Search results
Results from the WOW.Com Content Network
The Nash equilibrium for a two-player, zero-sum game can be found by solving a linear programming problem. Suppose a zero-sum game has a payoff matrix M where element M i,j is the payoff obtained when the minimizing player chooses pure strategy i and the maximizing player chooses pure strategy j (i.e. the player trying to minimize the payoff ...
The first theorem in this sense is von Neumann's minimax theorem about two-player zero-sum games published in 1928, [2] which is considered the starting point of game theory. Von Neumann is quoted as saying "As far as I can see, there could be no theory of games
Solving mean payoff games can be shown to be polynomial-time equivalent to many core problems concerning tropical linear programming. [8] Another closely related game to the mean payoff game is the energy game, in which the Maximizer tries to maximize the smallest cumulative sum within the play instead of the long-term average.
The concept of a mixed-strategy equilibrium was introduced by John von Neumann and Oskar Morgenstern in their 1944 book The Theory of Games and Economic Behavior, but their analysis was restricted to the special case of zero-sum games. They showed that a mixed-strategy Nash equilibrium will exist for any zero-sum game with a finite set of ...
The power rule for differentiation was derived by Isaac Newton and Gottfried Wilhelm Leibniz, each independently, for rational power functions in the mid 17th century, who both then used it to derive the power rule for integrals as the inverse operation. This mirrors the conventional way the related theorems are presented in modern basic ...
Yao's principle may be interpreted in game theoretic terms, via a two-player zero-sum game in which one player, Alice, selects a deterministic algorithm, the other player, Bob, selects an input, and the payoff is the cost of the selected algorithm on the selected input.
There’s a lot about the rationale behind his thinking; because of zero-sum bias, Alex explains, Trey likely thought that his father’s affection for Veronica meant there was less for him.
In the mathematical theory of games, in particular the study of zero-sum continuous games, not every game has a minimax value. This is the expected value to one of the players when both play a perfect strategy (which is to choose from a particular PDF). This article gives an example of a zero-sum game that has no value. It is due to Sion and ...