300 research outputs found
Finding Optimal Strategies in a Multi-Period Multi-Leader-Follower Stackelberg Game Using an Evolutionary Algorithm
Stackelberg games are a classic example of bilevel optimization problems,
which are often encountered in game theory and economics. These are complex
problems with a hierarchical structure, where one optimization task is nested
within the other. Despite a number of studies on handling bilevel optimization
problems, these problems still remain a challenging territory, and existing
methodologies are able to handle only simple problems with few variables under
assumptions of continuity and differentiability. In this paper, we consider a
special case of a multi-period multi-leader-follower Stackelberg competition
model with non-linear cost and demand functions and discrete production
variables. The model has potential applications, for instance in aircraft
manufacturing industry, which is an oligopoly where a few giant firms enjoy a
tremendous commitment power over the other smaller players. We solve cases with
different number of leaders and followers, and show how the entrance or exit of
a player affects the profits of the other players. In the presence of various
model complexities, we use a computationally intensive nested evolutionary
strategy to find an optimal solution for the model. The strategy is evaluated
on a test-suite of bilevel problems, and it has been shown that the method is
successful in handling difficult bilevel problems.Comment: To be published in Computers and Operations Researc
Stackelberg Game for Distributed Time Scheduling in RF-Powered Backscatter Cognitive Radio Networks
In this paper, we study the transmission strategy adaptation problem in an
RF-powered cognitive radio network, in which hybrid secondary users are able to
switch between the harvest-then-transmit mode and the ambient backscatter mode
for their communication with the secondary gateway. In the network, a monetary
incentive is introduced for managing the interference caused by the secondary
transmission with imperfect channel sensing. The sensing-pricing-transmitting
process of the secondary gateway and the transmitters is modeled as a
single-leader-multi-follower Stackelberg game. Furthermore, the follower
sub-game among the secondary transmitters is modeled as a generalized Nash
equilibrium problem with shared constraints. Based on our theoretical
discoveries regarding the properties of equilibria in the follower sub-game and
the Stackelberg game, we propose a distributed, iterative strategy searching
scheme that guarantees the convergence to the Stackelberg equilibrium. The
numerical simulations show that the proposed hybrid transmission scheme always
outperforms the schemes with fixed transmission modes. Furthermore, the
simulations reveal that the adopted hybrid scheme is able to achieve a higher
throughput than the sum of the throughput obtained from the schemes with fixed
transmission modes
Oracles & Followers: Stackelberg Equilibria in Deep Multi-Agent Reinforcement Learning
Stackelberg equilibria arise naturally in a range of popular learning
problems, such as in security games or indirect mechanism design, and have
received increasing attention in the reinforcement learning literature. We
present a general framework for implementing Stackelberg equilibria search as a
multi-agent RL problem, allowing a wide range of algorithmic design choices. We
discuss how previous approaches can be seen as specific instantiations of this
framework. As a key insight, we note that the design space allows for
approaches not previously seen in the literature, for instance by leveraging
multitask and meta-RL techniques for follower convergence. We propose one such
approach using contextual policies, and evaluate it experimentally on both
standard and novel benchmark domains, showing greatly improved sample
efficiency compared to previous approaches. Finally, we explore the effect of
adopting algorithm designs outside the borders of our framework
Prognostics-Based Two-Operator Competition for Maintenance and Service Part Logistics
Prognostics and timely maintenance of components are critical to the continuing operation of a system. By implementing prognostics, it is possible for the operator to maintain the system in the right place at the right time. However, the complexity in the real world makes near-zero downtime difficult to achieve partly because of a possible shortage of required service parts. This is realistic and quite important in maintenance practice. To coordinate with a prognostics-based maintenance schedule, the operator must decide when to order service parts and how to compete with other operators who also need the same parts. This research addresses a joint decision-making approach that assists two operators in making proactive maintenance decisions and strategically competing for a service part that both operators rely on for their individual operations. To this end, a maintenance policy involving competition in service part procurement is developed based on the Stackelberg game-theoretic model. Variations of the policy are formulated for three different scenarios and solved via either backward induction or genetic algorithm methods. Unlike the first two scenarios, the possibility for either of the operators being the leader in such competitions is considered in the third scenario. A numerical study on wind turbine operation is provided to demonstrate the use of the joint decision-making approach in maintenance and service part logistics
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