Catálogo de publicaciones - libros

An evolutionary game with three players — trade unions, financial investors and firms — is presented where each player has a short-term and a long-term maximizing strategy at hand. The short-term strategy maximizes current payoffs without taking into account benefits from future cooperation while long-term strategies depend on the cooperative behavior of the other players. We first determine equilibria arising in the static game and determine under which conditions long-term cooperation may emerge. We then endogenize the stochastic environment, making it subject to the strategies selected and show how additional equilibria and strategy cycles arise in an evolutionary set-up.

We adopt the robust control, or game theoretic, approach of [] to option pricing. In this approach, uncertainty is described by a restricted set of possible price trajectories, without endowing this set with any probability measure. We seek a hedge against every possible price trajectory.

In the absence of transaction costs, the continuous trading theory leads to a very simple differential game, but to an uninteresting financial result, as the hedging strategy obtained lacks robustness to the unmodeled transaction costs. (A feature avoided by the classical Black and Scholes theory through the use of unbounded variation cost trajectories. See [].)

We therefore introduce transaction costs into the model. We examine first the continuous time model. Its mathematical complexity makes it beyond a complete solution at this time, but the partial results obtained do point to a robust strategy, and as a matter of fact justify the second part of the paper.

In that second part, we examine the discrete time theory, deemed closer to a realistic trading strategy. We introduce transaction costs into the model from the outset and derive a pricing equation, which can be seen as a discretization of the quasi variational inequality of the continuous time theory. The discrete time theory is well suited to a numerical solution. We give some numerical results. In the particular case where the transaction costs are null, we recover our theory of [], and in particular the Cox, Ross and Rubinstein formula when the contingent claim is a convex function of the terminal price of the underlying security.

This paper exposes in voluntarily simple terms the concept of -adapted equilibrium introduced to represent and compute economic equilibria on stochastic markets. A model of the European gas market, that has been at the origin of the introduction of the concept, is recalled in this paper and the results obtained in 1987, when the contingent equilibrium has been computed for a time horizon extending until 2020, are compared with the observed trend in these markets over the last two decades. The information structure subsumed by this concept of -adapted strategies is then analyzed, using different paradigms of dynamic games. The paper terminates with some open and intriguing questions related to the time consistency and subgame perfectness of the dynamic equilibrium thus introduced.

The existence of Nash equilibria is investigated for one-stage and two-stage rent-seeking games with endogenous rent which depends on the aggregate expenditure by all rent-seeking agents such as individuals, firms or countries. Under reasonable assumptions on lottery production functions and rent function, both games turn out to have a unique equilibrium. The conditions for the equilibrium aggregate expenditure by all agents to increase in the first stage and for the total rent over two stages to dissipate are derived for the two-stage rent-seeking games.

The purpose of this paper is to compare two ways of modelling exploitation of common renewable resource by a large group of players.

We develop a mathematical model within a game theoretical framework to capture the flow control problem for variable rate traffic at a bottleneck node. In this context, we also address various issues such as pricing and allocation of a single resource among a given number of users. We obtain a distributed, end-to-end flow control using cost functions defined as the difference between particular pricing and utility functions. We prove the existence and uniqueness of a Nash equilibrium for two different utility functions. The paper also discusses three distributed update algorithms, parallel, random and gradient update, which are shown to be globally stable under explicitly derived conditions. The convergence properties and robustness of each algorithm are studied through extensive simulations.

In a recent paper, Pan and Başar [] have studied the control of large scale Jump Linear systems in which the transitions of the jump Markov chain can be separated into sets having strong and weak interactions. They obtained an approximating reduced-order aggregated problem which is the limit as the rate of transitions of the faster time scale (which is a multiple of some parameter 1/) goes to infinity. In this paper we further investigate the solution of that problem as a function of the parameter . We show that the related optimal feedback policy and the value admit a Taylor series in terms of , and we compute its coefficients.

In this paper we develop two new parallel algorithms for differential games based on the principle of “data replication”. This technique is efficient on distributed memory architectures such as IBM/PS2 or Digital Alpha and is coupled with a domain decomposition techniques to construct an approximation scheme for the Isaacs equation in ℝ. The algorithms are presented for a 2-domain decomposition and some hints are given for the case of subdomains having crossing points. The above parallel algorithms have the same fixed point as the serial algorithm so that convergence to the viscosity solution of the Isaacs equation is guaranteed by previous results. The efficiency of the above algorithms is discussed analyzing some numerical tests which include the homicidal chauffeur game.

In this paper, we study the linear quadratic Nash games for infinite horizon singularly perturbed systems (SPS). In order to solve the generalized algebraic Lyapunov equation (GALE) corresponding to the generalized Lyapunov iterations, we propose a new algorithm which is based on the fixed point iterations. Furthermore, we also propose a new algorithm which is based on the Kleinman algorithm for solving the generalized cross-coupled algebraic Riccati equations (GCARE). It is shown that the resulting algorithm guarantees the quadratic convergence.

This paper models adaptive learning behavior in a simple coordination game that Van Huyck, Cook and Battalio (1994) have investigated in a controlled laboratory setting with human subjects. We consider how populations of arti- ficially intelligent players behave when playing the same game. We use the genetic programming paradigm, as developed by Koza (1992, 1994), to model how a population of players might learn over time. In genetic programming one seeks to breed and evolve highly fit computer programs that are capable of solving a given problem. In our application, each computer program in the population can be viewed as an individual agent’s forecast rule. The various forecast rules (programs) then repeatedly take part in the coordination game evolving and adapting over time according to principles of natural selection and population genetics.We argue that the genetic programming paradigm that we use has certain advantages over other models of adaptive learning behavior in the context of the coordination game that we consider. We find that the pattern of behavior generated by our population of artificially intelligent players is remarkably similar to that followed by the human subjects who played the same game. In particular, we find that a steady state that is theoretically unstable under a myopic, best-response learning dynamic turns out to be stable under our genetic-programming-based learning system, in accordance with Van Huyck et al.’s (1994) finding using human subjects. We conclude that genetic programming techniques may serve as a plausible mechanism for modeling human behavior, and may also serve as a useful selection criterion in environments with multiple equilibria.