Competing in a Queue for Resource Allocations among Non-Cooperative Agents

In this paper, we investigate a multi-agent noncooperative game for resource allocations based on an M/D/1 queuing model. Specifically, agents with common goals to maximize utility are deployed to compete with each other to bid or bribe for quicker service provided by the server. The bid/bribe of each agent in the queue is not revealed, but the outcomes, in terms of the pair of (bid/bribe; total waiting time), are publicly available from the server. Agents choose from one of three available strategies: random strategy, Nash equilibrium strategy and linear regression strategy, for their decision-makings. Bayesian update is integrated into the linear regression technique for searching an optimal bid/bribe. Besides, weighted average, second order autoregressive process (AR(2)), and random walk are utilized to predict service speed. After each agent obtained service, it reevaluates its strategy and adjusts it accordingly. Results show that in the long run, the dominant strategy depends on the service speed. When the service speed is low, random strategy dominates the society. But if the service speed is high, linear regression strategy dominates. The model can be extended to study agent-based social simulations and decentralized scheduling for resource allocations in an open multi-agent system.