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Optimization Induced Equilibrium Networks [article]

Xingyu Xie, Qiuhao Wang, Zenan Ling, Xia Li, Yisen Wang, Guangcan Liu, Zhouchen Lin
2021 arXiv   pre-print
Then, the equilibrium model of the unit layer can be derived, named Optimization Induced Equilibrium Networks (OptEq), which can be easily extended to deep layers.  ...  Implicit equilibrium models, i.e., deep neural networks (DNNs) defined by implicit equations, have been becoming more and more attractive recently.  ...  We propose the corresponding equilibrium model of the new unit layer, named Optimization Induced Equilibrium Networks (OptEq).  ... 
arXiv:2105.13228v3 fatcat:m2whdgdhkndolgcfmriw4u7q3e

Pricing Traffic Networks with Mixed Vehicle Autonomy [article]

Negar Mehr, Roberto Horowitz
2019 arXiv   pre-print
In a traffic network, vehicles normally select their routes selfishly. Consequently, traffic networks normally operate at an equilibrium characterized by Wardrop conditions.  ...  First, we study the possibility of inducing such optimal equilibria by imposing a set of undifferentiated prices, i.e. a set of prices that treat both human-driven and autonomous vehicles similarly at  ...  Therefore, although the social delay of one induced equilibrium is optimal, the social delay of other induced equilibria might not be optimal.  ... 
arXiv:1904.01226v1 fatcat:u7yv4oylmnamxmq67gzteqo4oq

On the Existence of Optimal Taxes for Network Congestion Games with Heterogeneous Users [chapter]

Dimitris Fotakis, George Karakostas, Stavros G. Kolliopoulos
2010 Lecture Notes in Computer Science  
On the positive side, we show the existence of weakly-optimal taxes for single-source network games.  ...  We consider network congestion games in which a finite number of non-cooperative users select paths.  ...  In the following, we show that any weakly-optimal tax vector β induces an equilibrium of total latency at least 28, and thus this game does not admit strongly-optimal taxes.  ... 
doi:10.1007/978-3-642-16170-4_15 fatcat:4wxvp3rh2rfztctnwosrx4pm6y

Pricing for Coordination in Open–Loop Differential Games

Daniel Calderone, Lillian J. Ratliff, S. Shankar Sastry
2014 IFAC Proceedings Volumes  
In addition, we present conditions when the induced equilibrium is a global equilibrium.  ...  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.  ...  This motivates the design of coordinating mechanisms that induce agents to play a Nash equilibrium with desirable properties, namely an equilibrium that is socially optimal.  ... 
doi:10.3182/20140824-6-za-1003.02655 fatcat:rftge2btxvgtff3ru3nbvvcdhy

Impacts of network constraints on electricity market equilibrium

Youfei Liu, F.F. Wu
2006 2006 IEEE Power Engineering Society General Meeting  
The available literature has shown by simulation that multiple market equilibria or no pure equilibrium may be induced after the inclusion of network constraints (transmission constraints).  ...  This paper presents a systematical analysis for the impacts of network constraints on the market equilibrium in oligopolistic electricity markets.  ...  On the other hand, if the binding network constraints induce some inconsistent generators' bidding behavior, then there may be no pure Nash equilibrium.  ... 
doi:10.1109/pes.2006.1709396 fatcat:soi2ssissrhf3dzlg5bpuqarm4

Impacts of Network Constraints on Electricity Market Equilibrium

Youfei Liu, Felix F. Wu
2007 IEEE Transactions on Power Systems  
The available literature has shown by simulation that multiple market equilibria or no pure equilibrium may be induced after the inclusion of network constraints (transmission constraints).  ...  This paper presents a systematical analysis for the impacts of network constraints on the market equilibrium in oligopolistic electricity markets.  ...  On the other hand, if the binding network constraints induce some inconsistent generators' bidding behavior, then there may be no pure Nash equilibrium.  ... 
doi:10.1109/tpwrs.2006.889083 fatcat:qmhw4m3wxnfozielkkkwkazvxa

Cost-Balancing Tolls for Atomic Network Congestion Games

Dimitris Fotakis, Paul G. Spirakis
2008 Internet Mathematics  
Our main result is that for congestion games on series-parallel networks with strictly increasing latency functions, the optimal solution is induced as the unique pure Nash equilibrium of the game with  ...  Hence any given configuration is induced as a pure Nash equilibrium of the modified game with the corresponding cost-balancing tolls.  ...  An extended abstract of this work appeared in Internet and Network Economics: Third International Workshop, WINE 2007, San Diego, CA, USA, December 12-14, 2007, Proceedings, Lecture Notes in Computer Science  ... 
doi:10.1080/15427951.2008.10129175 fatcat:qhvay7qi45hcbasgf3bzoksczm

Dynamic Tolling for Inducing Socially Optimal Traffic Loads [article]

Chinmay Maheshwari and Kshitij Kulkarni and Manxi Wu and Shankar Sastry
2021 arXiv   pre-print
How to design tolls that induce socially optimal traffic loads with dynamically arriving travelers who make selfish routing decisions?  ...  We propose a two-timescale discrete-time stochastic dynamics that adaptively adjusts the toll prices on a parallel link network while accounting for the updates of traffic loads induced by the incoming  ...  That is, the tolls eventually induce a perturbed socially optimal flow.  ... 
arXiv:2110.08879v1 fatcat:ysejf6xh2zg7ratf3lijjxzat4

Taxing Subnetworks [chapter]

Martin Hoefer, Lars Olbrich, Alexander Skopalik
2008 Lecture Notes in Computer Science  
Given a network and a subset of edges, on which we can impose taxes, the problem is to find taxes inducing an equilibrium flow of minimal networkwide latency cost.  ...  If all edges are taxable, then marginal cost pricing is known to induce the socially optimal flow for arbitrary multi-commodity networks.  ...  [5] show existence of taxes inducing the optimal flow for single-commodity networks and heterogeneous users that value tax versus latency in an individual way.  ... 
doi:10.1007/978-3-540-92185-1_35 fatcat:hzooiwsad5gfvjzjpxzswuktfq

Demand-Independent Optimal Tolls [article]

Riccardo Colini-Baldeschi, Max Klimm, Marco Scarsini
2017 arXiv   pre-print
Network tolls are a prominent and popular way to induce an optimum flow in equilibrium.  ...  Wardrop equilibria in nonatomic congestion games are in general inefficient as they do not induce an optimal flow that minimizes the total travel time.  ...  Beckmann et al. (1956) showed that marginal cost pricing always induces the system optimal flow as a Wardrop equilibrium.  ... 
arXiv:1708.02737v1 fatcat:7nurlpdvb5eszpxf3x6lezrolq

Stackelberg Routing on Parallel Networks With Horizontal Queues

Walid Krichene, Jack D. Reilly, Saurabh Amin, Alexandre M. Bayen
2014 IEEE Transactions on Automatic Control  
We show that it is optimal for this new class of latency on parallel networks.  ...  We provide a simple polynomial-time algorithm for computing the best Nash equilibrium, i.e. the one which achieves minimal total cost.  ...  Figure 5 : 5 Non-compliant first (NCF) strategys and its induced equilibrium.  ... 
doi:10.1109/tac.2013.2289709 fatcat:4eutiuqxjbbfnl4wk3loir3pga

Pricing network edges for heterogeneous selfish users

Richard Cole, Yevgeniy Dodis, Tim Roughgarden
2003 Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03  
network users is both necessary and sufficient for the existence of edge prices that induce an optimal routing while requiring only moderate taxes, and mention consequences.  ...  When many different sets of edge prices induce a minimum-latency Nash equilibrium, can we efficiently compute the "best" one?  ...  Let τ be an optimal tax for (G, ℓ, α), inducing a flow f τ at Nash equilibrium that induces the same flow on edges as an acyclic minimum-latency flowf .  ... 
doi:10.1145/780615.780618 fatcat:xscp4whydjfuzautibux3ej5ca

Pricing network edges for heterogeneous selfish users

Richard Cole, Yevgeniy Dodis, Tim Roughgarden
2003 Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC '03  
network users is both necessary and sufficient for the existence of edge prices that induce an optimal routing while requiring only moderate taxes, and mention consequences.  ...  When many different sets of edge prices induce a minimum-latency Nash equilibrium, can we efficiently compute the "best" one?  ...  Let τ be an optimal tax for (G, ℓ, α), inducing a flow f τ at Nash equilibrium that induces the same flow on edges as an acyclic minimum-latency flowf .  ... 
doi:10.1145/780542.780618 dblp:conf/stoc/ColeDR03 fatcat:b7ev4xna3ne4bfee7b3ieoey5a

Location Games on Networks: Existence and Efficiency of Equilibria

Gaëtan Fournier, Marco Scarsini
2018 Mathematics of Operations Research  
., the ratio of the worst equilibrium cost and the optimal cost, and the price of stability, i.e., the ratio of the best equilibrium cost and the optimal cost.  ...  We consider a game where a finite number of retailers choose a location, given that their potential consumers are distributed on a network.  ...  We perform this comparison in term of the induced price of anarchy, i.e., the ratio of the worst equilibrium cost and the optimal cost, and the induced price of stability, i.e., the ratio of the best equilibrium  ... 
doi:10.1287/moor.2017.0921 fatcat:32g4w6n72vbolonyhbexr5b4u4

Optimal Collaterals in Multi-Enterprise Investment Networks [article]

Moshe Babaioff, Yoav Kolumbus, Eyal Winter
2021 arXiv   pre-print
We show that for acyclic investment networks, the network environment does not necessitate any additional collaterals, and systemic risk can be fully handled by optimal bilateral collateral contracts between  ...  Furthermore, the minimum total collateral that will sustain the efficient level of investment as a unique equilibrium may be arbitrarily higher, even in simple cyclic investment networks, compared with  ...  In contrast, in our setting the network of investment opportunities induces a game of the investors, and an equilibrium is a Nash equilibrium of the game.  ... 
arXiv:2011.06247v2 fatcat:4hmcnnxsorayfljetoet4o5jh4
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