Abstract
Game theory has been widely used in wireless networks for solving problems of conflict and cooperation among rational agents. A particularly interesting branch of game theory is evolutionary game theory (EGT), where population evolves over time. In EGT, the players circumspectly adapt the most successful strategies over time. This adaptation is done by replicator dynamics. In the first part of this chapter, we take a quick tour of the fundamental concepts in classical and evolutionary game theory. Followed by this, we look at diverse applications of EGT with a focus on communication networks. Subsequently, we discuss about a particularly popular game based, called the Rock-Scissors-Paper (RSP) game. This chapter concludes with an application of the RSP game to OMNs by considering the relationship that exists among different cooperation strategies of the nodes.
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Notes
- 1.
- 2.
Refer to [227] for more details.
- 3.
Portions of this chapter are reproduced with kind permission from Springer Science+Business Media: Next-Generation Wireless Technologies, Cooperation in Delay Tolerant Networks, 2013, 15–35, Sudip Misra, Sujata Pal, Barun Kumar Saha.
- 4.
This example is taken from http://www.math.wsu.edu/math/faculty/lih/464-16pp.pdf.
- 5.
Please refer [230] for more details.
- 6.
Named in the honor of Lloyd S. Shapley, who has immense contributions to game theory, and was awarded the Nobel Prize in Economic Sciences in 2012 jointly with Alvin E. Roth.
- 7.
The terms players and nodes are uses interchangeably in the rest of this chapter.
- 8.
The wording of this example is borrowed from [238], p. 3179.
- 9.
Synergy factor (\(\alpha \)) is the estimation of profit gained due to cooperation.
- 10.
ALOHA stands for Additive Links On-line Hawaii Area.
- 11.
In Pareto optimal resource allocation, the payoff of no nodes is better off without at least one node in a less advantageous position.
- 12.
Licensed users are known as Primary Users (PUs).
- 13.
Secondary users are the cognitive and unlicensed users.
- 14.
Note that an exploiter does not receive nor forward (replicate) messages created by other exploiters in the OMN.
- 15.
As discussed earlier, only isolators directly forward a message to its corresponding destination; cooperators and exploiters replicate a message. However, here we use “forward” to represent both these kind of actions. The exact meaning should be evident based on the group of nodes that take the Forward action.
- 16.
To understand how a node “declines” to receive a message, let us recollect the summary vectors from Chap. 2. When a node sends a list of message IDs that it is (un)willing to receive in response to a summary vector, it can exclude(include) the specific message ID that it does not want to receive.
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Misra, S., Saha, B.K., Pal, S. (2016). Evolutionary Game in Wireless Networks. In: Opportunistic Mobile Networks. Computer Communications and Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-29031-7_6
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DOI: https://doi.org/10.1007/978-3-319-29031-7_6
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