Online stochastic matching, poisson arrivals, and the natural linear program

AbstractWe consider a stochastic matching model with a general compatibility graph, as introduced by Mairesse and Moyal (2016). We show that the natural necessary condition of stability of the system is also sufficient for the natural ‘first-come, first-matched’ matching policy. To do so, we derive the stationary distribution under a remarkable product form, by using an original dynamic reversibility property related to that of Adan, Bušić, Mairesse, and Weiss (2018) for the bipartite matching model.

Download Full-text

Dynamic Stochastic Matching Under Limited Time

Proceedings of the 21st ACM Conference on Economics and Computation ◽

10.1145/3391403.3399524 ◽

2020 ◽

Cited By ~ 1

Author(s):

Ali Aouad ◽

Ömer Saritaç

Keyword(s):

Limited Time ◽

Dynamic Stochastic ◽

Stochastic Matching

Download Full-text

Discrete-Time Constrained Average Stochastic Games with Independent State Processes

Mathematics ◽

10.3390/math7111089 ◽

2019 ◽

Vol 7 (11) ◽

pp. 1089

Author(s):

Wenzhao Zhang

Keyword(s):

Discrete Time ◽

Stochastic Games ◽

Transition Probability ◽

Existence Condition ◽

Linear Program ◽

Global Minimizer ◽

Independent State ◽

Occupation Measures ◽

Best Response ◽

Mathematic Program

In this paper, we consider the discrete-time constrained average stochastic games with independent state processes. The state space of each player is denumerable and one-stage cost functions can be unbounded. In these game models, each player chooses an action each time which influences the transition probability of a Markov chain controlled only by this player. Moreover, each player needs to pay some costs which depend on the actions of all the players. First, we give an existence condition of stationary constrained Nash equilibria based on the technique of average occupation measures and the best response linear program. Then, combining the best response linear program and duality program, we present a non-convex mathematic program and prove that each stationary Nash equilibrium is a global minimizer of this mathematic program. Finally, a controlled wireless network is presented to illustrate our main results.

Download Full-text