environments in which players can freely discuss their strategies but cannot make binding commitments .It emphasizes the immunization to deviations that are self-enforcing...
(CPNE) in which the equilibria are immune to multilateral deviations that are self-enforcing. Every correlated strategy supported by iterated strict dominance
Dominance (game theory)
In game theory, strategic dominance occurs when one strategy is better than another strategy for one player, no matter how that player's opponents may play...
and on the Pareto frontier is a CPNE. Further, it is possible for a game to have a Nash equilibrium that is resilient against coalitions less than a specified size k. CPNE is related to the theory of the core
Core (economics)
The core is the set of feasible allocations that cannot be improved upon by a subset of the economy's consumers. A coalition is said to improve upon or block a feasible allocation if the members of that coalition are better off under another feasible allocation that is identical to the first...
.