Abstract

Abstract: What should it mean for an agent toknowor believe an assertion is true with probability:99? Di erent papers [FH88, FZ88a, HMT88] givedi erent answers, choosing to use quite di erent probability spaces when computing the probability that an agent assigns to an event. We showthat each choice can be understood in terms of a betting game. This betting game itself can be understood in terms of three types of adversaries in uencing three di erent aspects of the game. The rst selects the outcome of all nondeterministic choices in the system� the second represents the knowledge of the agent's opponent in the betting game (this is the key place the papers mentioned above di er) � the third is needed in asynchronous systems to choose the time the bet is placed. We illustrate the need for considering all three types of adversaries with a number of examples. Given a class of adversaries, we show howto assign probability spaces to agents in a way most appropriate for that class, where \most appropriate " is made precise in terms of this betting game. We conclude by showing how di erent assignments of probability spaces (corresponding to di erent opponents) yield di erent levels of guarantees in probabilistic coordinated attack.

Citations