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  • Research Article
  • Open Access

Modeling Misbehavior in Cooperative Diversity: A Dynamic Game Approach

EURASIP Journal on Advances in Signal Processing20092009:927140

  • Received: 1 November 2008
  • Accepted: 14 April 2009
  • Published:


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.


  • Nash Equilibrium
  • Evolutionary Game
  • Dynamic Game
  • Evolutionary Stable Strategy
  • Static Game

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Authors’ Affiliations

Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, 5 MetroTech, Brooklyn, NY 11201, USA
Department of Computer and Information Science, Polytechnic Institute of New York University, 5 MetroTech, Brooklyn, NY 11201, USA


© S. Dehnie and N. Memon. 2009

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.