International Journal on Advanced Computer Theory and Engineering (IJACTE)
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Cooperative Game Theory Approach for the Cognitive Radio Users
1
Harshali Patil, 2Seema Purohit
1
Associate Professor, MET-ICS, Mumbai, 2Director ,NMITD, Mumbai
Email: 1harshalip_ics@met.edu, 2supurohit@gmail.com
Abstract— Wireless mobile communication plays a vital
role in our life. The facility of anywhere anytime
communication services availability can be handled by
management of resources efficiently. The quality of service
offered to users may be enhanced through innovative
protocols and new technologies. Future trends in wireless
computing should take into account resource allocation,
resource sharing and network/terminal cooperation as well.
Cognitive radio is novel way to solve spectrum
underutilization problem and to improve utilization of
electromagnetic radio spectrum.
In cognitive network the radio parameters were modified to
achieve network objectives, which can be through-put
maximization, reliability, or spectral or energy efficiency. In
these networks, the licensed spectrum and dynamic
spectrum sharing is based on opportunistic communication
which plays an important role in resource allocation. The
traditional spectrum sharing approaches based on fully
cooperative, static and centralised network environment are
no longer applicable.
Cognitive radio networks (CRN) has created a significant
research interest due to the unique opportunistic spectrum
sharing of channels when not used by the licensed user
(known as white spaces). Game theory has been recognized
as an important tool for studying, modelling and analysing
the cognitive interaction process.
Index Terms— cognitive radio, primary users, secondary
users, game theory, spectrum sharing, resource allocation,
Nash equilibrium, one shot game
I. INTRODUCTION
through the study of the utilization of the existed radio
spectrum: (1) some spectrum is used most of the time; (2)
most of the spectrum is not used in the most of time [3].
There are three possible dynamic spectrum access (DSA)
approaches that have been suggested as possible solutions
to improve spectrum utilization: (1) open sharing, (2)
hierarchical access and (3) dynamic exclusive use [4].
Dynamic spectrum access is an important aspect of
cognitive radio [5]. In Cognitive Radio (CR) Secondary
Users (SUs) access spectrum holes left by the licensed
users i.e. Primary Users (PUs). While the primary user
(PU) is not using the spectrum, CRs (secondary users) can
share the spectrum with the licensed users (primary users)
by monitoring and adapting to the environment. The
secondary users (SUs) must be able to detect the signal of
the PU to sense the presence of the PU. The various
methods used for spectrum sensing are matched filter
detectors, energy detectors, cyclostationary detectors or
wave-let detectors [6]. It has been shown that the
detection probability of the Primary user (PU), which may
be fed due to path loss or shadowing (hidden terminal),
can be improved [7]-[9].
In cognitive network users are intelligent and have the
ability to observe, learn and act to optimize their
performance. Users will cooperate with others if
cooperation can bring them more benefit. The radio
environment is keeps changing, and because of unreliable
and broadcast nature of wireless channels, user mobility,
dynamic topology and traffic variations. In traditional
spectrum sharing technique, a small change in the radio
environment triggers the network controller to re-allocate
the spectrum resources, which results in a lot of
communication overhead. To tackle these challenges
game theory has naturally become an important tool that
is ideal and essential in studying, modeling and analyzing
the cognitive interaction process [10].
Resource provisioning is one of the most challenging and
important aspect in communication networks. Radio
resources are scarce resources. A recent study concludes
that most of them have been already licensed to existing
operators. The radio spectrum studies showed that,
licensed spectrum remains unoccupied for large amount
II. COGNITIVE RADIO
of time [1]. Cognitive radio(CR) is an efficient way to
utilize the spectrum holes . The term cognitive radio was
“Cognitive radio is an intelligent wireless communication
invented in 1999 by J. Mitola III. Cognitive radio (CR) is
system that is aware of its surrounding environment (i.e.
a technology proposed to improve spectrum utilization of
its outside world), and uses methodology of
wireless communication. It is used to address the issue of
understanding-by-building to learn from environment and
inefficient spectrum management and increasing demand
adapt its internal states to statistical variations in the
of spectrum resources [2]. Two rules have been found
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International Journal on Advanced Computer Theory and Engineering (IJACTE)
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incoming RF stimuli by making corresponding changes in
certain operating parameters (e.g. transmit power, carrier
frequency and modulation strategy) in real time, with two
primary objectives in mind: highly reliable
communication whenever and wherever needed; efficient
utilization of radio spectrum.” [17, 18].
ij denotes the payoff assigned to player i after choosing
resource j.
Mapping of game theory elements to networks is as
follows
Game
component
Players
Resources
Strategies
Payoffs
Figure 1: Cognitive Radio block diagram
Through spectrum sensing and analysis, cognitive radio
can detect white spaces, which is a portion of frequency
band that is not being used by primary user. On the other
hand, when primary user starts using licensed spectrum
again, the cognitive radio through sensing, so that no
harmful interference would be generated.
Figure 2: Spectrum white spaces/holes.
III. GAME THEORY
Game theory is related to the actions of makers who are
conscious that their actions affect each other. A game
consist of a principal and a finite set of players P= {1,
2,3,........,n} each of which selects strategy si Si with the
objective of maximizing his utility The utility function
ui(s): SR represents each player’s sensitivity to
everyone’s actions. According to above the game can be
modelled as G=(P, A, Si, ij) where:
P= {1,2,3,…..,n} denotes the set of players
A= {1, 2, 3, n} denotes the available resources in the
game (action set)
Si denotes the set of strategies for player i, i.e. all possible
choices from set A
Entities, processes or elements of
wireless networks
Customers/ Service providers and
Network nodes
All kinds of resources needed by nodes
to
communicate
successfully
(bandwidth, power spectrum etc),
income
A decision regarding a certain action of
the player, depending on the
application field (forward packet, set
power level, accept new call, etc)
Estimated by utility functions, based on
QoS merits (SNR, delay, throughput
etc)
Table 1: Mapping of game theory to networks
There are two types of games: non-cooperative and
cooperative game. In non-cooperative games, each player
selects strategies without coordination with others. The
strategy profile s is the vector containing the strategies of
all players: s=(si) , i  N ={s1,s2,….sn}. In a cooperative
game, the players cooperatively try to come to an
agreement, and the players have a choice to bargain with
each other so that they can gain maximum benefit. The
benefit is what could have obtained by playing the game
without cooperation [11]. Let the players set be
N={1,2,3---,n}. Non empty subsets of N,S,T N are
called a coalition. The coalition form of an n-player game
is given by the pair (N, u), where u is the characteristic
function [12]. A coalition that includes all of the players is
called a grand coalition. The characteristic function
assigns each coalition S its maximum gain, the excepted
total income of the coalition denoted u(S). The core is the
set of all feasible outcomes that no player or coalition can
improve upon by acting for themselves. The objective is
to allocate the resources so that the total utility of the
coalition is maximized.
IV. NASH EQUILIBRIUM
Game theory is a mathematical tool that analyzes the
strategic interactions among multiple decision makers.
The equilibrium strategies are chosen by players in order
to maximize their individual payoffs. In game theory, the
Nash equilibrium is a solution for a game involving two or
more players, in which no player has anything to gain by
changing only his strategy unilaterally.
The Nash
equilibrium is achieved if each player has chosen a
strategy and no player can benefit by changing his strategy
while the other player keeps their strategy unchanged. In
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such situation the current set of strategy choices and the
corresponding payoffs constitute Nash equilibrium.
This helps you to probe one another's strategies and is
known as a mixed-strategy.
In cognitive radio network, secondary users (SUs) do not
own a
5.2 Repeated games
spectrum license. These users are also called as
unlicensed users. The spectrum license holder as known
as licensed user or primary users (PUs). Spectrum sharing
between the secondary users those who access the
unlicensed spectrum band is referred as open spectrum
sharing. In open spectrum sharing all users have equal
right to use unlicensed spectrum bands. Spectrum sharing
in between primary users (PUs) and secondary users
(SUs) in licensed spectrum bands is referred to as
hierarchical access model or licensed spectrum sharing.
Uniqueness of equilibrium is one of the desirable
properties. If there is one only equilibrium, we can predict
the equilibrium strategy for players and resulting
performance of the cognitive radio network. The
cognitive network players’ behavior can be modified by
tuning the design parameters of the game.
V. KEY GAME FORMS
In the static game, players move simultaneously without
knowing what the other players do. The case of sequential
interaction, the framework falls in the realm of dynamic
games. These games are represented in an extensive form
as opposed to the strategic form. Following are some
game forms that are critical to the application of game
theory to Radio Resource Management (RRM)
The key decision about allocation of licensed band to
unlicensed user is based on many factors. Factors
considered are network availability, network strength,
spectrum usage pattern, switching time etc. If the
unlicensed user request arrives and the hole is available
the allocation request will be granted to the user. During
the allocation process if a licensed user request comes
then unlicensed user will be on hold till channel becomes
free or a new hole is identified or until timeout operation.
User allotment to available channels is a real time priority
based scheduling. White space (hole) allocation to an
unlicensed user can be treated as a repeated game.
Punishment to the secondary user/unlicensed user will be
always in terms of delayed allocation. A bit more time as
compared to the switching decision time and spectrum
sensing time will be required.
A repeated game is sequence of stages where each stage is
the same normal form game. When the game has an
infinite number of stages, the game is said to have an
infinite horizon game. Based on their knowledge of the
game – past actions, future expectations, and current
observations - players choose strategies – a choice of
actions at each stage. These strategies can be fixed,
contingent on the actions of other players, or adaptive.
Further, these strategies can be designed to punish players
who deviate from agreed upon behavior. When
punishment occurs, players choose their actions to
minimize the payoff of the offending player. However,
even when the other players are minimizing the payoff a
player i, i is still able to achieve some payoff vi. Thus
there is a limit to the how much a player can be punished.
As estimations of future values of ui are uncertain, many
repeated games modify the original objective functions by
discounting the expected payoffs in future stages by
k to player i is given by[13,15]
ui,k
One shot game is where game is played once. Players do
not know much about other players. When playing
a repeated game, a one-shot strategy may not be the best
move: You and your opponent can get better returns in the
long run by cooperating (not confessing) (prisoners
dilemma) at times and defecting (confessing) at others.
ui(a)
(1)
5.3 Myopic games
A myopic game is defined here as a repeated game in
which there is no communication between the players,
memory of past events, or speculation of future events.
Any adaptation by a player can still be based on
knowledge of the current state of the game. As players
have no consideration of future payoffs, the Folk theorem
does not hold for myopic games and the convergence to
steady-state behaviour must occur through other means.
Two convergence dynamics possible in a myopic game
are the best response dynamic and the better response
dynamic. Both dynamics require additional structure in
the stage game to ensure convergence.
Definition: Best response dynamic [14, 15]
At each stage, one player i N is permitted to deviate from
ai to some randomly selected
action bi
5.1 One shot games
k
Ai iff
ui(bi, a-i) ≥ ui(ci, a-i)
 ci ≠ bi  Ai and
ui(bi, a-i) > ui(a)
(2)
Definition: Better response dynamic [14, 15]
At each stage, one player i N is permitted to deviate from
ai to some randomly selected
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action bi
Ai iff
ui(bi, a-i) > ui(ai, a-i)
VII. CONCLUSION
(3)
The work done on Ad-hoc Networks is Cooperation with
and without incentives (Currency & reputation, Virtual
money and Cost, Reducing Selfish behaviour). Sensor
Networks has proposed work/solutions for Cooperative
Packet forwarding, MAC Protocol, non-cooperative
Solutions etc. In cognitive radio the work proposed is in
resource allocation and IEEE 802.22 Working Group. In
cellular and Wi-Fi networks(WWANs and WLANs) the
work proposed Resource Allocation, Selfish behaviour,
and reputation based networks. Game theory can model
the various interactions in wireless networks as games at
different levels of protocol stack [16].
We can implement open spectrum game model as a one
shot game and can study of behaviour of throughput
function and parameter dependency [Bit Error Rate
(BER)]. One shot game can be played multiple times to
enforce cooperation and comparing the results may give
most effective scheme for maximizing throughput. The
open spectrum repeated games can be evaluated for
different punishment strategies like ‘tit for tat’ and
fictitious play to discourage the player deviation.
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VI. SYSTEM MODEL
Consider a spectrum sharing in unlicensed band where an
N secondary user in same area coexists to compete for
spectrum access in unlicensed band. For simplicity we
assume each user as a transmitter receiver pair and all
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Players: N secondary users
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