194		9. Coexisting Wireless LANs as Multi Stage Game
	all resulting		all resulting
	payoffs		payoffs
n=1	BEST RESPONSE:	n=1	COOPERATE:
	BEH-B		BEH-C

Figure 9.2: Strategy STRAT-B as machine. The state is labeled with BEST RESPONSE and the behavior is BEH-B as defined in Section 8.3.2.2, p. 184.

Figure 9.3: Strategy STRAT-C as machine. The state is labeled with COOPERATE and the behavior is BEH-C as defined in Section 8.3.2.3, p. 185.

9.2.2Experimental Results

In the following, the static strategies STRAT-P, STRAT-B, and STRAT-C are analyzed and compared with each other.

9.2.2.1Scenario

A game with the following requirements is analyzed:
	Θ1req		Θreq2		=	0.6				0.6
	∆1	,	∆2				0.4		,	0.23	.
	req		req

Player 1 attempts to allocate resources for a longer duration than player 2. Hence, as a result of the analysis in Section 8.3.2.3, p. 185, player 2 can be considered as the weaker player. The Nash equilibrium of this game is unique and given by the action profile

a* =	1		0.6		, a	2	*	=		0.86		,	(9.4)
	a * =		0.032							0.02
and the resulting payoff in Nash equilibrium is
V* ((a1* ), (a2* ))				= (0.81;						0.37 ).			(9.5)

Numerical searches indicate that this Nash equilibrium is not Pareto efficient, which means that in this particular game it may be beneficial for both players to cooperate rather than attempting to maximize the individual payoffs per SSG. This will be discussed in the following Section 9.2.2.2. In this section, the results given in Section 9.2.2.4–9.2.2.6 are reviewed. Results for three different approaches of the CCHC coexistence game of two overlapping BSSs are presented. Section 9.2.2.4, p. 202, shows the simulation and analytical results for the simplest

9.2 Static Strategies

195

approach where both players take actions without dynamic behavior adaptation, according to the static strategy STRAT-P. This scenario represents two overlapping BSSs that follow their requirements when allocating resources, without taking into account the mutual influences between the competing BSSs. It is the scenario against which all other scenarios are evaluated and compared, because it represents behaviors that occur when players do not follow any game approach. Section 9.2.2.5, p. 203, shows the simulation and analytical results for the approach where both players take actions that attempt to maximize the individual payoffs, based on the history of their observations. This is referred to as best response, according to the static strategy STRAT-B. Finally, Section 9.2.2.6, p. 204, shows the simulation and analytical results for the approach where both players take actions cooperatively, according to the static strategy STRAT-C.

Three figures are given per section, each figure being comprised by some subfigures. The first figure at the beginning of each section illustrates the required, demanded, and observed QoS parameters (see for example for the first section, Figure 9.4, p. 202) as a result of the repeated interactions of the players. The second figure in each section indicates the behaviors that are selected by the players per stage, and the observed utilities and payoffs (see for example in Figure 9.5, p. 202). The third figure in each section illustrates in its left subfigure the probabilities of resource allocation delays that result if the respective static strategies are selected for a long duration (see for example Figure 9.6, p. 203, left subfigure). Finally, this third figure in each section illustrates in its right subfigure the throughput and payoff results that are typically found when the requirements for share of capacity of both players are varied. Note that in the latter figure the required resource allocation intervals remain as they have been defined in this section, but the required share of capacities are varied between 0.1 and 0.8:

	Θ1req		Θreq2		=		Θ1		Θ2
	1	,	2				req ,		req	,
							0.4		0.23
	∆req		∆req

with Θ1req = Θreq2 = 0.1…0.8 . In all games analyzed here, the EDCF background simulates an offered traffic of 5 Mbit/s, which is modeled through an Ethernet

traffic trace file (see Appendix B for an explanation of the simulation environment). The TXOPlimit that defines the maximum duration of resource allocations of the EDCF is set to 300µs , which is relatively small and therefore limits the influence of the EDF on the results. All results are discussed in the next section, each approach independently.