Graph continuous function: Difference between revisions

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==Notation and preliminaries==

Consider a [[game]] with <math>N</math> agents with agent <math>i</math> having strategy <math>A_i\subseteq\Bbb{R}</math>; write <math>\mathbf{a}</math> for an N-tuple of actions (iei.e. <math>\mathbf{a}\in\prod_{j=1}^NA_j</math>) and <math>\mathbf{a}_{-i}=(a_1,a_2,\ldots,a_{i-1},a_{i+1},\ldots,a_N)</math> as the vector of all agents' actions apart from agent <math>i</math>.

Let <math>U_i:A_i\longrightarrow\Bbb{R}</math> be the payoff function for agent <math>i</math>.