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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.
I prefer the ordered pair, mainly because it's the most standard notation but also because it's easier to edit than the two-row table. Color-coding is nice when first introducing the idea of a payoff matrix, to clarify whose payoff is whose (I always had trouble remembering that, even after I'd been studying the subject for a while.)
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.
"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.
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 .
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