The international stock pollutant control: a stochastic formulation

In this paper we provide a stochastic dynamic game formulation of the economics of international environmental agreements on the transnational pollution control when the environmental damage arises from stock pollutant that accumulates, for accumulating pollutants such as CO2 in the atmosphere. To improve the cooperative and the noncooperative equilibrium among countries, we propose the criteria of the minimization of the expected discounted total cost. Moreover, we consider Stochastic Dynamic Games formulated as Stochastic Dynamic Programming and Cooperative versus Noncooperative Stochastic Dynamic Games. The performance of the proposed schemes is illustrated by a real data based example.Stochastic optimal control, Markov decision processes, Stochastic dynamic programming, Stochastic dynamic games, International pollutant control, Environmental economics, Sustainability,

The international stock pollutant control: a stochastic formulation

In this paper we provide a stochastic dynamic game formulation of the economics of international environmental agreements on the transnational pollution control when the environmental damage arises from stock pollutant that accumulates, for accumulating pollutants such as CO2 in the atmosphere. To improve the cooperative and the noncooperative equilibrium among countries, we propose the criteria of the minimization of the expected discounted total cost. Moreover, we consider Stochastic Dynamic Games formulated as Stochastic Dynamic Programming and Cooperative versus Noncooperative Stochastic Dynamic Games. The performance of the proposed schemes is illustrated by a real data based example

Controlling the international stock pollutant with policies depending on target values

In this paper a stochastic dynamic game formulation of the economics of international environmental agreements on the transnational pollution control, when the environmental damage arises from stock pollutant that accumulates, for accumulating pollutants such as CO2 in the atmosphere is provided. To improve the non-cooperative equilibrium among countries, we propose a different criterion to the minimization of the expected discounted total cost. Moreover, we consider Cooperative versus Noncooperative Stochastic Dynamic Games formulated as Markov Decision Processes (MDP). We propose a new alternative where the decision-maker wants to maximize the probability that some total performance of the dynamical game does not exceed a target value during a fixed period of time. The task requirements are therefore formulated as probabilities rather than expectations. This approach is different from the standard MDP, which uses performance criteria based on the expected value of some index. We present properties of the optimal policies obtained under this new perspective.Stochastic optimal control, Markov Decision Processes, Stochastic Dynamic Programming, Stochastic Dynamic Games, International pollutant control, Environmental economics, Sustainability, Probability criterion

Stochastic fictitious play with continuous action sets

Continuous action space games are ubiquitous in economics. However, whilst learning dynamics in normal form games with finite action sets are now well studied, it is not until recently that their continuous action space counterparts have been examined. We extend stochastic fictitious play to the continuous action space framework. In normal form games with finite action sets the limiting behaviour of a discrete time learning process is often studied using its continuous time counterpart via stochastic approximation. In this paper we study stochastic fictitious play in games with continuous action spaces using the same method. This requires the asymptotic pseudo-trajectory approach to stochastic approximation to be extended to Banach spaces. In particular the limiting behaviour of stochastic fictitious play is studied using the associated smooth best response dynamics on the space of finite signed measures. Using this approach, stochastic fictitious play is shown to converge to an equilibrium point in two-player zero-sum games and a stochastic fictitious play-like process is shown to converge to an equilibrium in negative definite single population games

Pure Subgame-Perfect Equilibria in Free Transition Games

We consider a class of stochastic games, where each state is identified with a player. At any moment during play, one of the players is called active. The active player can terminate the game, or he can announce any player, who then becomes the active player. There is a non-negative payoff for each player upon termination of the game, which depends only on the player who decided to terminate. We give a combinatorial proof of the existence of subgame-perfect equilibria in pure strategies for the games in our class.mathematical economics;

Zero-Sum Stochastic Stackelberg Games

Zero-sum stochastic games have found important applications in a variety of fields, from machine learning to economics. Work on this model has primarily focused on the computation of Nash equilibrium due to its effectiveness in solving adversarial board and video games. Unfortunately, a Nash equilibrium is not guaranteed to exist in zero-sum stochastic games when the payoffs at each state are not convex-concave in the players' actions. A Stackelberg equilibrium, however, is guaranteed to exist. Consequently, in this paper, we study zero-sum stochastic Stackelberg games. Going beyond known existence results for (non-stationary) Stackelberg equilibria, we prove the existence of recursive (i.e., Markov perfect) Stackelberg equilibria (recSE) in these games, provide necessary and sufficient conditions for a policy profile to be a recSE, and show that recSE can be computed in (weakly) polynomial time via value iteration. Finally, we show that zero-sum stochastic Stackelberg games can model the problem of pricing and allocating goods across agents and time. More specifically, we propose a zero-sum stochastic Stackelberg game whose recSE correspond to the recursive competitive equilibria of a large class of stochastic Fisher markets. We close with a series of experiments that showcase how our methodology can be used to solve the consumption-savings problem in stochastic Fisher markets.Comment: 29 pages 2 figures, Appeared in NeurIPS'2

Stationary Equilibria in Stochastic Games: Structure, Selection, and Computation

This paper is the first to introduce an algorithm to compute stationary equilibria in stochastic games, and shows convergence of the algorithm for almost all such games. Moreover, since in general the number of stationary equilibria is overwhelming, we pay attention to the issue of equilibrium selection. We do this by extending the linear tracing procedure to the class of stochastic games, called the stochastic tracing procedure. From a computational point of view, the class of stochastic games possesses substantial difficulties compared to normal form games. Apart from technical difficulties, there are also conceptual difficulties,, for instance the question how to extend the linear tracing procedure to the environment of stochastic games. We prove that there is a generic subclass of the class of stochastic games for which the stochastic tracing procedure is a compact one-dimensional piecewise differentiable manifold with boundary. Furthermore, we prove that the stochastic tracing procedure generates a unique path leading from any exogenously specified prior belief, to a stationary equilibrium. A well-chosen transformation of variables is used to formulate an everywhere differentiable homotopy function, whose zeros describe the (unique) path generated by the stochastic tracing procedure. Because of differentiability we are able to follow this path using standard path-following techniques. This yields a globally convergent algorithm that is easily and robustly implemented on a computer using existing software routines. As a by-product of our results, we extend a recent result on the generic finiteness of stationary equilibria in stochastic games to oddness of equilibria.mathematical economics and econometrics ;

The agglomeration effect of the Athens 2004 Olympic Games

In this paper, we analyze the spatial distribution of economic activity and labor market variables in Greece from 1980 to 2006. Using a distance-based method within a stochastic point process, we identify two periods with opposite trends regarding the concentration of economic activity in the Greek territory. First, twenty years (1980- 1999) of a moderately decreasing trend of agglomeration due to systematic e®orts by the Greek governments to decentralize the economic activity away from the capital. Second, a short period (2000-2006) of sharp increases in agglomeration, coinciding -in space and time- with the public and private investments for the 2004 Olympic Games in Athens. In the same period, a similar e®ect of a smaller size is observed on the concentration of the labor force, employment and unemployment.Concentration, Olympic Games, D-function, L-function, K-function, point process, spatial economics.

Stochastic learning dynamics and speed of convergence in population games

We study how long it takes for large populations of interacting agents to come close to Nash equilibrium when they adapt their behavior using a stochastic better reply dynamic. Prior work considers this question mainly for 2 × 2 games and potential games; here we characterize convergence times for general weakly acyclic games, including coordination games, dominance solvable games, games with strategic complementarities, potential games, and many others with applications in economics, biology, and distributed control. If players' better replies are governed by idiosyncratic shocks, the convergence time can grow exponentially in the population size; moreover, this is true even in games with very simple payoff structures. However, if their responses are sufficiently correlated due to aggregate shocks, the convergence time is greatly accelerated; in fact, it is bounded for all sufficiently large populations. We provide explicit bounds on the speed of convergence as a function of key structural parameters including the number of strategies, the length of the better reply paths, the extent to which players can influence the payoffs of others, and the desired degree of approximation to Nash equilibrium