Sep 25, 2012 feedback stackelberg solutions of infinite horizon stochastic differential games in models and methods in economics and management sciences, essays in honor of charles s. Teamoptimal closedloop stackelberg strategies in hierarchical control. Sethi, feedback stackelberg solutions of infinite horizon stochastic differential games, in models and methods in economics and management science eds. An anticipative feedback solution for the infinite horizon, linearquadratic, dynamic, stackelberg game.
An infinite horizon is longer than any finite horizon, even if that finite time period is a googol plex years, a googol plex being a googol raised to the googolth power, where a googol is 10 raised to the 100th power, which is many orders of magnitude greater than the latest estimate for the number of subatomic particles in the known universe. An anticipative feedback solution for infinite horizon linearquadratic dynamic stackelberg games. According to the lq stochastic optimal control theory of the meanfield type, a sufficient condition for the optimization of the follower has been put forward. The idea comes from kydland 1977 who suggested deriving a consistent. A cooperative stochastic differential game of transboundary. One of the main results in the theory is that the solution is provided by the linearquadratic regulator lqr, a feedback controller. This paper deals with the feedback stackelberg strategies for the discretetime meanfield stochastic systems in infinite horizon. Infinite horizon linear quadratic optimal control for. The idea comes from kydland 1977 who suggested deriving a consistent feedback solution for an infinite horizon, linearquadratic, dynamic, stackelberg game by varying the. Dynamic noncooperative game theory tamer basar, geert jan. In this paper, an infinitehorizon teamoptimal incentive stackelberg strategy is investigated for a class of stochastic linear systems with many noncooperative leaders and one follower.
An anticipative feedback solution for infinitehorizon linear. In traditional stackelberg security game models the attacker knows only the probability that each target is covered by the defender, but is oblivious to the detailed timing of the coverage schedule. The task is to develop a plan that minimizes the expected cost or maximize expected reward over some number of stages. Infinitehorizon teamoptimal incentive stackelberg games. In this framework, the government is the leader, setting monetary and fiscal policies, taking into. The purpose of the paper is to derive and illustrate a new suboptimalconsistent feedback solution for infinitehorizon linearquadratic dynamic stackelberg games which is in the same solution space as the infinite horizon dynamic programming feedback solution, but which puts the leader in a preferred equilibrium position. Aboukandil, closedform solution for discretetime linearquadratic stackelberg games, j. This solution lies in the same solution space as the infinite horizon, dynamicprogramming, feedback solution but puts the leader in a preferred equilibrium position. Selfconsistent feedback stackelberg equilibria for. This paper is concerned with openloop stackelberg equilibria of twoplayer linearquadratic differential games with mixed leadership. The idea comes from kydland 1977 who suggested deriving a consistent feedback solution for an. Alberto bressan, yilun jiang, 2019, dynamic games and applications approximation of sweeping processes and controllability for a setvalued evolution. This solution lies in the same solution space as the infinite horizon, dynamicprogramming, feedback solution. Applying the karushkuhntucker kkt conditions, the necessary conditions for the existence and uniqueness of the stackelberg strategies are derived and the stackelberg strategies are expressed as linear feedback forms involving the state and its mean based on the solutions k i, k i, i 1, 2 of a set of crosscoupled stochastic algebraic.
Management consulting infinite horizons consulting, llc. Afterwards we apply a version of the folk theorem and obtain a wide range of sustainable efficient equilibria, one of which coincides with the nash bargaining solution. Assuming that the state space is onedimensional, we prove that the nash equilibrium solution in feedback form is stable under nonlinear perturbations. This was previously called feedback stackelberg strategy 19 to distinguish it from closed loop stackelberg strategy. Citeseerx document details isaac councill, lee giles, pradeep teregowda. It also includes the stackelberg solution of a nonscalar differential game problem. An anticipative feedback solution for the infinitehorizon. What is an infinite horizon economy economics job market rumors. An anticipative feedback solution for the infinite horizon chen, baoline on. The theory of optimal control is concerned with operating a dynamic system at minimum cost. Feedback stackelberg solutions of infinitehorizon stochastic.
The purpose of the paper is to derive and illustrate a new suboptimalconsistent feedback solution for infinite horizon linearquadratic dynamic stackelberg games which is in the same solution space as the infinite horizon dynamic programming feedback solution, but which puts the leader in a preferred equilibrium position. Childhood and youth in germany and the united states, 19351967 oct 8, 2010 by roderick stackelberg. An anticipative feedback solution for the infinite horizon, linearquadratic, dynamic, stackelberg game, j. Feedback stackelberg strategies for the discretetime meanfield stochastic systems have been studied in infinite horizon. This solution lies in the same solution space as the infinitehorizon, dynamicprogramming, feedback solution but puts the leader in a preferred equilibrium position.
The paper introduces a concept of self consistent stackelberg equilibria for stochastic games in infinite time horizon, where the two players adopt feedback strategies and have exponentially. Although finding the solutions is based on the classical lagrangemultipliers technique, the treatment of bilinear matrix inequalities bmis can be avoided. We present a new solution algorithm for infinite horizon integrated assessment models, relying on a neural net approximation of the value function within an iterative version of the bellman equation. Solving infinite horizon growth models with an environmental. However, because the terms closedloop and feedback are interchangeably used in. Models and methods in economics and management science, 315, international series in operations research and management science, vol. An anticipative feedback solution for the infinite horizon, linear. A and infinite horizon optimal feedback control lab. Section 4 treats the infinite horizon version of the general problem, and obtains explicit and computationally attractive expressions.
Uniqueness of conservative solutions to the camassaholm equation via characteristics. Selfconsistent feedback stackelberg equilibria for infinite horizon. Citeseerx control of preferences in social networks. Since optimal stationary s, s policies are relatively simple to characterize, it is easy. Crossref qingyuan qi and huanshui zhang, output feedback control and stabilization for networked control systems with packet losses, ieee transactions on cybernetics, 47, 8, 2223, 2017. Simulations under different theories are compared with experiment data. These two theories can be compared by analyzing the corrections against different perturbation onsets. The maximum principle for global solutions of stochastic stackelberg differential games, siam journal on control and optimization, 2019, 575, 343444. Existing infinite horizon dynamic games often rely on the assumption of timeinvariant game structures for the derivation of equilibrium solutions. Mathematics stack exchange is a question and answer site for people studying math at any level and professionals in related fields. The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is called the lq problem. Thus, we exclude from its purview dynamic games played in discrete time. Feedback stackelberg solutions of infinitehorizon stochastic differential games article pdf available in ssrn electronic journal 198 september 2012 with 178 reads how we measure reads.
In many game situations, the game horizon would last for an indefinitely long period and one has to consider them as infinite horizon games. Definitions of infinite solutions, synonyms, antonyms, derivatives of infinite solutions, analogical dictionary of infinite solutions english. We leverage the best of breed solutions and the best of breed engineering to secure our clients throughout their it environment. Linear quadratic differential games with mixed leadership. Static outputfeedback incentive stackelberg game for discrete. Pdf for stochastic stackelberg differential games played by a leader and a follower, there. For the last two of them, an inefficient feedback stackelberg solution is first analyzed. Infinite horizon is our attempt to visualise a single moment in time, the cognitive shift experienced by an astronaut. In the fourth section, we treat the cayleymoser problem, a.
Feedback stackelberg solutions of infinitehorizon stochastic differential games in models and methods in economics and management sciences, essays in honor of charles s. In this chapter, we present a number of problems whose solutions may be e. Bensoussan a, chen s, sethi sp 2014 feedback stackelberg solutions of infinite horizon stochastic differential games. Our main focus will be on stackelberg equilibrium solutions in.
Oct, 2016 we consider a noncooperative game in infinite time horizon, with linear dynamics and exponentially discounted quadratic costs. Sethi, feedback stackelberg solutions of infinitehorizon stochastic differential games, in models and methods in economics. Selfconsistent feedback stackelberg equibria for infinite horizon. Wei zhang, jianghai hu and alessandro abate, 2012, infinite horizon switched lqr problems in discrete time. We present a sufficient condition for a feedback stackelberg equilibrium of a stochastic differential game on an infinite horizon. Moreover, necessary condition for the existence of solution for csares is also developed. In this paper, we model two ways of transboundary pollution. An anticipative feedback solution for infinite horizon linearquadratic dynamic stackelberg games an anticipative feedback solution for infinite horizon linearquadratic dynamic stackelberg games. The idea for the solution comes from kydlands 1977 suggestion to. Infinite resource solutions is a company with genuine integrity and one which values their employees and their clients.
A modification of the stackelberg strategy which satisfies the principle of optitnality is now defined. Our friends over at echoic audio provided the beautiful, emotive soundtrack. An anticipative feedback solution for the infinitehorizon, linearquadratic, dynamic, stackelberg game. Kogan, international series in operations research. Stackelberg solutions in discretetime infinite dynamic games are 3, 10. We consider the problem of deriving optimal marketing policies for the spread of innovations in a social network. The general and executive management teams are tangible, fair, thorough, and transparent. An anticipative feedback solution for the infinite horizon, linearquadratic, dynamic, stackelberg game article in journal of economic dynamics and control 26910. Pdf the maximum principle for global solutions of stochastic. Recent interest in biological games and mathematical finance make this classic 1982 text a necessity once again. Static output feedback stackelberg strategy of infinite horizon. Feedback stackelberg strategies for the discretetime mean. This paper derives and illustrates a new suboptimalconsistent feedback solution for an infinite horizon, linearquadratic, dynamic, stackelberg game. Feedback stackelbergnash equilibria in mixed leadership.
This letter investigates an infinitehorizon incentive stackelberg game for. In traditional stackelberg security game models the attacker knows only the probability that each target is covered by. Unlike other books in the field, this text provides an overview of the analysis of dynamicdifferential zerosum and nonzerosum games and simultaneously stresses the role of different information patterns. In the infinite horizon, however, duggan recasts odysseus as a survivor of the afghanistan war. Selfconsistent feedback stackelberg equilibria for infinite horizon stochastic games. This paper derives and illustrates a new suboptimalconsistent feedback solution for an infinitehorizon, linearquadratic, dynamic, stackelberg game. An anticipative feedback solution for infinitehorizon. Moreover, by means of the close interrelationship between the riccati equations and the set of equations satisfied by. The analysis shows that, in a generic setting, the linearquadratic game can have either one or infinitely many.
However, because the terms closedloop and feedback are interchangeably used in other contexts. Hiroaki mukaidani and hua xu, infinite horizon linearquadratic stackelberg games for discretetime stochastic systems, automatica, 76, 301, 2017. We seek to compute policies that account for i endogenous network influences, ii the presence of competitive firms, that also wish to influence the network, and iii possible uncertainties in the network. Odysseus problems of homer fidelity, family, relationships with the gods are refigured as issues of us aggression, drug abuse among soldiers, and, well, infidelity. An anticipative feedback solution for the infinite horizon, linearquadratic, dynamic, stackelberg game jan 21, 20 by baoline chen and peter a.
Pdf feedback stackelberg solutions of infinitehorizon. Stability of feedback solutions for infinite horizon. Pdf stackelberg equilibria for discretetime dynamic games part i. A moment so profound so all encompassing and beautiful that words were simply not enough. The classical proofs for the existence of a stationary s, s inventory policy that minimizes the total discounted or average cost over an infinite horizon are lengthy because they depend heavily on the optimality results for corresponding finite horizon models. Feedback stackelberg solutions of infinite horizon stochastic differential games in models and methods in economics and management sciences, essays in honor of charles s. Infinite understands that enterprise security architecture is a combination of people process and platform.
Survey of nash and stackelberg equilibrim strategies in. Each player maximizes her profit over the game horizon. Capital accumulation and income distribution as the. An anticipative feedback solution for the infinite. What is the difference between finite and infinite horizon. Explicit conditions are obtained for both the finite and infinite horizon problems under which the cls solution is a representation of the optimal feedback solution of a related team problem which is defined as the joint minimization of the leaders cost function. Considering the fact that transboundary pollution control calls for the cooperation between interested parties, this paper studies a cooperative stochastic differential game of transboundary industrial pollution between two asymmetric nations in infinite horizon level. In this paper we characterize the feedback equilibrium of a general infinite horizon stackelberg nash differential game where the roles of the players are mixed.
Nash equilibrium solution nash solution stackelberg equilibrium solution. Stackelberg meaning and origin of the name stackelberg. He has various trials and tribulations getting home. An anticipative feedback solution for the infinite horizon. Therefore, there are no associated termination actions. Stackelberg equilibria for discretetime dynamic games part i. Stackelberg games form the core of a number of tools deployed for computing optimal patrolling strategies in adversarial domains, such as the us federal air marshall service and the us coast guard. We prove that, under some appropriate assumptions on the coefficients, there exists a unique stackelberg solution to such a differential game. Brief paper teamoptimal closedloop stackelberg strategies. This condition gives rise to a system of elliptic partial differential equations involving a static stackelberg game at the level of hamiltonian. Kogan, international series in operations research and management science 198, springer, 2014, 315. An incentive structure is adopted which allows for the leaders teamoptimal nash solution. Robust nash static output feedback strategy for uncertain markov jump.
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