【Penalize】 , 【fine】 ,  【amerce】 ,  【mulct】  mean to punish by depriving of something.

【Penalize】 usually presupposes a violation of laws or rules intended to maintain discipline or fair treatment for all; it implies exaction by an authority of a pecuniary penalty or a forfeiture of an advantage or, especially in games, the imposition of a handicap.

【Fine】  and  【amerce】  are chiefly found in technical legal use in reference to court cases, but their implications in extended use are not materially different. They and their corresponding nouns  【fine】  and amercement are distinguishable in that  【fine】  implies that the amount exacted is, within certain limits, prescribed by the law, while  【amerce】  and amercement indicate that it has been left to the discretion of the judge.

【Mulct】 implies subjection to a superior power which can legally or illegally exact a penalty (usually in money) for a breach of discipline or for failure to comply with its edicts. Sometimes it merely implies a 【fine】 or amercement or a withholding of money due. Often the word suggests forcible imposition or exaction of a heavy or oppressive penalty.