188	8. The Superframe as Single Stage Game

However, this behavior cannot guarantee that player i itself may achieve a satisfying payoff. If one or all players behave according to BEH-D, the resulting payoffs are low due to the very long and many resource allocations.

8.3.2.5Available Behaviors

In Figure 8.6, the action space of a player and the resulting consequences on the opponent players are indicated. The two illustrated cases at the left and right border of the action space, (a) deferring from resource access completely and (b) occupying all resources for the complete duration of the SSG, are not defined in the game model. Further, as part of the game model, ∆ ≤ 0.1. Indicated in the figure are areas where a player may meet its requirement by playing the best response, where a player may cooperate, and where it behaves selfish by blocking the opponent. The collision probability depends on the number of resource allocation attempts and increases with decreasing ∆dem of all players.

1	(a)
	channel			allocation	U∆	1		process
				process				allocation
∆dem	communicationother	area is useless for
		CCHC and time			“reduced
		bounded services
					probability
					of collision“
	for	UΘ	0	(requirement)
	search				“desirable			“selfish
					area“			behavior“
	access,			“support			“best
				of EDCF“			response“	allocation
				allocation				process
	from				“cooperation“
				process
				UΘ	0	collisions“
	defer
						“many
0		0			Θdem

(b)

busy tone

1

Figure 8.6: Portfolio of available actions, the corresponding utilities and the resulting consequences on the opponents. The extreme cases of (a) deferring from resource access as part of DFS and (b) occupying all resources all the time, are not part of the game model, and therefore not part of the action space.

Chapter 9

COEXISTING WIRELESS LANS AS MULTI STAGE

GAME

9.1	Strategies in MSGs.............................................................	190
9.2	Static Strategies ..................................................................	192
9.3	Dynamic Strategies ...........................................................	206

WITH THE UNDERSTANDING of the SSG and the definition of behaviors that allow interacting players to dynamically take actions in order to achieve certain payoffs as the instantaneous outcome of an

SSG, it is now possible to investigate realistic CCHC coexistence scenarios with the help of a Multi Stage Game (MSG). In an MSG, an SSG is played repeatedly with behaviors selected per SSG. All players take actions individually at the beginning of each stage. Players in an MSG follow a certain strategy. Strategies define what behavior to select in which SSG. Strategies can be understood as state machines where behaviors are selected from SSG to SSG based on the history of resulting payoffs. In general, an uncountable number of strategies and behaviors can be defined for an MSG; here the investigation is restricted to elementary strategies that will be defined in the following, and the behaviors defined in the previous chapter. These strategies and behaviors allow analyzing the concept of cooperation in this chapter, motivated by the analysis of Axelrod (1984). This chapter evaluates the advantages and drawbacks of the game approach developed in this thesis. The CCHC coexistence problem will be evaluated with and without the game approach that has been introduced in the previous chapters.

A strategy is a description of how a player intends to play by selecting behaviors throughout the MSG. The behaviors that are used by the strategies are BEH-P,