Abstract
The theorems in [7] dealing with classes 1A, 2A and 2B do not depend on the strategy sets being disjoint, and include all Silverman games where at least one player has an optimal pure strategy, except the symmetric 1 by 1 case:
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THEOREM 2.1. In the symmetric Silverman game (S,T,ν), suppose that there is an element c in S such that c < Tci for all ci in S, and that S n (c,Tc) = Φ. Then pure strategy c is optimal.
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PROOF. Let A(x,y) be the payoff function. By symmetry the game value is 0. Since A(c,y) = 1,0 or ν according as y < c, y = c or y ≥ Tc, we have A(c, y) ≥ 0 for every y in S.
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© 1991 Springer-Verlag Berlin Heidelberg
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Heuer, G.A., Leopold-Wildburger, U. (1991). Games with saddle points. In: Balanced Silverman Games on General Discrete Sets. Lecture Notes in Economics and Mathematical Systems, vol 365. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-95663-8_2
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DOI: https://doi.org/10.1007/978-3-642-95663-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54372-5
Online ISBN: 978-3-642-95663-8
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