No-regret learning for cost constrained resource selection game

In this paper, a general game model, called cost constrained resource selection game (CC-rsg) is presented to model and analyze the setting where agents with cost constraint competitively share a global set of resources. We prove that a Nash equilibrium exists in any instance of CC-rsg. In addition, we study a no-regret learning process in which agents play with two observations of so-called recency effect and recency bias. Also, a no-regret algorithm is presented which is characterized by these observations. In order to determine all feasible strategy of an agent, an algorithm based on top-down search in the strategy search tree is proposed. Furthermore, we show that in a CC-rsg, if each agent adheres to this no-regret algorithm, the group behavior converges to a Nash equilibrium.