15 research outputs found
Exploiting Weak Supermodularity for Coalition-Proof Mechanisms
Under the incentive-compatible Vickrey-Clarke-Groves mechanism, coalitions of
participants can influence the auction outcome to obtain higher collective
profit. These manipulations were proven to be eliminated if and only if the
market objective is supermodular. Nevertheless, several auctions do not satisfy
the stringent conditions for supermodularity. These auctions include
electricity markets, which are the main motivation of our study. To
characterize nonsupermodular functions, we introduce the supermodularity ratio
and the weak supermodularity. We show that these concepts provide us with tight
bounds on the profitability of collusion and shill bidding. We then derive an
analytical lower bound on the supermodularity ratio. Our results are verified
with case studies based on the IEEE test systems
Designing Coalition-Proof Reverse Auctions over Continuous Goods
This paper investigates reverse auctions that involve continuous values of
different types of goods, general nonconvex constraints, and second stage
costs. We seek to design the payment rules and conditions under which
coalitions of participants cannot influence the auction outcome in order to
obtain higher collective utility. Under the incentive-compatible
Vickrey-Clarke-Groves mechanism, we show that coalition-proof outcomes are
achieved if the submitted bids are convex and the constraint sets are of a
polymatroid-type. These conditions, however, do not capture the complexity of
the general class of reverse auctions under consideration. By relaxing the
property of incentive-compatibility, we investigate further payment rules that
are coalition-proof without any extra conditions on the submitted bids and the
constraint sets. Since calculating the payments directly for these mechanisms
is computationally difficult for auctions involving many participants, we
present two computationally efficient methods. Our results are verified with
several case studies based on electricity market data
Multi-robot task allocation for safe planning under dynamic uncertainties
This paper considers the problem of multi-robot safe mission planning in
uncertain dynamic environments. This problem arises in several applications
including safety-critical exploration, surveillance, and emergency rescue
missions. Computation of a multi-robot optimal control policy is challenging
not only because of the complexity of incorporating dynamic uncertainties while
planning, but also because of the exponential growth in problem size as a
function of the number of robots. Leveraging recent works obtaining a tractable
safety maximizing plan for a single robot, we propose a scalable two-stage
framework to solve the problem at hand. Specifically, the problem is split into
a low-level single-agent planning problem and a high-level task allocation
problem. The low-level problem uses an efficient approximation of stochastic
reachability for a Markov decision process to handle the dynamic uncertainty.
The task allocation, on the other hand, is solved using polynomial-time forward
and reverse greedy heuristics. The safety objective of our multi-robot safe
planning problem allows an implementation of the greedy heuristics through a
distributed auction-based approach. Moreover, by leveraging the properties of
the safety objective function, we ensure provable performance bounds on the
safety of the approximate solutions proposed by these two heuristics. Our
result is illustrated through case studies
Actuator Placement for Optimizing Network Performance under Controllability Constraints
With the rising importance of large-scale network control, the problem of
actuator placement has received increasing attention. Our goal in this paper is
to find a set of actuators minimizing the metric that measures the average
energy consumption of the control inputs while ensuring structural
controllability of the network. As this problem is intractable, greedy
algorithm can be used to obtain an approximate solution. To provide a
performance guarantee for this approach, we first define the submodularity
ratio for the metric under consideration and then reformulate the structural
controllability constraint as a matroid constraint. This shows that the problem
under study can be characterized by a matroid optimization involving a weakly
submodular objective function. Then, we derive a novel performance guarantee
for the greedy algorithm applied to this class of optimization problems.
Finally, we show that the matroid feasibility check for the greedy algorithm
can be cast as a maximum matching problem in a certain auxiliary bipartite
graph related to the network graph
Game Theoretic Analysis of Electricity Market Auction Mechanisms
We consider two prominent mechanisms for the electricity market; the pay-as-bid mechanism, currently applied in certain control reserve markets, and the proposed Vickrey- Clarke-Groves mechanism, an established auction mechanism used in advertising and spectrum auctions, for example. Bringing in tools from game theory and auction theory, we compare the Nash equilibria of these two mechanisms in terms of social efficiency and strategic behavior of the players. Furthermore, by formulating a coalitional game corresponding to the electricity market, we propose alternative mechanisms that incentivize truthful bidding while ensuring shill bidding is not profitable. Finally, we analyze the proposed mechanisms in a case study based on electricity market data