Supermodular mechanism design
Supermodular mechanism design
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超模块化机构设计
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发表时间：
2010
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通讯作者：
Laurent Mathevet
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作者：
Laurent Mathevet
本文介绍了一种机制设计方法，该方法允许使用对有限理性具有健壮性的机制来处理多重均衡问题。这种方法是构建超模块机制的工具，即诱导具有战略互补性的博弈的机制。在拟线性环境中，我证明了，如果一个社会选择函数可以通过一种机制来实现，该机制可以产生有限的战略替代--而不是战略互补--那么这个机制就可以转化为一个实现社会选择函数的超模块机制。如果社会选择函数也满足某种效率标准，那么它就承认了一种平衡预算的超模块机制。在这些结果的基础上，我解决了多重均衡问题。给出了一个社会选择函数可用一个超模机构实现的充分条件，该超模机构的均衡包含在所有超模机构中的最小区间内。其次是超模在唯一均衡下可实现性的条件。最后，我为具有一般偏好的环境中的超模块实现提供了一个启示原则。
This paper introduces a mechanism design approach that allows dealing with the multiple equilibrium problem, using mechanisms that are robust to bounded rationality. This approach is a tool for constructing supermodular mechanisms, i.e., mechanisms that induce games with strategic complementarities. In quasilinear environments, I prove that if a social choice function can be implemented by a mechanism that generates bounded strategic substitutes—as opposed to strategic complementarities—then this mechanism can be converted into a supermodular mechanism that implements the social choice function. If the social choice function also satisfies some efficiency criterion, then it admits a supermodular mechanism that balances the budget. Building on these results, I address the multiple equilibrium problem. I provide sufficient conditions for a social choice function to be implementable with a supermodular mechanism whose equilibria are contained in the smallest interval among all supermodular mechanisms. This is followed by conditions for supermodular implementability in unique equilibrium. Finally, I provide a revelation principle for supermodular implementation in environments with general preferences.