  In this paper, we introduce a game theoretic framework for studying the
problem of minimizing the delay of instantly decodable network coding (IDNC)
for cooperative data exchange (CDE) in decentralized wireless network. In this
configuration, clients cooperate with each other to recover the erased packets
without a central controller. Game theory is employed herein as a tool for
improving the distributed solution by overcoming the need for a central
controller or additional signaling in the system. We model the session by
self-interested players in a non-cooperative potential game. The utility
functions are designed such that increasing individual payoff results in a
collective behavior achieving both a desirable system performance in a shared
network environment and the Nash bargaining solution. Three games are
developed: the first aims to reduce the completion time, the second to reduce
the maximum decoding delay and the third the sum decoding delay. We improve
these formulations to include punishment policy upon collision occurrence and
achieve the Nash bargaining solution. Through extensive simulations, our
framework is tested against the best performance that could be found in the
conventional point-to-multipoint (PMP) recovery process in numerous cases:
first we simulate the problem with complete information. We, then, simulate
with incomplete information and finally we test it in lossy feedback scenario.
Numerical results show that our formulation with complete information largely
outperforms the conventional PMP scheme in most situations and achieves a lower
delay. They also show that the completion time formulation with incomplete
information also outperforms the conventional PMP.
