Technological investment games among wireless telecommunications service providers

Patrick Maillé, Bruno Tuffin, Jean-Marc Vigne
2011 International Journal of Network Management  
With the development of new technologies in a competitive context, infrastructure investment and licence purchase as well as existing technology maintenance are crucial questions for current and emerging operators. This paper presents a three-level game analyzing this problem. At the highest level, the operators decide on which technologies to invest, given that some may already own licences or infrastructures. We limit ourselves to the realistic case where technologies are 3G, WiFi and WiMAX.
more » ... t the intermediate level, with that set of operated technologies fixed, operators determine their service price. Finally, at the lowest level, customers choose their provider depending on the best combination of price and available quality of service. At each level, the best decision of actors depends on the actions of others, the interactions hence requiring to be studied as a (noncooperative) game. The model is analyzed by backward induction, meaning that decisions at a level depend on the equilibria reached at the lower levels. Different real-life cost scenarios are studied. Our model aims at helping both the operators to make their final decision on technological investments, and the regulator to determine a proper licence fee range for a better competition among providers. This paper is organized as follows. In Section 2, we present the basic model that will be used: the user behavior, the set of providers and available technologies, and the three levels of game. The lowest level of game, that is the competition among users looking for the network with the best combination of price and QoS, is analyzed in Section 3; the equilibrium is characterized, and existence and uniqueness are discussed. Section 4 analyzes the pricing game for fixed technologies, anticipating what the reaction of users would be. The third level of game, the game on technologies, is described in Section 5. This game makes use of the revenues at the pricing-game level, and pastes the infrastructure and licence A Nash equilibrium of the pricing game does not always exist. However, when there is one, the prices set by providers satisfy a relation similar to the ones proved in [12, 13] . Proposition 4.2. Assume Assumption 3.1 holds and that, on its support, the demand function D is Consider again, as well as in the rest of the paper, a zone covered by a single base station, for a period of one month. Estimated infrastructure plus licence costs, if any, are therefore also divided by the 10 4 zones in France and by the duration in months of the licence rights. As presented in Section 5, we define a cost per zone and per month at provider i for technology t and a cost matrix (c 1 (S 1 ), c 2 (S 2 )) S1,S2⊂T .
doi:10.1002/nem.776 fatcat:gxotmjtul5cmplzldval3raygi