Catálogo de publicaciones - libros

We investigate a hybrid noncooperative game motivated by the practical problem of joint power control and base station (BS) assignment in code division multiple access (CDMA) wireless data networks. We model the integrated power control and BS assignment problem such that each mobile user’s action space includes not only the transmission power level but also the respective BS choice. Users are associated with specific cost functions consisting of a logarithmic user preference function in terms of service levels and convex pricing functions to enhance the overall system performance by limiting interference and preserving battery energy. We study the existence and uniqueness properties of pure strategy Nash equilibrium solutions of the hybrid game, which constitute the operating points for the underlying wireless network. Since this task cannot be accomplished analytically even in the simplest cases due to the nonlinear and complex nature of the cost and reaction functions of mobiles, we conduct the analysis numerically using grid methods and randomized algorithms. Finally, we simulate a dynamic BS assignment and power update scheme, and compare it with “classical” noncooperative power control algorithms in terms of aggregate signal-to-interference ratio levels obtained by users.

We introduce the concept of nonlinear pricing within the context of our previous Stackelberg network game model and view the Internet Service Provider’s (ISP’s) policy as an incentive policy, and the underlying game as a reverse Stackelberg game. We study this incentive-design problem under complete information as well as incomplete information. In both cases, we show that the game is not generally incentive controllable (that is, there may not exist pricing policies that would lead to attainment of a Pareto-optimal solution), but it is ɛ-incentive controllable (that is, the ISP can induce a behavior on the users that is arbitrarily close to a Pareto-optimal solution). The paper also includes a comparative study of the solutions under linear and nonlinear pricing policies, illustrated by numerical computations.

This paper presents a dynamic game model of international terrorism. The time horizon is finite, about the size of one presidency, or infinite. Quantitative and qualitative analyses of incentive Stackelberg strategies for both decisionmakers of the game (“theWest” and “International Terror Organization”) allow statements about the possibilities and limitations of terror control interventions. Recurrent behavior is excluded with monotonic variation in the frequency of terror attacks whose direction depends on when the terror organization launches its terror war. Even optimal pacing of terror control operations does not greatly alter the equilibrium of the infinite horizon game, but outcomes from theWest’s perspective can be greatly improved if the game is only “played” for brief periods of time and if certain parameters can be influenced, notably those pertaining to the terror organization’s ability to recruit replacements.

We take a differential game approach to model the Ramsey growth model from the standpoint of the representative firm. We identify parametric conditions such that the economy cannot reach the Ramsey golden rule, due to the presence of a stable demand-driven equilibrium. This may happen under Cournot and Bertrand behaviour, as well as social planning. We show that a wave of horizontal mergers can indeed drive the economy towards the Ramsey golden rule.

This paper extends previous research on the effects of process imitation on economic growth by accounting for stochastic intra-industry spillovers. We employ a non-Schumpeterian growth model to determine the impact of such spillovers on investment in industries where firms are either neck-and-neck or unleveled. Our central finding is that, in an economy where the representative industry is a duopoly, research and development (RD) spillovers positively affect economic growth. While other non-Schumpeterian models assume that the imitation rate of laggard firms is unaffected by the RD effort of the leader firm, we consider the case where the latter’s RD activity generates some positive externality on its rivals’ research. In this construct, the duopolists in each industry play a two-stage game. In the first stage, they invest in RD which can reduce their costs of production only if they successfully innovate and they compete with each other by using Markovian strategies. In the second stage, they compete in the product market. At any point in time, an industry can be either in the neck-and-neck state or in an unleveled state where the leader is n steps ahead of the follower. At the steady state, the inflow of firms to an industry must be equal to the outflow. By determining the steady state investment levels of each industry, we demonstrate a positive monotonic relationship between the spillover rate and economic growth.

In this chapter, we develop a dynamic model of collaboration between a manufacturer and its supplier, where the fundamental issue is, for each player, how to allocate own resources between improving an existing product and developing a new one. We study the optimal time path of effort allocation for each player in a noncooperative setting, and then look into the cooperative setting. We finally conduct a numerical analysis and observe how the optimal dynamics of key variables change as parameters of the game vary.

An infinite-horizon differential game between a manufacturer and a retailer is considered. The players control their marketing efforts, and the sales share of the online channel is the state of the system. The manufacturer seeks to maximize her profit made on both the indirect and direct channels and faces, aside from her marketing effort, a logistics cost of selling online. The retailer seeks to keep consumers buying offline through her effort. A feedback Nash equilibrium is identified and results are discussed.

This chapter deals with the imitation of fashion products, an issue that attracts considerable interest in practice. Copying of fashion originals is a major concern of designers and, in particular, their financial backers. Fashion firms are having a hard time fighting imitations, but legal sanctions are not easily implemented in this industry. We study an alternative strategy that has been used by designers. Instead of fighting the imitators in the courtroom, designers fight them in the market. The designer markets her products in two separate markets. Typically, there is a “high-class” market in which the products are sold in exclusive stores at high prices. Customers in this market seek exclusivity and their utility diminishes when they see an increasing number of copies around. Their perception of the brand tends to dilute which poses a serious threat to a fashion company. The second market is a “middle-class” market in which there are many more buyers, and the fashion firm competes directly with the imitators in this market. This market can be used to practice price discrimination, to sell off leftover inventories, and to get a spin-off from the design. This chapter models the decision problems of the fashion firm and the imitators as a two-period game in which firms make pricing decisions and decisions on when to introduce their products in the markets. In addition, the fashion firm decides how much effort to spend to increase its brand image in the two markets.

In this chapter we show how certain noncooperative Cournot-Nash dynamic games arising in service pricing and resource allocation may be articulated as differential variational inequalities. We show how such problems may be solved using a fixed point algorithm having continuous time optimal control subproblems.

The Markov chain approximation method is a widely used, relatively easy to apply, and efficient family of methods for the bulk of stochastic control problems in continuous time, for reflected jump-diffusion type models. It is the most general method available, it has been shown to converge under broad conditions, via probabilistic methods, and there are good algorithms for solving the numerical problems, if the dimension is not too high (see the basic reference [16]). We consider a class of stochastic differential games with a reflected diffusion system model and ergodic cost criterion, where the controls for the two players are separated in the dynamics and cost function. The value of the game exists and the numerical method converges to this value as the discretization parameter goes to zero. The actual numerical method solves a stochastic game for a finite state Markov chain and ergodic cost criterion. The essential conditions are nondegeneracy of the diffusion and that a weak local consistency condition hold “almost everywhere” for the numerical approximations, just as for the control problem. The latter is close to a minimal condition. Such ergodic and “separated” game models occur in risk-sensitive and robust control.