Chapter 7

THE GAME MODEL

7.1	Overview.............................................................................	132
7.2	The Single Stage Game (SSG) Competition Model.........	133
7.3	The Multi Stage Game (MSG) Competition Model ........	150
7.4	Estimating the Demands of the Opponent Player..........	152
7.5	Concluding Remark...........................................................	156

THIS CHAPTER introduces a model derived from game theory, that describes the CCHC coexistence problem as a game of decision makers. A game model is based on a set of decision makers (here entities within a

CCHC device) that are called players (Fudenberg and Tirole 1991). The model will be used to analyze the coexistence problem that was identified in the previous chapters. After an overview about the approach taken in the next Section 7.1, Section 7.2 introduces the Single Stage Game (SSG) including the concepts of action, utility, preference and behavior. Section 7.3 introduces the Multi Stage Game (MSG), which will serve for the investigation of static and dynamic strategies, and rational behavior versus cooperation. Further, the prediction method that allows coexisting entities to estimate the demands of other coexisting entities is described in Section 7.4. This prediction method serves as estimator of QoS requirements of different coexisting CCHCs throughout the analysis that follows in the next chapters. The SSG will be used in Chapter 8 for an in-depth analysis of the problem, and for the definition of various kinds of so-called behaviors for coexisting entities.

The MSG will finally serve as the rational behind the concept of cooperation of coexisting entities, as studied in Chapter 9 in the context of the CCHC coexistence problem.

132	7. The Game Model

The vocabulary of game theory is not standardized. In this thesis, the notation and terminology of Osborne and Rubinstein (1994) and Neumann and Morgenstern (1953) are used, with many definitions taken from Fudenberg and Tirole (1991), Debreu (1959), and Green and Heller (1981).

7.1Overview

A dynamic game model is applied to study the CCHC coexistence. The game model comprises a set of players that choose their actions in each stage of the game to maximize their expected own utility in the stage, given their assessment of their opponent’s actions in that particular stage. Utilities are defined in Section 7.2.3. An action of a player is the selection of a certain way of resource allocation by a CCHC. The game model is called dynamic as players periodically adapt their action to the environment after each period of the game. At each game stage a player observes the action of its opponent together with its own utility, which is measured in the CCHC case based on the mutual influence of the player’s interactions, see Section 7.2.3.

The SSG competition model that is discussed in the next section, describes one such stage of the game. Based on that model, the MSG competition model covers the dynamic effects in repeated SSGs. Whereas an SSG is played once, the MSG represents a repeated interaction of players. The MSG competition model helps to understand social phenomena between players that interact for a longer time. Section 7.2 introduces the competition model of the SSG. Section 7.3 extends the SSG to the multi stage case.

In Section 7.4, a prediction method is described that allows a player to estimate the demands of its opponent player. This approach gives way for the usage of game models with complete knowledge, i.e., games where each player determines its action after observing past actions of its opponent players and determining the demands of those opponent players from the observed actions10. However, knowing the demands does not imply that the actual requirements are known to the opponent players. This differentiates the coexistence scenario from an interworking scenario, as discussed earlier in this thesis.

10Games where the interacting players do not have any means to determine the requirements of their opponent player from their observation are referred to as games without complete knowledge.