Balanced Silverman games on general discrete sets (Q1189397)

This book deals with a special type of 2-person zero-sum game in which each player's strategy represents a choice of a number of a given non- empty set. The higher number wins unless it is not ``much higher'' in an exactly defined sense depending on the antiplayer's choice. In such a case the player looses and pays a constant penalty to his partner. The usual approach to such games is based on the concept of a so-called `essential subgame' which is a Silverman game with reduced sets of strategies whose optimal strategies are identical with those of the original game. After presenting the results known from the literature and concerning mostly weary special cases of games with either identical or disjoint sets of strategies, the main attention is paid to games with more general strategy sets. It is shown that in many cases they can be reduced to finite and not very large sets of strategies, and the types of the obtained subgames are specified.