493 research outputs found
On a Class of Multistage Stochastic Hierarchical Problems
In this paper, following the multistage stochastic approach proposed by Rockafellar and Wets, we analyze a class of multistage stochastic hierarchical problems: the Multistage Stochastic Optimization Problem with Quasi-Variational Inequality Constraints. Such a problem is defined in a suitable functional setting relative to a finite set of possible scenarios and certain information fields. The key of this multistage stochastic hierarchical problem turns out to be the nonanticipativity: some constraints have to be included in the formulation to take into account the partial information progressively revealed. In this way, we are able to study real-world problems in which the hierarchical decision processes are characterized by sequential decisions in response to an increasing level of information. As an application of this class of multistage stochastic hierarchical problems, we focus on the study of a suitable Single-Leader-Multi-Follower game
A Coevolutionary Particle Swarm Algorithm for Bi-Level Variational Inequalities: Applications to Competition in Highway Transportation Networks
A climate of increasing deregulation in traditional highway transportation,
where the private sector has an expanded role in the provision of traditional
transportation services, provides a background for practical policy issues to be investigated.
One of the key issues of interest, and the focus of this chapter, would
be the equilibrium decision variables offered by participants in this market. By assuming
that the private sector participants play a Nash game, the above problem can
be described as a Bi-Level Variational Inequality (BLVI). Our problem differs from
the classical Cournot-Nash game because each and every player’s actions is constrained
by another variational inequality describing the equilibrium route choice of
users on the network. In this chapter, we discuss this BLVI and suggest a heuristic
coevolutionary particle swarm algorithm for its resolution. Our proposed algorithm
is subsequently tested on example problems drawn from the literature. The numerical
experiments suggest that the proposed algorithm is a viable solution method for
this problem
A Hierarchical Game with Strategy Evolution for Mobile Sponsored Content and Service Markets
In sponsored content and service markets, the content and service providers
are able to subsidize their target mobile users through directly paying the
mobile network operator, to lower the price of the data/service access charged
by the network operator to the mobile users. The sponsoring mechanism leads to
a surge in mobile data and service demand, which in return compensates for the
sponsoring cost and benefits the content/service providers. In this paper, we
study the interactions among the three parties in the market, namely, the
mobile users, the content/service providers and the network operator, as a
two-level game with multiple Stackelberg (i.e., leader) players. Our study is
featured by the consideration of global network effects owning to consumers'
grouping. Since the mobile users may have bounded rationality, we model the
service-selection process among them as an evolutionary-population follower
sub-game. Meanwhile, we model the pricing-then-sponsoring process between the
content/service providers and the network operator as a non-cooperative
equilibrium searching problem. By investigating the structure of the proposed
game, we reveal a few important properties regarding the equilibrium existence,
and propose a distributed, projection-based algorithm for iterative equilibrium
searching. Simulation results validate the convergence of the proposed
algorithm, and demonstrate how sponsoring helps improve both the providers'
profits and the users' experience
Establishing Nash equilibrium of the manufacturer-supplier game in supply chain management
We study a game model of multi-leader and one-follower in supply chain optimization where n suppliers compete to provide a single product for a manufacturer. We regard the selling price of each supplier as a pre-determined parameter and consider the case that suppliers compete on the basis of delivery frequency to the manufacturer. Each supplier’s profit depends not only on its own delivery frequency, but also on other suppliers’ frequencies through their impact on manufacturer’s purchase allocation to the suppliers. We first solve the follower’s (manufacturer’s) purchase allocation problem by deducing an explicit formula of its solution. We then formulate the n leaders’ (suppliers’) game as a generalized Nash game with shared constraints, which is theoretically difficult, but in our case could be solved numerically by converting to a regular variational inequality problem. For the special case that the selling prices of all suppliers are identical, we provide a sufficient and necessary condition for the existence and uniqueness of the Nash equilibrium. An explicit formula of the Nash equilibrium is obtained and its local uniqueness property is proved
Variational Inequality Approach to Stochastic Nash Equilibrium Problems with an Application to Cournot Oligopoly
In this note we investigate stochastic Nash equilibrium problems by means of
monotone variational inequalities in probabilistic Lebesgue spaces. We apply
our approach to a class of oligopolistic market equilibrium problems where the
data are known through their probability distributions.Comment: 19 pages, 2 table
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