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We explore a reputation game based on utility function.This game models "Hold-up" situations potentially regulated with a reputation mechanism.In this game,players may adopt an opportunistic behavior or a fair-play attitude.This kind of behavior will determine each players pay-off and impact each players reputation.Reputation is determined by the valuation of reciprocal behaviors adopted by player and has strong influence on contracting opportunities.With the help of utility function we verify,in this reputation game,how the agents take their optimal strategy to maximizing each corresponding utility function.