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28 lis 2009 · Firstly, PHP doesn't have multi-dimensional arrays, it has arrays of arrays. Secondly, you can write a function that will do it: function declare($m, $n, $value = 0) { return array_fill(0, $m, array_fill(0, $n, $value)); }
2 sie 2019 · The normal (or strategic form) game is usually represented by a matrix which shows the players, strategies, and payoffs. When a game is presented in normal form, it is presumed that each player acts simultaneously or, at least, without knowing the actions of the other.
PHP supports multidimensional arrays that are two, three, four, five, or more levels deep. However, arrays more than three levels deep are hard to manage for most people. The dimension of an array indicates the number of indices you need to select an element.
The matrix provided is a normal-form representation of a game in which players move simultaneously (or at least do not observe the other player's move before making their own) and receive the payoffs as specified for the combinations of actions played.
A normal form describes a simultaneous, finite game using matrix representation. The word „game“ is taken from the game theory which studies how to solve decision problems between participants of the game, most often between people.
Identify situations in which normal form games are a suitable model of a problem. Manually calculate the best responses and Nash equilibria for two-player normal form games. Compare and contrast pure strategies and mixed strategies.
Normal-form game¶ A "Normal-form" game has three components: A set of players, represented by a vector $I$ A vector of actions, $A_i$ that each player can take; A matrix of pay-offs, $U$ dependent on both the actions of each player as well as the actions of the opponents