Reference no: EM131333046
Consider the following two-player game with payoffs in R2:
(a) Write down the payoff function Uπ in the game Gπ for every π = (π1, π2) ∈ R2 (for the definition of Uπ see Equation (14.68) on page 588).
b) Draw the graph of the function val(Gπ ). That is, on the two-dimensional plane, where the x axis is identified with π1, and the y axis is identified with π2, draw val(Gπ1,π2 ) at each point.
(c) For the following sets C, compute the value of min 
as a function of π, and determine which of them are approachable by Player 1.
(i) C1 = {(1/2, 1/2)}.
(ii) C2 = [(0,1), (1,0)].
(iii) C3 = [(0,1), (0,0)].
(iv) C4 is the triangle whose vertices are (1,1), (1,0), and (1/2,1/2).
(v) C5 is the parallelogram whose vertices are (1/2, 1), (1/4, 1), (1/2, 0), and (3/4,0).
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