Abstract
Interactions among selfish users sharing a common transmission channel can be modeled as a non-cooperative game using the game theory framework. When selfish users choose their transmission probabilities independently without any coordination mechanism, Nash equilibria usually result in a network collapse. We propose a methodology that transforms the non-cooperative game into a Stackelberg game. Stackelberg equilibria of the Stackelberg game can overcome the deficiency of the Nash equilibria of the original game. A particular type of Stackelberg intervention is constructed to show that any positive payoff profile feasible with independent transmission probabilities can be achieved as a Stackelberg equilibrium payoff profile. We discuss criteria to select an operating point of the network and informational requirements for the Stackelberg game. We relax the requirements and examine the effects of relaxation on performance.
Highlights
In wireless communication networks, multiple users often share a common channel and contend for access
We show that the manager can implement any transmission probability profile as a Stackelberg equilibrium using a class of intervention functions
If the Stackelberg contention game is played repeatedly and the users anticipate that the strategy profile of the other users will be the same as that of the last period, it can be shown that under certain conditions there is a sequence of intervention functions convergent to g∗ that the manager can employ to have the users reach the intended Nash equilibrium p, approaching the Stackelberg equilibrium
Summary
Multiple users often share a common channel and contend for access. EURASIP Journal on Advances in Signal Processing does not require that the actions of players be enforceable To apply this approach to the medium access problem, signals need to be conveyed from a mediator to all users, and users need to know the correct meanings of the signals. Chen et al [12, 13] use game theoretic models to study random access Their approach is to capture the information and implementation constraints using the game theoretic framework and to specify utility functions so that a desired operating point is achieved at a Nash equilibrium. If conditions under which a certain type of dynamic adjustment play converges to the Nash equilibrium are met, such a strategy update mechanism can be used to derive a distributed algorithm that converges to the desired operating point This control-theoretic approach to game theory assumes that users are obedient.
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