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• Print publication year: 2017
• Online publication date: May 2017

# 4 - Game Theory

from Part II - Techniques for Modeling and Analysis of Radio Resource Allocation Methods in Wireless Networks

## Summary

Fundamentals of Game Theory

Brief History

In a typical optimization problem, we need to maximize/minimize an objective function by controlling the values of a vector that satisfies a set of constraints. In this case there is only one party that controls the system, and its actions do not depend or are not affected by other parties. However, in practice, there are many situations in which we must make decisions to optimize an objective function in presence of other parties, and their actions can change the outcome we expect. The information about the decisions of other parties may or may not be available to us at the time we make our decisions or moves. Since each party has its own objective and is usually selfish, it will try to maximize its benefit. In such a case, the solution of a normal optimization problem may not result in the best profit for every party. If any party thinks it can achieve a better payoff, it will act alone, and thus, the solution may not be useful. Therefore, we may wish to find a solution (i.e., an equilibrium) that everyone is satisfied with and hence does not want to move. Game theory is able to provide such a solution. It is a branch of applied mathematics that “uses models to study interactions with incentive structures” among different decision-makers. In game theory, we need to anticipate the opponents’ moves and reply with the best action to optimize the objective.

Game theory has a quite young history. It started with the work of Augustin Cournot's Mathematical Principles of the Theory of Wealth in 1938 where he studied a duopoly using formal game-theoretic analysis. Emile Borel's series of papers during 1921–1926 defined strategies of a game. In 1944, game theory was established as a separate mathematical field due to the book Theory of Games and Economic Behavior by Von Neumann and Oskar Morgenstern. This book provided much of the basic terminology and problem setup that is still in use today. Then in 1950, John Nash proved that finite games have always have an equilibrium point, at which all players choose actions that are best for them given their opponent's choices.

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[1] , , , and , “Game theoretic approaches for multiple access in wireless networks: A survey,” IEEE Communications Surveys and Tutorials, vol. 13, no. 3, Third Quarter, 2011, pp. 372–395.
[2] , , , and , ldquo;CDMA uplink power control as a noncooperative game,” 40th IEEE Conference on Decision and Control, Dec. 2001.
[3] , ,, , and , Game Theory in Wireless Communication Networks: Theory, Models and Applications. Cambridge University Press, 2012.
[4] , An Introduction to Game Theory. Oxford University Press, 2009.
[5] and , “Game Theory inWireless Networks: A Tutorial,” Technical Report LCA-REPORT, 2006.
[6] , , , and , “Hierarchical competition for downlink power allocation in OFDMA femtocell networks,” IEEE Transactions on Wireless Communications, vol. 12, no. 4, Apr. 2013, pp. 1543–1553.
[7] , , and , “K-player Bayesian waterfilling game for fading multiple access channels,” 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2009.
[8] , , and , “Distributed resource allocation in wireless networks under uncertainty and application of Bayesian game,” IEEE Communications Magazine, Special Issue on “Game Theory in Wireless Networks,” vol. 49, no. 8, Aug. 2011, pp. 120–127.
[9] and , Networks, Crowds, and Markets: Reasoning About a Highly Connected World. Cambridge University Press, 2010.
[10] , , , and , “Evolutionary games in wireless networks,” IEEE Transaction on Systems, Man, and Cybernetics – Part B: Cybernetics, vol. 40, no. 3, June 2010, pp. 634–646.
[11] and , “Dynamics of network selection in heterogeneous wireless networks: An evolutionary game approach,” IEEE Transactions on Vehicular Technology, vol. 58, no. 4, May 2009, pp. 2008–2017.
[12] , , and , “Dynamics of multiple-seller and multiple-buyer spectrum trading in cognitive radio networks: A game theoretic modeling approach,” IEEE Transactions on Mobile Computing, vol. 8, no. 8, Aug. 2009, pp. 1009–1022.
[13] and , “Bargaining strategies for networked multimedia resource management,” IEEE Transaction on Signal Processing, vol. 55, no. 7, 2007, pp. 3496–3511.
[14] , , , , and , “Exploiting mobility diversity in sharing wireless access: A game theoretic approach,” IEEE Transactions on Wireless Communications, vol. 9, no. 12, Oct. 2010, pp. 3866–3877.
[15] , , and , “Cooperative packet delivery in hybrid wireless mobile networks: A coalitional game approach,” IEEE Transactions on Mobile Computing, vol. 12, no. 5, May 2013, pp. 840–854.
[16] , , and , “Coalition-based cooperative packet delivery under uncertainty: A dynamic Bayesian coalitional game,” IEEE Transactions on Mobile Computing, vol. 12, no. 2, Feb. 2013, pp. 371–385.
[17] and , “A game-theoretic look at the Gaussian multi-access channel,” Proc. DIMACS Workshop on Network Information Theory, pp. 87–106, 2003.
[18] , , , and , “Auction-based resource allocation in cognitive radio systems,” IEEE Communications Magazine, 4th Quarter 2012, Special Issue on “Communications Network Economics,” vol. 50, no. 11, Nov. 2012, pp. 108–120.
[19] , , and , “Dynamic spectrum access in IEEE 802.22-based cognitive wireless networks: A game theoretic model for competitive spectrum bidding and pricing,” IEEE Wireless Communications, vol. 16, no. 2, Apr. 2009, pp. 16–23.
[20] and , “Combinatorial Auctions: A Survey,” INFORMS Journal on Computing, vol. 15, no. 3, 2003, pp. 284–309.
[21] and , “Virtualization of 5G cellular networks as a hierarchical combinatorial auction,” IEEE Transactions on Mobile Computing, vol. 15, no. 10, Oct. 2016, pp. 2640– 2654