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Pricing in linear-quadratic dynamic games

Lillian J. Ratliff, Samuel Coogan, Daniel Calderone, S. Shankar Sastry
2012 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
We study a hierarchical linear-quadratic game with many dynamically coupled Nash followers and an uncoupled leader.  ...  The leader influences the game by choosing the quadratic dependence on control actions for each follower's cost function.  ...  dynamic games and we formulate the problem of designing pricing mechanisms for linear-quadratic dynamic games in discrete and continuous time as a convex feasibility problem.  ... 
doi:10.1109/allerton.2012.6483440 dblp:conf/allerton/RatliffCCS12 fatcat:tzbsz5sqxna3zkio6dmxx55fe4

Detecting the traders' strategies in minority–majority games and real stock-prices

V. Alfi, A. De Martino, L. Pietronero, A. Tedeschi
2007 Physica A: Statistical Mechanics and its Applications  
Price dynamics is analyzed in terms of a model which includes the possibility of effective forces due to trend followers or trend adverse strategies.  ...  Then we also analyze real (NYSE) stock-prices dynamics and it is possible to derive an indication for the the "sentiment" of the market for time intervals of at least one day. 89.65+Gh,  ...  The simplest assumption is to adopt a linear dependence: P (t + 1) − P (t) ∝ P (t) − P M (t) (2) In this case, the price dynamics can be described in terms of a RW with the existence of a linear force.  ... 
doi:10.1016/j.physa.2007.02.081 fatcat:5cfpjcgbhnfihfhf5fe7k4fqtu

Optimal Demand Response and Supply Schedule Under Market-Driven Price: A Stackelberg Dynamic Game Approach [article]

Yunhan Huang
2019 arXiv   pre-print
In this work, we use a Stackelberg infinite discrete-time dynamic game model to study the optimal supply schedule and the optimal demand response under a market-driven dynamic price.  ...  A set of linear constraints is developed to characterize the Stackeberg equilibrium. Simulation results show that the price is driven to a reasonable value.  ...  of the price (1) and (2) from a generalized stochastic linear quadratic dynamics game.  ... 
arXiv:1911.07365v1 fatcat:vi26heoyvbefjdrovz4eto2oye

Page 8366 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
(J-HROSEGD; Higashi-Hiroshima) The linear quadratic dynamic game for discrete-time descriptor systems.  ...  Game Theory Rev. 5 (2003), no. 4, 361-374. Summary: “The linear quadratic zero-sum dynamic game for dis- crete time descriptor systems is considered.  ... 

Bidding strategies in dynamic electricity markets

Ashkan R. Kian, Jose B. Cruz
2005 Decision Support Systems  
The optimal bidding strategies are developed mathematically using dynamic game theory. We deal with games that are nonlinear in the state equations.  ...  Attention is given to a problem, where the objective functions are quadratic in the deviations of trajectories from desired trajectories and quadratic in the control deviations from the nominal controls  ...  Therefore, we extend the existing theory for linear-quadratic tracking games to discrete-time non-linear-quadratic tracking games.  ... 
doi:10.1016/j.dss.2004.09.004 fatcat:rfpx2x6ihjdylnpykuyltefs4y

Dynamic Price Competition with Price Adjustment Costs and Product Differentiation

Gianluigi Vernasca
2003 Social Science Research Network  
We study a discrete time dynamic game of price competition with spatially di¤erentiated products and price adjustment costs.  ...  Moreover, we obtain the same convergence result when adjustment costs tend to in...nity. -Keywords: price adjustment costs, di¤erence game, Markov perfect equilibrium, Open-loop equilibrium.  ...  Moreover, in some cases linear quadratic models or linear quadratic approximations of non-linear games provide a good representation of oligopolistic behaviour especially around a deterministic steady  ... 
doi:10.2139/ssrn.486743 fatcat:ayjqcfgj2jdajngarcxpoh75si

Pricing for Coordination in Open–Loop Differential Games

Daniel Calderone, Lillian J. Ratliff, S. Shankar Sastry
2014 IFAC Proceedings Volumes  
We provide a method for designing a quadratic pricing scheme to induce a desired local Nash equilibrium in an open-loop differential game with nonlinear dynamics.  ...  The results are applied to the problem of inducing network managers to invest in security in a multi-network with an epidemic model of the spread of malware.  ...  In Ratliff et al. (2012) ; Calderone et al. (2013) ; Coogan et al. (2013) the problem of finding prices to induce a socially optimal Nash equilibrium in a linear quadratic game is solved.  ... 
doi:10.3182/20140824-6-za-1003.02655 fatcat:rftge2btxvgtff3ru3nbvvcdhy

Evolutionarily Stable Conjectures and Social Optimality in Oligopolies

Swapnika Reddy Rachapalli, Praveen Kulshreshtha
2013 Theoretical Economics Letters  
Following the evolutionary game-theoretic approach to analyze Conjectural Variations (CV) in oligopolies, a model is developed to derive the Evolutionarily Stable Strategies (ESS) for quantity-setting  ...  and price-setting oligopolies with CV, producing heterogeneous goods.  ...  An earlier version of the paper was presented at the "International Conference on Game Theory and Operations Research Applications (in honor of Prof. C. R. Rao and Prof.  ... 
doi:10.4236/tel.2013.31003 fatcat:www2cjyvrvgndjgo3d6vs45kkm

Page 4819 of Mathematical Reviews Vol. , Issue 2003f [page]

2003 Mathematical Reviews  
Differential games with linear dynamics and payoff functionals quadratic in the control variables and nonquadratic in the phase variables are analyzed with the help of pseudo-Ricatti equation techniques  ...  (NL-TILB-ER; Tilburg) Robust equilibria in indefinite linear quadratic differential games. (English summary) TSDG2002, Vol. I, IIT (St. Petersburg), 139-157, St. Petersburg State Univ. Inst.  ... 

Book announcements

2000 Discrete Applied Mathematics  
4.4.1 Pricing Game with Substitute Products 4.4.2 Production Game with Complementary Products 4.4.3 Multimarket Oligopoly 4.4.4 Arms Race Game 4.4.5 Trading Partner Search Game 4.4.6 Optimal  ...  Computation in Cellular Automata: A Selected Review 4.1 Introduction 4.2 Von Neumann's Self-Reproducing Cellular Automation 4.3 Universal Computation in Cellular Automata 4.4 Dynamics and Computation  ... 
doi:10.1016/s0166-218x(00)90007-6 fatcat:cemhaoz7rzdmdoec7pjjqiur2a

Page 3764 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews  
prices using a discrete deterministic nonlinear price model (125-148); Claus Weddepohl, Price adjustment models in a production economy (149-164); Daniel Léonard and Kazuo Nishimura, Nonlinear dynamics  ...  Selected papers from the 6th Workshop on Optimal Control, Dynamic Games, Nonlinear Dynamics and Adaptive Systems held in Vienna, May 1997, Edited by H. Dawid, G. Feichtinger and R. F. Hartl. Ann.  ... 

Strategic Delegation and Dynamic Competition

Engelbert J. Dockner, Clemens Löffler
2009 Social Science Research Network  
In this paper we analyze strategic delegation under the assumption that firms operate in dynamic oligopolies.  ...  We derive the optimal strategic incentive in this setting and point out that the dynamic incentive can be replicated by a static one in which firms play a conjectural variations equilibrium in the output  ...  In the case of linear demand and quadratic costs the dynamic conjectures consistent with closed-loop steady state equilibria are negative, constant, symmetric, and vary continuously with the discount rate  ... 
doi:10.2139/ssrn.1469439 fatcat:qubhiaqs3zdzfm33mz624k7kee

A Dynamic Model of Oligopoly in the Coffee Export Market

Larry S. Karp, Jeffrey M. Perloff
1993 American Journal of Agricultural Economics  
A linear-quadratic, dynamic feedback oligopoly model that nests various market structures is used to estimate the degree of competitiveness and the adjustment paths of the two largest coffee exporters,  ...  A linear-quadratic, dynamic feedback oligopoly model that nests various rnarket structures is used to eslimate the degree of cor~lpetitiveness and the adjusrrnent paths of the two largest coffee exporters  ...  The Linear-Qr~ndr~tic Dyrrornic Morirl The game-theoretic literature ahounds with very general dynamic models of oligopoly that do not lend themselves to estimation.  ... 
doi:10.2307/1242929 fatcat:46zog5lqtrhe5c44x2ng6lq5bm

A dynamic model of oligopoly and oligopsony in the U.S. potato-processing industry

Ani L. Katchova, Ian M. Sheldon, Mario J. Miranda
2005 Agribusiness  
from price taking through Nash-Cournot behavior to collusion+ In addition, we estimate market conduct and associated price distortions in a sub-game perfect, dynamic-feedback model, and compare the results  ...  In this paper, we estimate oligopoly and oligopsony price distortions in the U+S+ potato chips and frozen French fries sectors, based on a linear-quadratic, multi-period optimization model of processors  ...  SUMMARY AND CONCLUSIONS In this paper, we develop a linear-quadratic dynamic model to estimate oligopoly and oligopsony price distortions in the potato chips and frozen French fries sectors+ The empirical  ... 
doi:10.1002/agr.20055 fatcat:lu6pxnmu6rhanphf7vx55szqty

Page 3574 of Mathematical Reviews Vol. , Issue 89F [page]

1989 Mathematical Reviews  
author develops a pricing game with m sellers and n buyers.  ...  (YU-BELG-OS); Gaijjic, Z. (1-RTG4-EE) Recursive solution of linear-quadratic Nash games for weakly interconnected systems. J. Optim. Theory Appl. 56 (1988), no. 3, 463-477.  ... 
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