Exercise 2 Prove that in the beauty contest game the strategy profile (1, . . . , 1) is a Nash equilibrium.
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Solution proposed by Roberto Tauraso, Dipartimento di Matematica, Universit`a di Roma “Tor Vergata”, via della Ricerca Scientifica, 00133 Roma,
Since we are comparing two polynomials, it follows that the identity holds for all x
This is a contradiction because a positive integer is the sum of two squares if and only if all the prime factors congruent to 3 mod 4 have an even exponent in
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analogously BB ′ and CC ′ are the bisectors of the angles ∠ABC
when “real” status (the correction) of the past is received from server. compare it with corresponding
Client-side prediction + server correction, if game status not overly complex. or, slow
The Pb nuclei do not man- ifest any such effect in their groundstate, the stabilizing effect of the Z=82 shell closure seems to be so strong that even when the neutron shell is