Modeling misbehavior in cooperative diversity: a dynamic game approach

  • Authors:
  • Sintayehu Dehnie;Nasir Memon

  • Affiliations:
  • Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Brooklyn, NY;Department of Computer and Information Science, Polytechnic Institute of New York University, Brooklyn, NY

  • Venue:
  • EURASIP Journal on Advances in Signal Processing - Special issue on game theory in signal processing and communications
  • Year:
  • 2009

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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.