Iaetsd game theory and auctions for cooperation in

Game Theory and Auctions for Cooperation in
a Wireless Network: A Survey
Dr.R.Dhaya
Associate Professor
Dept of computer science and engineering
Velammal Engineering College,
Chennai, India.
dhayavel2005@gmail.com
Anjana Devi.J
PG Scholar
Dept of computer science and engineering
Velammal Engineering College,
Chennai, India.
anjanajavar@gmail.com
Abstract---Cooperative communication has great
potential to amend the wireless channel capacity by
exploiting the antennas on wireless contrivances for
spatial diversity. However, applications of cooperative
communication are marginally visually perceived in
authenticity. A main obstruction blocking its wide
applications is the lack of incentives for wireless nodes
to participate in cooperative communication. We first
survey the subsisting game theoretic solutions for
providing cooperation incentives in cooperative
communications. In this paper, we survey the most
conspicuous works dwelling within the literature, and
point towards paramount research directions.
Keywords—cooperativecommunications, game theory,
auction theory.
I. INTRODUCTION
Today cooperative communication is an active
area of research, and wireless devices are evolving
into multipurpose systems with data extensive
applications running on them, by this such
applications require strong error protection and high
speed connectivity. Those requirements, and along
with the exploding growth of wireless networks and
limited spectrum resources, have created capacity
crunch and high interference in today’s wireless
networks. This causes in situation that a move
towards the development of new wireless techniques
which can achieve a more efficient use of the
available spectrum or energy consumption. An
approach called cooperative communications
promises to deliver some of the benefits of multi-
input multi-output within the given constraints.
Cooperative communication refers to the
collaborative processing and retransmission of the
overheard information at those stations surrounding
the source. Because of the cooperation takes full
advantage of the nature of the wireless channel and
create diversity, in particular transmission diversity,
thereby achieving tremendous improvements in
system robustness, capacity, delay, interference, and
coverage range.
II. COOPERATIVE COMMUNICATION
In wireless networks, cooperative transmission is
used as a means to combat channel fading (Fig.1). In
cooperative communications, relays are assigned to
help a source node to deliver its information to its
destination node. Since transmission in the wireless
channel is overheard by neighboring station which
can process these signals and retransmit them in
order to facilitate better reception. In these schemes,
some overhearing nodes are also involved in the
signal transmission by relaying the received signal
from the source to the destination. Cooperative
communications can achieve spatial diversity because
signals bearing the same information go through
uncorrelated channels introduced by cooperating
nodes [1]. Each node in a cooperative communication
transmits data of their own and acts a cooperative
agent for other nodes (Fig. 2).
Fig. 1: cooperative communication.
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Fig. 2: Each mobile node is both a user and a relay.
Cooperative transmission can obtain spatial
diversity without using multiple antennas, thus
achieving more reliable transmission or consuming
less power. Since wireless channels vary with time, a
source node may not always need help from a relay
node, Therefore it is more sensible that cooperation is
only initiated when it is necessary and beneficial and
secondly, one or more appropriate relay nodes need
to be selected among multiple potential helpers in the
network.
More generally a relay channel (RC) has many
device nodes, but only one source and sink. The
device nodes without sources and sinks are called
relays and aid communication, perhaps generously,
or through incentives, or competitively. Source node
doesn’t use the relay nodes if it leads to the capacity
lesser than its own direct transmission [9].
Cooperation among the nodes is required for
achieving the cooperative communication. Not all the
nodes will be willing to act as a relay node for it has
to consume its own resources and energy. Game
theory is used for analyzing and solving the problems
in a cooperative network.
Cooperative networks include three different
topologies: a) one- to- one, b) one- to- many, c)
many- to-one as depicted in Fig.3.
Fig.3.a) One-to-one
Fig3.b) one-to-many
Fig 3.c) many-to-one
Fig 3.Cooperative Communication topologies.
The cooperative communication is better
explained with one to one user model. Most
cooperative transmission schemes involve two phases
of transmission: a coordination phase, where users
exchange their own source data and control messages
with each other and/or the destination, and a
cooperation phase, where the users cooperatively
retransmit their messages to the destination.
A basic cooperation system consists of two users
transmitting to a common destination, as illustrated in
Fig. 4. At any instant in time, one user acts as the
source while the other user serves as the relay. In the
coordination phase (i.e., Phase I), the source user
broadcasts its data to both the relay and the
destination and, in the cooperation phase (i.e., Phase
II), the relay r forwards the source’s data (either by
itself or by cooperating with the source) to enhance
reception at the destination. The two users may
interchange their roles as source and relay at different
instants in time. To enable such cooperation among
users, different relay technology can be employed.
d
r
S
dr
s1
s2
s3
rnr3
d
r2r1
S
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8

Fig 4.Illustration of cooperative communication.
Relaying Technology:
There are several relaying techniques that can be
employed by the cooperating relays. We compute the
achievable capacity under cooperative
communications. When node u transmits a signal to
node v with power Pu, the signal-to-noise ratio
(SNR) at node v, denoted by SNRuv, is

||,||0 vuN
P
SNR u
uv 
Where N0 is the ambient noise, ||u,v|| is the
Euclidean distance between nodes u and v, and α is
the path loss exponent which is between 2 and 4 in
general, depending on the characteristics of the
communication medium.
A. Decode-and-Forward Relaying Scheme
Decode-and-forward (DF) relaying schemes refer
to cases where the relay explicitly decodes the
message transmitted by the source s and forwards a
newly generated signal to the destination d. These
schemes are also known as regenerative relaying
schemes. The achievable capacity from s to d is
    rdsdsrrDF SNRSNRSNR
W
dPrsC  1log,1logmin
2
),,,( 22
B. Amplify-and-Forward Relaying Scheme
In amplify-and-forward (AF) relaying schemes,
the relay amplifies the analog signal received from
the source and forwards it to the destination (without
explicitly decoding or demodulating the messages or
symbols) . These schemes are also referred to as non-
regenerative relaying schemes. Here, relays need not
have knowledge of the encoding or modulation
schemes employed at the source. Moreover, in
addition to its low complexity, AF schemes are also
desirable when the quality of the s-r link is not
sufficient to guarantee reliable decoding at the relay.
In this case, amplifying the analog signal preserves
soft information that can be further exploited at the
destination. The achievable capacity from s to d is








1
.
1log
2
),,,( 2
rdsr
rdsr
sdrAF
SNRSNR
SNRSNR
SNR
W
dPrsC
C. Coded cooperation Relaying Scheme
In coded cooperation schemes different portions
of the same message are transmitted in the two
phases. Specifically, the source message is encoded
in the first portion of the codeword that is transmitted
by the source in Phase I and incremental redundancy
(e.g., in the form of extra parity symbols) can be
transmitted in the second portion of the codeword by
either the source or the relay in Phase II.
We adopt the cooperative communication model
wth analog network coding [2], where each group of
source nodes is assigned a single relay node. Denote
by W the amount of bandwidth a relay node can
utilize. Let Nrj be the white noise at relay node rj .
Given the transmission power Prj of relay node rj , the
channel capacity from source node si ∈ gk,where gk is
the group agent to which the source node belongs. to
destination node di through relay node rj can be
calculated by a simplified channel capacity model as
follows.














gks
rjsidirjk
dirjrjsi
disi
k
iii
i
SNRSNRg
SNRSNR
SNR
g
W
drsC
,,
,,
,2
||
.
1log
1||
),,(

Where
 
  2
2
1||
1||
1 rk
di
rrjk
g
N
Ng


 


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9

III. GAME THEORY
The essence of game theory is the formal study of
interactions between several decision-makers who
can have conflicting or common interests. By
interactions, it is meant that what the others do has an
impact on each decision-maker (called a player), and
what he/she gets from an interactive situation does
not only depend on his/her decisions. The mapping
from the components in a game to the elements in
cooperative communications is shown in Table I.
TABLE I
COMPONENTS OF GAMES IN COOPERATIVE
COMMUNICATIONS
Components in the
Game
Elements in Cooperative
Communication
Players
Strategy
Utility/Payoff
Source nodes and/or relay
nodes.
Power control,
Spectrum allocation,
Relay nodes(s) or source
node(s) selection,
To cooperate or not
Price.
Data rate,
Profit, e.g., revenue minus
cost.
A strategic form game is an ordered triplet: G=(k,
{Si}i∈k, ≥i) Where K is the set of players, Si is the set
of strategies of player i, and ≥ i is a preference order
over the set of action profiles for player i. The
strategic form is the most used form, in both game
theory and wireless literature. It is generally more
convenient for mathematical analysis and is usable
for both discrete and continuous strategy sets. In fact,
the most common form relies on the existence of a
cost/reward/payoff/utility function for each player.
The utility of a player is the measurement function on
the possible outcome determined by the strategies of
all players and is denoted by ui. In wireless
communications, the performance metrics (e.g., the
quality of service) are generally known, which give
the utility functions to be used directly [4].
Forwarder’s dilemma:
Two source nodes want to send a packet to their
respective destination nodes. To reach its destination,
the packet has to go through an intermediate node
which is actually the other source node. Each source
node can decide to forward the packet to the
destination of the other source (Forward) or drop it
(Drop) (Fig.5) .
Fig 5: The communication scenario under study:
Each source node decides to forward the packet to
destinations and has to go through to another source
node. For this, each source node has to decide
simultaneously either to forward or drop the received
packets.
The utility of each source is assumed to have the
form “utility = benefit x cost” where the benefit is 1
if the packet is forwarded and 0 if it is dropped; the
cost of transmitting is c > 0.This is shown in tabular
form in Table II.
TABLE II
Forwarder’s dilemma in matrix form.
Classification of games:
A. Dynamic vs static games
Dynamic games generally assume that source
nodes can extract some information from past moves,
observations, and chosen strategies and take this into
account to adjust current and future moves. In static
games, source nodes have certain knowledge
(information assumptions, behavior assumptions) and
this does not change.
B. Cooperative vs non-cooperative games
In non-cooperative games, the individual goals
and strategies can be distinguished, whereas in
cooperative games this is not always possible. A key
distinction between the two types of game is to know
whether commitments are enforceable or not: in
cooperative games commitments are fully binding
dst2 dst1
P2P1
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and enforceable, while they are not in non-
cooperative games.
Scope of a game theory includes the discussions
on rationality, selfishness, interactions and the
solution concepts.
 Rationality:
For implementing advanced game theoretic
algorithms in real systems, identifying the players
plays an important role in modeling the strategic
structure of the environment of a terminal.
Additionally, wireless networks also have some
specific features, which makes the problem of
rationality even more complicated. In heterogeneous
networks where players optimize different
performance criteria, some players can be perceived
as non-rational from a given other player’s point of
view. Of course, this depends on the knowledge of
the considered player.
 Selfishness:
Modeling players as selfish decision-makers leads
to incorrect predictions. But in wireless games selfish
players are seems to be, in general, the most relevant
assumption.
 Interaction:
A game corresponds to a situation where
(autonomous) decision-makers interact. The
interaction in wireless networks depends on the
scenario. Often interaction does exist because
terminals share common resources. For example,
when users exploit the same band at the same time, in
the same geographical area, some multiuser
interference occurs. Decisions made by the players
are inter-dependent,in the sense that their
performance metric depends on what the other
players do:this is the interaction through actions. It is
useful to know that there can be interaction between
players even if the player’s utility does not directly
depend on the actions of the others.
 Solution Concepts
The best response is the strategy which produces
the most favorable outcome for a player, taking other
players' strategies. The concept of a best response is
central to John Nash's best-known contribution,
the Nash equilibrium, the point at which each player
in a game has selected the best response (or one of
the best responses) to the other players' strategies .If
Source node i chooses the action F (forward) the
best-response of Source node -i is to drop. If Source
node i chooses the action D (Drop) the best-response
of Source node -i is to drop. From this, the output of
the global best-response correspondence BR (see
1.14) equals (D,D) for all the four possible action
profiles. The unique fixed-point of this
correspondence is clearly (D,D) i.e. (0,0), which is
the unique Nash equilibrium of the game.
Extensive-form game :
An extensive-form game is a specification of a
game in game theory, allowing (as the name
suggests) explicit representation of a number of
important aspects, like the sequencing of players'
possible moves, their choices at every decision point,
the (possibly imperfect) information each player has
about the other player's moves when he makes a
decision, and his payoffs for all possible game
outcomes. Extensive-form games also allow
representation of information. The Stackelberg game
is an extensive form game, which is used to model
the competition between one player, called the leader,
and a set of players, called the followers. In this
game, the leader takes action first and then the
followers take actions. The leader knows ex ante that
the followers observe its action and take actions
accordingly. The NE in the Stackelberg game is
called Stackelberg Equilibrium.
In a nut shell game theory states that it is
common to be in situations where the outcome of a
situation depends not only on what we do, but also on
what other people do. This is clearly the case when
participating in an auction. In cooperative network
the players of the auction under consideration are
base stations, laptops, mobile phones, routers,
servers, and so on. Obviously, the engineers who
design these machines are directed by the economic
policy of their company or institution, which
indicates that identifying the players is not always
obvious in wireless communications. Nonetheless,
there is a difference between considering a telecoms
operator or a mobile phone to be a player – the nature
of the action or decision to be taken is different. For
an operator involved in a spectrum auction, the action
to be taken may be a price, whereas the possible
actions available to a mobile phone may be to decide
which access points or base stations to be connected
to [3]. Indeed, interaction between wireless terminals
like mobile phones is naturally present in wireless
networks, since interference often exists or/and
common resources must be shared.
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IV. AUCTIONS IN COOPERATIVE NETWORK
An auction is a process of trading resources by
offering them up for bidding, and selling the items to
the highest bidder. In economic terms, it is also a
method to determine the value of a resource whose
price is unknown. An auction is organized by an
auctioneer, who distributes grid Market-Oriented
Resource Management and Scheduling. The
mechanism consists of determining the winner and
setting the price.
Auction schemes can be broadly classified into three
categories:
 Pricing or credit based schemes
 Reputation based schemes ; and
 Commodity exchanged schemes.
Credit-based schemes consider packet forwarding as
a market model where nodes providing a service are
remunerated, whilst nodes receiving a service are
charged [5]. Hence, if a node wants to send its own
packets, it must forward packets for the benefit of
others. However, these schemes require tamper-
resistant hardware) or infrastructure-dependent credit
clearance that other nodes can trust [7], [8]. The
Reputation-based schemes discourage misbehavior
by estimating the nodes reputation and punishing
nodes with bad behavior .The scheme requires each
node to rate every other node with which it
communicates based on the service received or on
observing the behavior of neighbors by listening to
communications in the same transmission range.
According to the collected information, the reputation
system maintains a value for each observed node that
represents a reputation of its behavior. The reputation
mechanism allows avoiding sending packets through
misbehaving nodes [10]. In commodity exchange
mechanism, the source node takes other nodes as
relays for cooperative communication. In return, the
source node provides its own resource to help the
relay nodes achieve certain objectives.[6]
The auctions can be divided into three types
based on participants and commodity exchanged: a)
Single-sided auction, b) Double-sided auction, and c)
Combinatorial auctions.
A.Single-sided Auction:
Single-sided auctions are mechanisms, where only
buyers or sellers can submit bids or asks. Even
though the single-sided auction is the most widely
applied market model, it often leads to inefficient
allocation. The most prominent single sided auctions
are Vickrey Auction, Dutch Auction, First Price
Sealed Bid (FPSB), and English Auction.
 English Auction: In the English auction, the
auctioneer begins the auction with a reserve price
(lowest acceptable price). Auction continues in
rounds with increasing bid prices, until there is
no price increase. The item is then sold to the
highest bidder.
 Dutch Auction: In the Dutch auction the
auctioneer begins with a high asking price which
is lowered until some participant is willing to
accept the auctioneer’s price or a predetermined
minimum price is reached. That participant pays
the last announced price. This type of auction is
convenient when it is important to auction
resources quickly, since a sale never requires
more than one bid.
 Vickrey Auction: A Vickrey auction is a sealed-
bid auction, where bidders submit sealed bids.
The highest bidder wins, paying the price of the
second highest bid. This gives bidders incentives
to bid their true value. When multiple identical
units are auctioned, one obvious generalization is
to have all bidders pay the amount of the highest
non-winning bid.
 First Price Sealed Bid (FPSB) Auction: In this
type of auction, all bidders simultaneously
submit bids so that no bidder knows the bid of
any other participant. The highest bidder says the
price they submitted. In this case, the bid
strategy is a function of one’s private value and
the prior belief of other bidders’ valuations. The
best strategy is bid less than its true valuation
and it might still win the bid, but it all depends
on what the others bid.
B.Double Sided Auction:
In double auction, both providers and users submit
bids which are then ranked highest to lowest to
generate demand and supply profiles. From the
profiles, the maximum quantity exchanged can be
determined by matching selling offers (starting with
the lowest price and moving up) with demand bids
(starting with the highest price and moving down).
This format allows users to make offers and
providers to accept those offers at any particular
moment. In double auction, the winner determination
depends on different aspects such as aggregation,
resource divisibility and if goods are homogeneous or
are heterogeneous. Aggregation can come from the
supplier side or from the buyer side. If no
aggregation is allowed then each bid can be exactly
matched to one ask. Divisible goods can be allocated
partially. In the case that the bidder wants the entire
good or nothing then its bid is considered indivisible.
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C. Combinatorial Auctions:
Users may require a combination of multiple
resources such as CPUs, memory and bandwidth.
Combinatorial auction allows users and providers to
trade a bundle of multiple resources. It is
advantageous to users as they do not need to
participate in multiple negotiations with providers for
each resource required. Moreover, in some cases it
also leads to cost benefits. In combinatorial auction,
users express their preferences as bundles of
resources that need to be matched. The providers
submit their tasks and the auctioneer solves the
optimization problem of allocation. The only
drawback of combinatorial auction is the NP-
hardness of the matching problem which makes it
inapplicable for large scale settings. Various variants
of combinatorial auction are proposed in the literature
to allocate computational resources among grid users.
Main Issues to be focused in auction mechanism:
 Truthfulness implies that the dominant
strategy of each agent is to submit truthful
valuations of the products. It can be
achieved by unrelated bids of participating
agents to their payments [11],[12].
 Budget Balance means that the total
payment received from the buyers is no less
than the total payment to the sellers in an
auction.
 Individual Rationality means that no
winning buyer will be charged more than its
bid, and no winning seller will be paid less
than its ask.
V. CONCLUSION
In this article, we have briefly surveyed on the
game theory and auctions for the relay assignment in
cooperative communications, with the fixate on
designing cooperation incentive mechanisms. While
game theory has been extensively applied to
cooperative communications, there are still many
challenges to be resolved with an extra effort from
researchers.
REFERENCES
[1] J. Laneman, D. Tse, and G. Wornell, “Cooperative diversity in
wireless networks: Efficient protocols and outage behavior,”IEEE
Trans. Inf. Theory, vol. 50, pp. 3062–3080, 2004.
[2] S. Sharma, Y. Shi, J. Liu, Y. T. Hou, and S. Kompella, “Is
network coding always good for cooperative communications?”
Proc. 2010 IEEE INFOCOM.
[3] J. Huang, Z. Han, M. Chiang, and H. Poor, “Auction-based
resource allocation for cooperative communications,” IEEE JSAC,
vol. 26, pp. 1226–1237, 2008.
[4] M. Janzamin, M. Pakravan, and H. Sedghi, “A game-theoretic
approach for power allocation in bidirectional cooperative
communication,” in Proc. IEEE WCNC’10, pp. 1–6. 12
[5] N. Shastry and R. Adve, “Stimulating cooperative diversity in
wireless ad hoc networks through pricing,” in Proc. IEEE ICC’06,
pp. 3747–3752.
[6] H. Wang, L. Gao, X. Gan, X. Wang, and E. Hossain,
“Cooperative spectrum sharing in cognitive radio networks- a
game-theoretic approach,” in Proc. IEEE ICC’10.
[7] B. Wang, Z. Han, and K. Liu, “Distributed relay selection and
power control for multiuser cooperative communication networks
using stackelberg game,” IEEE Trans. Mobile Comput., vol. 8, pp.
975–990, 2009.
[8] G. Zhang, L. Cong, L. Zhao, K. Yang, and H. Zhang,
“Competitive resource sharing based on game theory in
cooperative relay networks,” ETRI Journal, vol. 31, pp. 89–91,
2009.
[9] D. Yang, X. Fang, and G. Xue, “HERA: An optimal relay
assignment scheme for cooperative networks,” IEEE JSAC,
accepted.
[10] Y. Chen and S. Kishore, “A game-theoretic analysis of
decode-and-forward user cooperation,” IEEE Trans. Wireless
Commun., vol. 7, pp. 1941–1951, 2008.
[11] D. Yang, X. Fang, and G. Xue, “Truthful auction for
cooperative communications,” in Proc. ACM MOBIHOC’11, pp.
89–98.
[12] D. Yang, X. Fang, and G. Xue, “Truthful auction for
cooperative communications with revenue maximization,” in Proc.
IEEE ICC’12, accepted.
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