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The subgame perfect equilibrium in addition to the Nash equilibrium requires that the strategy also is a Nash equilibrium in every subgame of that game. This eliminates all non-credible threats , that is, strategies that contain non-rational moves in order to make the counter-player change their strategy.
The decision of each player can be viewed as determining two angles. Symmetric Nash equilibria that attain a payoff value of / for each player is shown, and each player volunteers at this Nash equilibrium. Furthermore, these Nash equilibria are Pareto optimal. It is shown that the payoff function of Nash equilibria in the quantum setting is ...
Finding Nash equilibrium in a game takes exponential time in the size of the representation. If the graphical representation of the game is a tree, we can find the equilibrium in polynomial time. In the general case, where the maximal degree of a node is 3 or more, the problem is NP-complete.
The solutions are normally based on the concept of Nash equilibrium, and these solutions are reached by using methods listed in Solution concept. Most solutions used in non-cooperative game are refinements developed from Nash equilibrium , including the minimax mixed-strategy proved by John von Neumann .
The group's total payoff is maximized when everyone contributes all of their tokens to the public pool. However, the Nash equilibrium in this game is simply zero contributions by all; if the experiment were a purely analytical exercise in game theory it would resolve to zero contributions because any rational agent does best contributing zero, regardless of whatever anyone else does.
Number of pure strategy Nash equilibria: A Nash equilibrium is a set of strategies which represents mutual best responses to the other strategies. In other words, if every player is playing their part of a Nash equilibrium, no player has an incentive to unilaterally change their strategy.
This player will also predict that the other players know that as well and will behave accordingly, so the maximum feasible number becomes 25. But, again, other players should know that, too. This process repeats indefinitely, and concludes with all players selecting 0, the Nash equilibrium for this game.
Remarkably, and, to many, counter-intuitively, the Nash equilibrium solution is in fact just $2; that is, the traveler values the antiques at the airline manager's minimum allowed price. For an understanding of why $2 is the Nash equilibrium consider the following proof: Alice, having lost her antiques, is asked their value.