strong equilibria
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Author(s):  
Yu-Jui Huang ◽  
Zhou Zhou

A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined and allows for unambiguous economic interpretation. The terms “strong equilibria” and “weak equilibria” are coined for controls under the new and standard definitions, respectively. When the state process is a time-homogeneous continuous-time Markov chain, a careful asymptotic analysis gives complete characterizations of weak and strong equilibria. Thanks to the Kakutani–Fan fixed-point theorem, the general existence of weak and strong equilibria is also established under an additional compactness assumption. Our theoretic results are applied to a two-state model under nonexponential discounting. In particular, we demonstrate explicitly that there can be incentive to deviate from a weak equilibrium, which justifies the need for strong equilibria. Our analysis also provides new results for the existence and characterization of discrete-time equilibria under infinite horizon.


2014 ◽  
Vol 16 (04) ◽  
pp. 1450013 ◽  
Author(s):  
NIKOLAY ZENKEVICH ◽  
ANDREY ZYATCHIN

This paper introduces an extension of the vehicle routing problem by including several distributors in competition. Each customer is characterized by demand and a wholesale price. Under this scenario a solution may have unserviced customers and elementary routes with no customer visits. The problem is described as a vehicle routing game (VRG) with coordinated strategies. We provide a computable procedure to calculate a strong equilibrium (SE) in the VRG that is stable against deviations from any coalition. Following this procedure, we solve iteratively optimization subproblems for a single distributor, reducing the set of unserviced customers at each iteration. We prove that strong equilibria of one type exist for a VRG, and we provide conditions for another type to exist. We also introduce a semi-cooperative SE that helps reduce a set of strong equilibria in the VRG. Our methodology is suited for parallel computing, and could be efficiently applied to routing vehicles with a few compartments. It also calculates a numerical example for a three person VRG with six cars and twelve customers.


2013 ◽  
Vol 161 (13-14) ◽  
pp. 1843-1858 ◽  
Author(s):  
Leah Epstein ◽  
Michal Feldman ◽  
Tami Tamir ◽  
Łukasz Witkowski ◽  
Marcin Witkowski

2012 ◽  
Vol 53 (3) ◽  
pp. 441-453 ◽  
Author(s):  
Martin Hoefer ◽  
Alexander Skopalik

2012 ◽  
Vol 42 (2) ◽  
pp. 461-482 ◽  
Author(s):  
Tobias Harks ◽  
Max Klimm ◽  
Rolf H. Möhring
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