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In game theory, normal form is a description of a game. Unlike extensive form, normal-form representations are not graphical per se, but rather represent the game by way of a matrix.
De nition of Normal-Form Game. nite n-person game, G =< N; A; u >. N = f1; 2; :::; ng is the set of players. A = fA1; A2; :::; Ang is a set of available actions. = (a1; a2; :::; an) 2 A is an action pro le (or a pure strategy pro le). u = fu1; u2; :::ung is a set of utility functions for n agents.
Learn the basic concepts and examples of normal form games, where players choose strategies simultaneously and maximize utility. Find out how to compute Nash equilibria using continuity, dominance, and mixed strategies.
Learn the definition and properties of normal-form games, a model of multi-agent decision theory with common knowledge and utility functions. See examples of dominant strategy equilibrium and Nash equilibrium, and their computational complexity.
1 Normal Form Games. normal form Game G consists of three elements G = (I, S, u); where. I = {1, 2, . . . , n} is the set of decision makers, the players. S = S1, ×S2 × · · · × Sn describes the feasible actions of the players. The players choose a strategy. = (s1, s2, . . . , sn) ∈ S simultaneously. An outcome is obtained.
Analysis: The set of NE in this game is infinite (all pairs of numbers which sum up to exactly 100). Only one strategy (0) is weakly dominated. Yet people can predict quite well how this game will be played in reality
Learn the basics of normal-form games, a model of multiagent decision making with common knowledge and expected utility. Explore the concepts of dominant strategy, Nash equilibrium and PPAD complexity, with examples and proofs.
