Catálogo de publicaciones - libros

We describe conditions for the existence of a stationary Markovian equilibrium when total production or total endowment is a random variable. Apart from regularity assumptions, there are two crucial conditions: (i) —agents are ignorant of both total endowment and their own endowments when they make decisions in a given period, and (ii) —the endowment of each agent is in proportion, possibly random, to the total endowment. When these conditions hold, there is a stationary equilibrium. When they do not hold, such an equilibrium need not exist.

Zero-sum stochastic games with the expected average cost criterion and unbounded stage cost are studied. It is assumed that the transition probabilities of the Markov chains induced by stationary strategies satisfy a certain geometric drift condition. Under additional assumptions concerning especially the existence of -optimal strategies in corresponding one-stage games it is shown that the average optimality equation has a solution and that both players have -optimal stationary strategies.

Two players hold money and bid each day for a nondurable consumer good whose worth to each player is measured by a concave utility function. The money recirculates to the players according to a rule that treats them symmetrically. When the total reward is discounted and the discount factor is small, there is a Nash equilibrium in which the players make large bids. For a discount factor close to one and also for a game with long run average reward, there is a Nash equilibrium with small bids.

In repeated games where the payoff is accumulated along the play, the players face a problem since they have to take into account the impact of their choices both on the current payoff and on the future of the game.

We discuss the risk-sensitive Nash equilibrium concept in static non-cooperative games and two-stage stochastic games of resource extraction. Two equilibrium theorems are established for the latter class of games. Provided examples explain the meaning of risk-sensitive equilibria in games with random moves.

We present a generalization of Amir’s continuous model of nonsymmetric infinite-horizon discounted stochastic game of capital accumulation. We show that the game has a pure-strategy equilibrium in strategies that are nondecreasing and have Lipschitz property. To prove that, we use a technique based on an approximation of continuous model by the analogous discrete one.

We use in this paper the viability/capturability approach for studying the problem of characterizing the dynamic core of a dynamic cooperative game defined in a characteristic function form. In order to allow coalitions to evolve, we embed them in the set of fuzzy coalitions. Hence, we define the dynamic core as a set-valued map associating with each fuzzy coalition and each time the set of allotments is such that their payoffs at that time to the fuzzy coalition are larger than or equal to the one assigned by the characteristic function of the game. We shall characterize this core through the (generalized) derivatives of a valuation function associated with the game. We shall provide its explicit formula, characterize its epigraph as a viable-capture basin of the epigraph of the characteristic function of the fuzzy dynamical cooperative game, use the tangential properties of such basins for proving that the valuation function is a solution to a Hamilton-Jacobi-Isaacs partial differential equation and use this function and its derivatives for characterizing the dynamic core.

In this paper we investigate the existence and turnpike properties of overtaking Nash equilibria for an infinite horizon dynamic game in which the dynamic constraints are described by linear evolution equations in a Hilbert space.

In this paper the definition of cooperative game in characteristic function form is given. The notions of optimality principle and solution concepts based on it are introduced. The new concept of “imputation distribution procedure” (IDP) is defined and connected with the basic definitions of time-consistency and strong time-consistency. Sufficient conditions of the existence of time-consistent solutions are derived. For a large class of games where these conditions cannot be satisfied, the regularization procedure is developed and new c.f. constructed. The “regularized” core is defined and its strong time-consistency proved.

The many-player game of selling an asset, introduced by Sakaguchi and extended to monotone voting procedures by Yasuda, Nakagami and Kurano, is reviewed. Conditions for a unique equilibrium among stationary threshold strategies are given.