Search results
Results from the WOW.Com Content Network
A payoff function for a player is a mapping from the cross-product of players' strategy spaces to that player's set of payoffs (normally the set of real numbers, where the number represents a cardinal or ordinal utility—often cardinal in the normal-form representation) of a player, i.e. the payoff function of a player takes as its input a ...
Risk dominance and payoff dominance are two related refinements of the Nash equilibrium (NE) solution concept in game theory, defined by John Harsanyi and Reinhard Selten.A Nash equilibrium is considered payoff dominant if it is Pareto superior to all other Nash equilibria in the game. 1 When faced with a choice among equilibria, all players would agree on the payoff dominant equilibrium since ...
The rule goes as follows: if the first payoff number, in the payoff pair of the cell, is the maximum of the column of the cell and if the second number is the maximum of the row of the cell - then the cell represents a Nash equilibrium.
"A best response to a coplayer’s strategy is a strategy that yields the highest payoff against that particular strategy". [9] A matrix is used to present the payoff of both players in the game. For example, the best response of player one is the highest payoff for player one’s move, and vice versa.
The expected payoff for playing strategy 1 / 2 Y + 1 / 2 Z must be greater than the expected payoff for playing pure strategy X, assigning 1 / 2 and 1 / 2 as tester values. The argument for mixed strategy dominance can be made if there is at least one mixed strategy that allows for dominance.
Payoff functions, u: Assign a payoff to a player given their type and the action profile. A payoff function, u= (u 1 , . . . , u N ) denotes the utilities of player i Prior, p : A probability distribution over all possible type profiles, where p(t) = p(t 1 , . . . ,t N ) is the probability that Player 1 has type t 1 and Player N has type t N .
The excess of for a coalition is the quantity (); that is, the gain that players in coalition can obtain if they withdraw from the grand coalition under payoff and instead take the payoff (). The nucleolus of v {\displaystyle v} is the imputation for which the vector of excesses of all coalitions (a vector in R 2 N {\displaystyle \mathbb {R ...
As seen by the payoff matrix, there is no dominant strategy in the volunteer's dilemma. In a mixed-strategy Nash equilibrium , an increase in N players will decrease the likelihood that at least one person volunteers, which is consistent with the bystander effect .