Coalition-Based Cooperative Packet Delivery under Uncertainty: A Dynamic Bayesian Coalitional Game

Abstract

Cooperative packet delivery can improve the data delivery performance in wireless networks by exploiting the mobility of the nodes, especially in networks with intermittent connectivity, high delay and error rates such as wireless mobile delay-tolerant networks (DTNs). For such a network, we study the problem of rational coalition formation among mobile nodes to cooperatively deliver packets to other mobile nodes in a coalition. Such coalitions are formed by mobile nodes which can be either well behaved or misbehaving in the sense that the well-behaved nodes always help each other for packet delivery, while the misbehaving nodes act selfishly and may not help the other nodes. A Bayesian coalitional game model is developed to analyze the behavior of mobile nodes in coalition formation in presence of this uncertainty of node behavior (i.e., type). Given the beliefs about the other mobile nodes' types, each mobile node makes a decision to form a coalition, and thus the coalitions in the network vary dynamically. A solution concept called Nash-stability is considered to find a stable coalitional structure in this coalitional game with incomplete information. We present a distributed algorithm and a discrete-time Markov chain (DTMC) model to find the Nash-stable coalitional structures. We also consider another solution concept, namely, the Bayesian core, which guarantees that no mobile node has an incentive to leave the grand coalition. The Bayesian game model is extended to a dynamic game model for which we propose a method for each mobile node to update its beliefs about other mobile nodes' types when the coalitional game is played repeatedly. The performance evaluation results show that, for this dynamic Bayesian coalitional game, a Nash-stable coalitional structure is obtained in each subgame. Also, the actual payoff of each mobile node is close to that when all the information is completely known. In addition, the payoffs of the mobile nodes will be at least as high as those when they act alone (i.e., the mobile nodes do not form coalitions).