Random Access Games: Selfish Nodes with Incomplete Information

We analyze the behavior of selfish sensor nodes when they have uncertainties and incomplete information about one another. We consider a network of such selfish nodes contending for the access of a common wireless communication channel. In this scenario, sensor platforms have only subjective belief distributions about the pay-off functions of their opponents. We characterize the set of all pure strategy Nash equilibria under incomplete information for such selfish sensors. A monotonicity property for the Nash equilibrium strategies is identified. That is, there exists a critical cut-off threshold c^* such that if the cost of the collision is smaller than c^*, sensors transmit. Otherwise, backing-off becomes more beneficial for them. For the uniformly and exponentially distributed beliefs, we also pinpoint the location of this critical cut-off threshold.