Abstract

We consider the study of a class of optimization problems with applications towards profit maximization. One feature of the classical treatment of optimization problems is that the space over which the optimization is being performed, i.e., the input description of the problem, is assumed to be publicly known to the optimizer. This assumption does not always accurately represent the situation in practical applications. Recently, with the advent of the Internet as one of the most important arenas for resource sharing between parties with diverse and selfish interests, this distinction has become more readily apparent. The inputs to many optimizations being performed are not publicly known in advance. Instead they must be solicited from companies, computerized agents, individuals, etc. that may act selfishly to promote their own self-interests. In particular, they may lie about their values or may not adhere to specified protocols if it benefits them. An auction is

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