This paper provides a step-by-step guide to solving dynamic stochastic games using the homotopy method. The homotopy method facilitates exploring the equilibrium correspondence in a systematic fashion; it is especially useful in games that have multiple equilibria. We discuss the theory of the homotopy method and its implementation and present two detailed examples of dynamic stochastic games that are solved using this method.

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This paper provides a step-by-step guide to solving dynamic stochastic games using the homotopy method. The homotopy method facilitates exploring the equilibrium correspondence in a systematic fashion; it is especially useful in games that have multiple equilibria. We discuss the theory of the homotopy method and its implementation and present two detailed examples of dynamic stochastic games that are solved using this method.

We develop a structural model of brand management to estimate the value of a brand to a firm. In our framework, a brand's value is the expected net present value of future cash flows accruing to a firm due to its brand. Our brand value measure recognizes that a firm can change its brand equity by investing in advertising. We estimate quarterly brand values in the stacked chips category for the period 2001-2006 and explore how those values change over time. Comparing our brand value measure to its static counterpart, we find that a static measure, which ignores advertising and its ability to affect brand equity dynamics, yields brand values that are artificially high and that fluctuate too much over time. We also explore how changing the ability to build and sustain brand equity affects brand value. At our estimated parameterization, if brand equity were to depreciate more slowly, or if advertising were more effective at building brand equity, then brand value would increase. However, counterintuitively, we find that when the effectiveness of advertising is sufficiently high, increasing the rate at which brand equity depreciates can increase the value of a firm's brand, even as it reduces the value of the firm overall. History: K. Sudhir served as the editor-in-chief and Jean-Pierre Dubé served as associate editor for this article.

This paper explores the equilibrium correspondence of a dynamic quality ladder model with entry and exit using the homotopy method. This method is ideally suited for systematically investigating the economic phenomena that arise as one moves through the parameter space and is especially useful in games that have multiple equilibria. We briefly discuss the theory of the homotopy method and its application to dynamic stochastic games. We then present three main findings: First, the more costly and/or less beneficial it is to achieve or maintain a given quality level, the more a leader invests in striving to induce the follower to give up; the more quickly the follower does so; and the more asymmetric is the industry structure that arises. Second, the possibility of entry and exit gives rise to predatory and limit investment. Third, we illustrate and discuss the multiple equilibria that arise in the quality ladder model, highlighting the presence of entry and exit as a source of multiplicity.