Markovian Nash Equilibrium Research Articles

A goodwill model with predatory advertising

We investigate the dynamic advertising policies of two competing firms in a duopolistic industry, assuming a predatory phenomenon between their advertising campaigns. The resulting model is a differential game which is not linear-quadratic. We show that there exists a Markovian Nash equilibrium, and that it leads to time constant advertising strategies. According to this model, predatory advertising produces a negative externality: the interference between the advertising campaigns decreases the total demand of the market.

A Constructive Study of Markov Equilibria in Stochastic Games with Strategic Complementarities

We study a class of infinite horizon, discounted stochastic games with strategic complementarities. In our class of games, we prove the existence of a Stationary Markov Nash equilibrium, as well as provide methods for constructing this least and greatest equilibrium via a successive approximation scheme. We also provide new results on computable equilibrium monotone comparative statics results relative to ordered perturbations of the space of stochastic games. Under slightly stronger assumptions, we prove the stationary Markov Nash equilibrium values form a complete lattice, with least and greatest equilibrium value functions being the uniform limit of these successive approximations starting from pointwise lower and upper bounds.

A stochastic differential game of capitalism

We develop a stochastic differential game of capitalism to analyze the role of uncertainty. In the deterministic game, the firm’s rent is completely taxed away and the firm stops investing completely. In the stochastic game, the government does not tax the firm’s rent completely. The firm posts a positive rate of investment if the firm’s rent exceeds the labor’s income. Although the cooperative solution is indeterminate, cooperation is always Pareto optimal compared to the non-cooperative Markovian Nash equilibrium. For individual rationality, we apply a payoff distribution procedure based on Yeung and Petrosyan (2006) to derive a subgame-consistent solution.

Dynamics of competing with quality- and advertising-based goodwill

Goodwill formation is a complex process and many factors influence the formation of goodwill of a firm. The implications of advertising enabled goodwill formation are reported in several articles in the research literature. In this paper, we extend this stream of research by including quality in the goodwill formation process. We adopt a dynamic model of competition utilizing a differential game approach and derive expressions for open-loop Markovian Nash equilibrium investments in advertising and quality. The insights gained from the analysis of our model and from the equilibrium solutions are presented in the form of research propositions.

An overlapping generations stochastic differential game

The paper presents a noncooperative stochastic differential game played by an infinite number of overlapping generations of players. The number and types of players in future generations are uncertain and the state dynamics are given by a stochastic differential equation. A Markovian Nash equilibrium is characterized by a verification theorem of the Hamilton–Jacobi–Bellman type. A resource extraction game is offered as an illustration.

Learning by imitation

This paper introduces a learning algorithm that allows for imitation in recursive dynamic games. The Kiyotaki–Wright model of money is a well-known example of such decision environments. In this context, learning by experience has been studied before. Here, we introduce imitation as an additional channel for learning. In numerical simulations, we observe that the presence of imitation either speeds up social convergence to the theoretical Markov–Nash equilibrium or leads every agent of the same type to the same mode of suboptimal behavior. We observe an increase in the probability of convergence to equilibrium, as the incentives for optimal play become more pronounced.