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Duality in Dynamic Discrete Choice Models

Khai X. Chiong, Alfred Galichon, Matthew Shum
2015 Social Science Research Network  
The application of convex-analytic tools to dynamic discrete choice models, and the connection with two-sided matching models, is new in the literature.  ...  We show that the conditional choice probabilities and the choicespecific payoffs in these models are related in the sense of conjugate duality, and that the identification problem is a mass transport problem  ...  In the case when Q is a discrete distribution, the mass transport problem in the above proposition reduces to a linear-programming problem which coincides with the assignment game of Shapley and Shubik  ... 
doi:10.2139/ssrn.2700773 fatcat:hvubso3vtrar7bmlyoj2tgaic4

Optimal Pricing for Duopoly in Cognitive Radio Networks: Cooperate or not Cooperate?

2014 IEEE Transactions on Wireless Communications  
This strategy also requires each SU to know the average queueing delay, which is a non-trivial problem. Toward this end, we provide queueing delay analysis by using the M/G/1 queue with breakdown.  ...  From the BS's point of view, we consider a duopoly market based on the two paradigms: the opportunistic dynamic spectrum access (O-DSA) and the mixed O-DSA & dedicated dynamic spectrum access (D-DSA).  ...  ν(t + 1) with the gradient iterate (48); 3) Set t + 1 → t and go back to step 1 (until satisfying the termination criterion); between the two models: the non-cooperative and cooperative model in four  ... 
doi:10.1109/twc.2014.031914.131363 fatcat:yb2rzmtj65elniriu7mw6hwhp4

Learning to disagree in a game of experimentation

Alessandro Bonatti, Johannes Hörner
2017 Journal of Economic Theory  
When actions are hidden, there exists a unique symmetric equilibrium that involves randomization over stopping times. With two players, this is the unique equilibrium.  ...  We analyze strategic experimentation in which information arrives through fully revealing, publicly observable "breakdowns."  ...  In a dynamic, continuous-time setting, we are not aware of another paper with a clear economic interpretation in which mixed strategies must be considered to ensure existence, despite convex action sets  ... 
doi:10.1016/j.jet.2017.02.007 fatcat:vrnetqs3zzhupjk5o5lyb2r56a

Multiplicative weights in monotropic games [article]

Ioannis Avramopoulos
2014 arXiv   pre-print
Monotropic games generalize strictly concave potential games and zero sum games with a unique minimax solution. Within the class of monotropic games, we study a multiplicative weights dynamic.  ...  We introduce a new class of population games that we call monotropic; these are games characterized by the presence of a unique globally neutrally stable Nash equilibrium.  ...  My interest in multiplicative weights grew out of a summer internship at Akamai Technologies in the summer of 2000 where I had the opportunity and privilege to work with Gary Miller and Joel Wein and interact  ... 
arXiv:1404.4163v2 fatcat:uxyjho36s5dkhdr4r3leg7fare

Large Deviations and Stochastic Stability in the Small Noise Double Limit, I: Theory

William H. Sandholm, Mathias Staudigl
2014 Social Science Research Network  
The control problems are tractable in certain interesting cases, allowing analytical descriptions of the escape dynamics and long run behavior of the stochastic evolutionary process. *  ...  We show that in this double limit, escape from and transitions between equilibria can be described in terms of solutions to continuous optimal control problems.  ...  in terms of solutions to path cost minimization problems on the discrete set X N .  ... 
doi:10.2139/ssrn.2424044 fatcat:zex7zqudbnaydat5c4bfmm3bpa

Learning to Disagree in a Game of Experimentation

Alessandro Bonatti, Johannes Horner
2015 Social Science Research Network  
When actions are hidden, there exists a unique symmetric equilibrium that involves randomization over stopping times. With two players, this is the unique equilibrium.  ...  We analyze strategic experimentation in which information arrives through fully revealing, publicly observable "breakdowns."  ...  A fortiori, the problem arises in games, and there are well-known examples of zero-sum games with sectionally convex action spaces for which the optimal policies cannot be found within the class of pure  ... 
doi:10.2139/ssrn.2573222 fatcat:dsyx32blzbc3xcf3gpgh7asj2q

14th International Symposium on Mathematical Programming

1990 Mathematical programming  
If we use a decomposition approach in order to solve a minimization problem we often get an objective function in such a w a y that its domain dom 6 = n is not given explicitely to us.  ...  A v ariation of bundle methods is presented by means of which such a t ype of problems can be solved.In this variation a dynamic polyhedral model of dom is generated by means of normal vectors.In addition  ...  We consider examples to compare the new class of di erential games with well-known classes of games linear games with a quadratic functional and games with purely geometrical constraints and a terminal  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa


Stephen. J. Guy, Jatin Chhugani, Changkyu Kim, Nadathur Satish, Ming Lin, Dinesh Manocha, Pradeep Dubey
2009 Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation - SCA '09  
The overall approach, ClearPath, is general and can robustly handle dense scenarios with tens or hundreds of thousands of heterogeneous agents in a few milli-seconds.  ...  Our approach extends the notion of velocity obstacles from robotics and formulates the conditions for collision free navigation as a quadratic optimization problem.  ...  Acknowledgements This research is supported in part by ARO Contract W911NF-04-1-0088, NSF award 0636208, DARPA/RDECOM Contracts N61339-04-C-0043 and WR91CRB-08-C-0137, Intel, and Microsoft.  ... 
doi:10.1145/1599470.1599494 dblp:conf/sca/GuyCKSLMD09 fatcat:dcxaagyrerc33hzex3byzjxy3m

A characterization of a limit solution for finite horizon bargaining problems

Haruo Imai, Hannu Salonen
2011 International Journal of Game Theory  
We investigate a two-person random proposer bargaining game with a deadline.  ...  A bounded time interval is divided into bargaining periods of equal length and we study the limit of the subgame perfect equilibrium outcomes as the number of bargaining periods goes to infinity while  ...  Coles and Wright (1998) where the game has infinite horizon, and GHM where breakdown possibility with risk preference is employed with fixed length of a period.  ... 
doi:10.1007/s00182-011-0306-6 fatcat:ahgds2fskrdkbjuqhzpjfevgei

Recent advances in robust optimization: An overview

Virginie Gabrel, Cécile Murat, Aurélie Thiele
2014 European Journal of Operational Research  
With respect to the theory of robust optimization, this paper reviews recent results on the cases without and with recourse, i.e., the static and dynamic settings, as well as the connection with stochastic  ...  , (ii) a greater connection with decision sciences by linking uncertainty sets to risk theory, (iii) further results on nonlinear optimization and sequential decision-making and (iv) besides more work  ...  Acknowledgments The authors would like to thank the Associate Editor and three anonymous referees for their insightful comments and suggestions.  ... 
doi:10.1016/j.ejor.2013.09.036 fatcat:negoppbbu5hanjkdlccdwjb35a

Hybrid control synthesis for eventuality specifications using level set methods

Anastasios Trontis, Michael P. Spathopoulos
2003 International Journal of Control  
Due to the existence of set-valued disturbance inputs, the problem is studied in a game-theoretic framework.  ...  Having shown that a least restrictive solution does not exist, we propose a dynamic programming algorithm that computes the maximal initial set and a controller with the desired property.  ...  The control problem is concerned with an emergency shut-down sequence due to a cooling breakdown in the condenser.  ... 
doi:10.1080/00207170310001622512 fatcat:xpmbdqbs7zddhhj2b4smkvpyga

Dynamic relational contracts under complete information

Jonathan P. Thomas, Tim Worrall
2018 Journal of Economic Theory  
In the risk-averse case, the dynamics of actions and surplus may or may not be monotonic depending on whether or not a first-best allocation can be sustained.  ...  If the first-best allocation is not sustainable, there is a trade-off between risk sharing and surplus maximization; surplus may not be at its constrained maximum even in the long run and the "amnesia"  ...  In particular, we'd like to thank, Pierre Dubois, Francisco Gonzalez, Bruno Jullien and John Moore for very valuable comments. All errors are ours.  ... 
doi:10.1016/j.jet.2018.02.004 fatcat:k3p7kcrz7rcmzh7pfub2yebylu

Integration of control theory and scheduling methods for supply chain management

Kaushik Subramanian, James B. Rawlings, Christos T. Maravelias, Jesus Flores-Cerrillo, Lawrence Megan
2013 Computers and Chemical Engineering  
The set U is convex, closed and compact and contains the origin in its interior. The set X is convex, closed and contains the origin in its interior.  ...  For convex optimization problems, the Jacobi algorithm has the property that it generates feasible iterates with non-increasing objective function values.  ... 
doi:10.1016/j.compchemeng.2012.06.012 fatcat:zyfzmn6nbfbzlpfu24ajrxxfdy

The 10,000 Facets of MDP Model Checking [chapter]

Christel Baier, Holger Hermanns, Joost-Pieter Katoen
2019 Lecture Notes in Computer Science  
We survey the basic ingredients of MDP model checking and discuss its enormous developments since the seminal works by Courcoubetis and Yannakakis in the early 1990s.  ...  We discuss in particular the manifold facets of this field of research by surveying the verification of various MDP extensions, rich classes of properties, and their applications.  ...  Whereas for MDP model checking [72] , the set of achievable points is a convex area with finitely many corner points, for CTMDPs the convex area may have infinitely many corner points [135] .  ... 
doi:10.1007/978-3-319-91908-9_21 fatcat:yjsuwb5ibjff3cq3niatu6sbxq

Measuring and hedging financial risks in dynamical world [article]

Nicole El Karoui
2003 arXiv   pre-print
History began with the paradigm of zero-risk introduced by Black & Scholes stating that any random amount to be paid in the future may be replicated by a dynamical portfolio.  ...  This challenging question has generated a deep and intensive academic research in the 20 last years, based on super-replication (perfect or with respect to confidence level) and optimization.  ...  Ill-posed inverse problem The problem of determining local volatility can be viewed as a function approximation non linear problem from a finite data set.  ... 
arXiv:math/0305010v1 fatcat:qxslahtsazdazab7q3csynsmpy
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