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A Conceptual Mechanism Design Activity for an Introduction to Mechanical Engineering Course
A conceptual design activity is presented in this paper to introduce freshman students to motion transmission with simple gear train mechanisms. The activity requires students to select components from a catalog and perform kinematic simulations using CAD software. The activity described in this paper was implemented in an introduction to mechanical engineering course but it could also be deployed in an upper-level, undergraduate mechanisms course. The activity was successfully administered to a class of 221 students during the Spring 2017 semester but can be administered to smaller classes as well. A description of the activity is presented along with a discussion of the resources and personnel required (instructors and teaching assistants).
The activity is considered simple to implement, requiring only a computer station with CAD software available in most engineering schools. Continuous improvements to the project are made based on faculty observations and assessments, as well as a survey administered to the students.Cockrell School of Engineerin
Supermodular mechanism design
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.Implementation, mechanisms, learning, strategic complementarities, supermodular games
Robust Mechanism Design
The mechanism design literature assumes too much common knowledge of the environment among the players and planner. We relax this assumption by studying implementation on richer type spaces. We ask when ex post implementation is equivalent to interim (or Bayesian) implementation for all possible type spaces. The equivalence holds in the case of separable environments; examples of separable environments arise (1) when the planner is implementing a social choice function (not correspondence); and (2) in a quasilinear environment with no restrictions on transfers. The equivalence fails in general, including in some quasilinear environments with budget balance. In private value environments, ex post implementation is equivalent to dominant strategies implementation. The private value versions of our results offer new insights into the relation between dominant strategy implementation and Bayesian implementation.Mechanism design, Common knowledge, Universal type space, Interim equilibrium, Ex-post equilibrium, Dominant strategies
Mechanism Design with Strategic Mediators
We consider the problem of designing mechanisms that interact with strategic
agents through strategic intermediaries (or mediators), and investigate the
cost to society due to the mediators' strategic behavior. Selfish agents with
private information are each associated with exactly one strategic mediator,
and can interact with the mechanism exclusively through that mediator. Each
mediator aims to optimize the combined utility of his agents, while the
mechanism aims to optimize the combined utility of all agents. We focus on the
problem of facility location on a metric induced by a publicly known tree. With
non-strategic mediators, there is a dominant strategy mechanism that is
optimal. We show that when both agents and mediators act strategically, there
is no dominant strategy mechanism that achieves any approximation. We, thus,
slightly relax the incentive constraints, and define the notion of a two-sided
incentive compatible mechanism. We show that the -competitive deterministic
mechanism suggested by Procaccia and Tennenholtz (2013) and Dekel et al. (2010)
for lines extends naturally to trees, and is still -competitive as well as
two-sided incentive compatible. This is essentially the best possible. We then
show that by allowing randomization one can construct a -competitive
randomized mechanism that is two-sided incentive compatible, and this is also
essentially tight. This result also closes a gap left in the work of Procaccia
and Tennenholtz (2013) and Lu et al. (2009) for the simpler problem of
designing strategy-proof mechanisms for weighted agents with no mediators on a
line, while extending to the more general model of trees. We also investigate a
further generalization of the above setting where there are multiple levels of
mediators.Comment: 46 pages, 1 figure, an extended abstract of this work appeared in
ITCS 201
Mechanism Design with Limited Commitment
We develop a tool akin to the revelation principle for mechanism design with
limited commitment. We identify a canonical class of mechanisms rich enough to
replicate the payoffs of any equilibrium in a mechanism-selection game between
an uninformed designer and a privately informed agent. A cornerstone of our
methodology is the idea that a mechanism should encode not only the rules that
determine the allocation, but also the information the designer obtains from
the interaction with the agent. Therefore, how much the designer learns, which
is the key tension in design with limited commitment, becomes an explicit part
of the design. We show how this insight can be used to transform the designer's
problem into a constrained optimization one: To the usual truthtelling and
participation constraints, one must add the designer's sequential rationality
constraint.Comment: Added an omitted assumption in Section 4 (see footnote 21 and the
proof of Proposition 4.1
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