819 research outputs found
Game-Theoretic Pricing and Selection with Fading Channels
We consider pricing and selection with fading channels in a Stackelberg game
framework. A channel server decides the channel prices and a client chooses
which channel to use based on the remote estimation quality. We prove the
existence of an optimal deterministic and Markovian policy for the client, and
show that the optimal policies of both the server and the client have threshold
structures when the time horizon is finite. Value iteration algorithm is
applied to obtain the optimal solutions for both the server and client, and
numerical simulations and examples are given to demonstrate the developed
result.Comment: 6 pages, 4 figures, accepted by the 2017 Asian Control Conferenc
Convex-Concave Min-Max Stackelberg Games
Min-max optimization problems (i.e., min-max games) have been attracting a
great deal of attention because of their applicability to a wide range of
machine learning problems. Although significant progress has been made
recently, the literature to date has focused on games with independent strategy
sets; little is known about solving games with dependent strategy sets, which
can be characterized as min-max Stackelberg games. We introduce two first-order
methods that solve a large class of convex-concave min-max Stackelberg games,
and show that our methods converge in polynomial time. Min-max Stackelberg
games were first studied by Wald, under the posthumous name of Wald's maximin
model, a variant of which is the main paradigm used in robust optimization,
which means that our methods can likewise solve many convex robust optimization
problems. We observe that the computation of competitive equilibria in Fisher
markets also comprises a min-max Stackelberg game. Further, we demonstrate the
efficacy and efficiency of our algorithms in practice by computing competitive
equilibria in Fisher markets with varying utility structures. Our experiments
suggest potential ways to extend our theoretical results, by demonstrating how
different smoothness properties can affect the convergence rate of our
algorithms.Comment: 25 pages, 4 tables, 1 figure, Forthcoming in NeurIPS 202
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
Zero-Sum Stochastic Stackelberg Games
Zero-sum stochastic games have found important applications in a variety of
fields, from machine learning to economics. Work on this model has primarily
focused on the computation of Nash equilibrium due to its effectiveness in
solving adversarial board and video games. Unfortunately, a Nash equilibrium is
not guaranteed to exist in zero-sum stochastic games when the payoffs at each
state are not convex-concave in the players' actions. A Stackelberg
equilibrium, however, is guaranteed to exist. Consequently, in this paper, we
study zero-sum stochastic Stackelberg games. Going beyond known existence
results for (non-stationary) Stackelberg equilibria, we prove the existence of
recursive (i.e., Markov perfect) Stackelberg equilibria (recSE) in these games,
provide necessary and sufficient conditions for a policy profile to be a recSE,
and show that recSE can be computed in (weakly) polynomial time via value
iteration. Finally, we show that zero-sum stochastic Stackelberg games can
model the problem of pricing and allocating goods across agents and time. More
specifically, we propose a zero-sum stochastic Stackelberg game whose recSE
correspond to the recursive competitive equilibria of a large class of
stochastic Fisher markets. We close with a series of experiments that showcase
how our methodology can be used to solve the consumption-savings problem in
stochastic Fisher markets.Comment: 29 pages 2 figures, Appeared in NeurIPS'2
Minimum Violation Control Synthesis on Cyber-Physical Systems under Attacks
Cyber-physical systems are conducting increasingly complex tasks, which are
often modeled using formal languages such as temporal logic. The system's
ability to perform the required tasks can be curtailed by malicious adversaries
that mount intelligent attacks. At present, however, synthesis in the presence
of such attacks has received limited research attention. In particular, the
problem of synthesizing a controller when the required specifications cannot be
satisfied completely due to adversarial attacks has not been studied. In this
paper, we focus on the minimum violation control synthesis problem under linear
temporal logic constraints of a stochastic finite state discrete-time system
with the presence of an adversary. A minimum violation control strategy is one
that satisfies the most important tasks defined by the user while violating the
less important ones. We model the interaction between the controller and
adversary using a concurrent Stackelberg game and present a nonlinear
programming problem to formulate and solve for the optimal control policy. To
reduce the computation effort, we develop a heuristic algorithm that solves the
problem efficiently and demonstrate our proposed approach using a numerical
case study
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