document: A strategy for a payoff-switching differential game based on fuzzy reasoning In this paper , a new concept of a payoff-switching differential game is introduced . In this new game , any one player at any time may have several choices of payoffs for the future . Moreover , the payoff-switching process , including the time of payoff switching and the outcome payoff , of any one player is unknown to the other . Indeed , the overall payoff , which is a sequence of several payoffs , is unknown until the game ends . An algorithm for determining a reasoning strategy based on fuzzy reasoning is proposed . In this algorithm , the fuzzy theory is used to estimate the behavior of one player during a past time interval . By deriving two fuzzy matrices GSM , game similarity matrix , and VGSM , variation of GSM , the behavior of the player can be quantified . Two weighting vectors are selected to weight the relative importance of the player 's behavior at each past time instant . Finally a simple fuzzy inference rule is adopted to generate a linear reasoning strategy . The advantage of this algorithm is that it provides a flexible way for differential game specialists to convert their knowledge into a `` reasonable '' strategy . A practical example of guarding three territories is given to illustrate our main ideas
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extractive_keyphrases: payoff switching outcome payoff reasoning strategy fuzzy reasoning fuzzy matrices game similarity matrix weighting vectors fuzzy inference differential game
abstractive_keyphrases: payoff-switching differential game