Titlebook: Balanced Silverman Games on General Discrete Sets; Gerald A. Heuer,Ulrike Leopold-Wildburger Book 1991 Springer-Verlag Berlin Heidelberg 1

notion

2 , 2 ,games, in the sense that each player has a 2-component optimal mixed strategy. In this section we shall identify all irreducible 2 by 2 Silverman games, and in the next section are some theorems giving conditions under which games reduce to 2 by 2. “Game” hereafter will always mean “Silverman game.”

籠子

3 , 3 , W?. and W?. are already the essential sets. The nine diagonals and the solutions of the corresponding 3 by 3 games are given below. We abbreviate the diagonal elements -1 and +1 by - and +, respectively. P = (p., p.,p.) is the optimal strategy for Player I, Q = (q.,q.,q.) that for Player II. V is the game value.

DOSE

Reduction of balanced games to even order,uced game, corresponding to (A), (B), (C) and (D) in (8.0.4). In our description of these, the first nonzero main-diagonal element is again always -1, and off-diagonal zeros are concentrated in a middle segment of the first subdiagonal. The remainder of th€ matrix is the same in all cases, and may be described by the diagram in Figure 9.

genuine

HAVOC

Blood-Vessels

樹上結(jié)蜜糖

Karl Jousten,Uwe Friedrichsen,Erik LippeltWe conclude with brief remarks about the evidence that the reduced games obtained in Sections 8 and 9 are not further reducible. (Those in Sections 10 and 11 clearly are not.)

obstinate

Games with saddle points,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:

Angioplasty

戰(zhàn)役

2 , 2 , , = 1,We show now how all of the reduced games in Sections 8 and 9 reduce further, if . = 1, to 2 by 2 games with matrix ..