Weak Monotonicity Characterizes Deterministic Dominant-Strategy Implementation
证明，在多维类型下，一个确定性的社会选择函数是占优策略激励相容的，当且仅当它满足弱单调性条件。该条件要求，若改变某代理人类型导致结果变化，则新旧结果在新类型下的效用差不能小于在原类型下的效用差。
We characterize dominant-strategy incentive compatibility with multidimensional types. A deterministic social choice function is dominant-strategy incentive compatible if and only if it is weakly monotone (W-Mon). The W-Mon requirement is the following: If changing one agent's type (while keeping the types of other agents fixed) changes the outcome under the social choice function, then the resulting difference in utilities of the new and original outcomes evaluated at the new type of this agent must be no less than this difference in utilities evaluated at the original type of this agent.