150 7. The Game Model

The possibility of information exchange does not contradict the game approach that is taken here. There are still competing entities that have different interests.

The question arises if there is an action of a player that is optimal in the sense that it maximizes the observed payoff of a player. Further, it is of interest if there exists an action vector a*( n ) =( ai*( n ),a−i*( n )) , with a*( n ) Α , that maximizes the payoff for all players in the sense that no player can improve its

payoff	by unilaterally changing its action. If such an action vector exists, it is of
interest	if	it is unique, and a stable operation point, i.e., equilibrium point
in Α =×		Αi . It is further not necessary that this operation point is efficient,
	i N

which means that there can be another action vector that leads to higher payoffs for all players, but requires that all players take this action, with the individual risks for each player of observing very poor payoff results.

These questions that are most relevant for solutions to the problem of coexisting CCHCs are discussed in Chapter 8 with the help of an analytic approximation of the SSG. A deeper look is taken in the context of repeated interaction in Chapter 9.

7.3The Multi Stage Game (MSG) Competition Model

Repeated SSG are referred to as Multi Stage Games (MSGs) and introduced in this section. Coexisting CCHCs operate in relatively time-invariant radio environment. Due to the nomadic mobility in wireless LANs, coexisting CCHCs interact for such long durations that a large number of repeated SSGs can be assumed as representation of a typical CCHC coexistence scenario. The QoS requirements a player attempts to support may more dynamically change than the positions of the involved radio stations. The mobility of stations in a wireless network characterizes the dynamics of changes of the radio environment. This mobility is known to be small in indoor scenarios of wireless LANs. Here specifically the coordination of CCHCs that support integrated protocols such as HiperLAN/2 are in the focus of interest, not the direct support of any particular application. The changes of QoS requirements of CCHCs are not as dynamic as the changes of QoS requirements of characteristic applications.

It is therefore assumed in the following that the QoS requirements of a CCHC change slowly compared to speed of the decision processes. In the simulation that will be discussed later, this is taken into account by changing the actions from one profile to the other not in one step, but taking a number of stages for slow changes.

7.3 The Multi Stage Game (MSG) Competition Model

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Throughout the play of an MSG, the QoS requirements of each player will stay constant. In case the QoS requirements change, another MSG will be used to analyze the subsequent time for which the selected actions of the involved players have to adapt to the new QoS requirements.

MSGs allow the analysis of the dynamic effects of competition. In an MSG, players are able to condition their actions on the way their opponent played in previous stages.

This is done by applying strategies: a strategy completely describes how a player plays an MSG from the first stage to the final stage of the MSG (Shubik 1982:34). Based on a strategy, players select behaviors upon certain events, hence a dynamic interaction can be established where the players adapt their behavior. Still operating in the domain of alternatives that are available in the SSG, in an MSG, players are concerned with rapidly achieving a certain level of payoff that is stable until the end of interaction. While interacting, the moment when the MSG will end is not known to the individual players. The MSG is a finite game with unknown end.

In the context of the CCHC coexistence scenario, not the outcome after an SSG with its short duration is to be optimized by a player, but the resulting outcome over the complete time of interaction, i.e., the complete MSG. In addition, strategies must provide means to allow a player to assess in advance what level of QoS can be supported in a certain environment. For this purpose, a player has to understand the influence of any upcoming actions of the opponent player on the own payoff results. Once this influence of the opponent is known, mutual support may help to optimize the observed payoffs in the game, which often is beneficial for all players. This is called cooperation (Shubik, 1982). The concept of cooperation –in some publications referred to as mutuality– between players is helpful to understand what can be gained by mutual support and will be analyzed in the Chapter 9. See Stephens and Anderson (1994) for some interesting discussions about cooperation, and mutuality. A cooperating player implements a strategy that does not select a behavior for its best response (called rational behavior). Instead, it deviates towards a behavior that, if the opponent player also deviates from its best response, results in a larger payoff for both players. This is referred to as efficient behavior, see Section 8.3. With this behavior, based on mutual support, players may achieve a better outcome in an action profile that is not necessarily a stable operation point and thus requires what is referred to as cooperation. The next Chapter 8 will show that in the game of coexisting CCHCs, such an efficient action profile indeed exists. If a player knows from the past interaction that its opponent player also implements a similar rationale for coop-