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 ...
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.
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 ...
On the other hand, weakly dominated strategies may be part of Nash equilibria. For instance, consider the payoff matrix pictured at the right. Strategy C weakly dominates strategy D. Consider playing C: If one's opponent plays C, one gets 1; if one's opponent plays D, one gets 0. Compare this to D, where one gets 0 regardless.
In game theory, a bimatrix game is a simultaneous game for two players in which each player has a finite number of possible actions. The name comes from the fact that the normal form of such a game can be described by two matrices - matrix describing the payoffs of player 1 and matrix describing the payoffs of player 2.
"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 payoffs are provided in the interior. The first number is the payoff received by the row player (Player 1 in our example); the second is the payoff for the column player (Player 2 in our example). Suppose that Player 1 plays Up and that Player 2 plays Left. Then Player 1 gets a payoff of 4, and Player 2 gets 3.
When academics talk about coordination failure, most cases are that subjects achieve risk dominance rather than payoff dominance. Even when payoffs are better when players coordinate on one equilibrium, many times people will choose the less risky option where they are guaranteed some payoff and end up at an equilibrium that has sub-optimal payoff.