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We study the problem of online learning in two-sided non-stationary matching markets, where the objective is to converge to a stable match. In particular, we consider the setting where one side of the market, the arms, has fixed known set of preferences over the other side, the players. While this problem has been studied when the players have fixed but unknown preferences, in this work we study the problem of how to learn when the preferences of the players are time varying and unknown. Our contribution is a methodology that can handle any type of preference structure and variation scenario. We show that, with the proposed algorithm, each player receives a uniform sub-linear regret of {O˜(𝐿1/2𝑇𝑇1/2)} up to the number of changes in the underlying preferences of the agents, 𝐿𝑇. Therefore, we show that the optimal rates for single-agent learning can be achieved in spite of the competition up to a difference of a constant factor. We also discuss extensions of this algorithm to the case where the number of changes need not be known a priori. 

In this paper, we consider a general distributed system with multiple agents who select and then implement actions in the system. The system has an operator with a centralized objective. The agents, on the other hand, are selfinterested and strategic in the sense that each agent optimizes its own individual objective. The operator aims to mitigate this misalignment by designing an incentive scheme for the agents. The problem is difficult due to the cost functions of the agents being coupled, the objective of the operator not being social welfare, and the operator having no direct control over actions being implemented by the agents. This problem has been studied in many fields, particularly in mechanism design and cost allocation. However, mechanism design typically assumes that the operator has knowledge of the cost functions of the agents and the actions being implemented by the operator. On the other hand, cost allocation classically assumes that agents do not anticipate the effect of their actions on the incentive that they obtain. We remove these assumptions and present an incentive rule for this setup by bridging the gap between mechanism design and classical cost allocation. We analyze whether the proposed design satisfies various desirable properties such as social optimality, budget balance, participation constraint, and so on. We also analyze which of these properties can be satisfied if the assumptions of cost functions of the agents being private and the agents being anticipatory are relaxed.