Abstract
Cooperative diversity protocols are designed with the assumption that terminals always help each other in a socially efficient manner. This assumption may not be valid in commercial wireless networks where terminals may misbehave for selfish or malicious intentions. The presence of misbehaving terminals creates a social-dilemma where terminals exhibit uncertainty about the cooperative behavior of other terminals in the network. Cooperation in social-dilemma is characterized by a suboptimal Nash equilibrium where wireless terminals opt out of cooperation. Hence, without establishing a mechanism to detect and mitigate effects of misbehavior, it is difficult to maintain a socially optimal cooperation. In this paper, we first examine effects of misbehavior assuming static game model and show that cooperation under existing cooperative protocols is characterized by a noncooperative Nash equilibrium. Using evolutionary game dynamics we show that a small number of mutants can successfully invade a population of cooperators, which indicates that misbehavior is an evolutionary stable strategy (ESS). Our main goal is to design a mechanism that would enable wireless terminals to select reliable partners in the presence of uncertainty. To this end, we formulate cooperative diversity as a dynamic game with incomplete information. We show that the proposed dynamic game formulation satisfied the conditions for the existence of perfect Bayesian equilibrium.
Highlights
Cooperative wireless communications is based on the principle of direct reciprocity where wireless terminals attain some of the benefits of multiple input multiple output (MIMO) systems through cooperative relaying, that is, by helping each other
We show that the proposed dynamic game formulation satisfies the requirements for the existence of perfect Bayesian equilibrium
We show that the proposed dynamic Bayesian game model for cooperative communications satisfies the requirements for the existence of Perfect Bayesian Equilibrium (PBE) [9], (1) Requirement 1: at each information set the player with the move has some beliefs about which node in its information set has been reached
Summary
Cooperative wireless communications is based on the principle of direct reciprocity where wireless terminals attain some of the benefits of multiple input multiple output (MIMO) systems through cooperative relaying, that is, by helping each other. Game theoretic approaches have been proposed to design mechanisms that incentivize cooperation in commercial wireless networks. Since simultaneous decision making implies that players are unable to observe each other’s actions, static game models do not capture well dynamics of cooperative interactions. A dynamic Bayesian game framework has been proposed to model routing in energy constrained wireless ad hoc networks [5], which provides the motivation for our work. Motivated by the inadequacy of static game models to fully characterize cooperative communications, we formulate interactions of terminals in cooperative diversity as a dynamic game with incomplete information. We present a general dynamic game framework that may fit any of the existing cooperative diversity protocols. We show that the proposed model captures important aspects of existing cooperative diversity protocols.
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