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The purpose of this paper is to research stochastic dynamic investment games with stochastic interest rate model in continuous time between two investors. The market interest rate has the dynamics of Duffie‐Kan interest rate.

Recently, there has been an increasing interest in financial market models whose key parameters, such as the bank interest rate, stocks appreciation rates, and volatility rates, are modulated by stochastic interest rate. This paper uses the Duffie‐Kan stochastic interest rate model to develop stochastic differential portfolio games. By the HJB optimality equation, a general result in optimal control for a stochastic differential game with a general utility payoff function is obtained.

Derive a general result in optimal control for a stochastic differential game with a general utility payoff function. The explicit optimal strategies and value of the games are obtained for the constant relative risk aversion utility games of fixed duration.

Accessibility and availability of stochastic interest rate data are the main limitations, which apply.

The results obtained in this paper could be used as a guide to actual portfolio games.

This paper presents a new approach for the optimal portfolio model under compound jump processes. The paper is aimed at actual portfolio games.

Over the last years, powerful advances in the area of dynamic games have enriched game theory and made it more applicable to the modeling of real-world competitive strategies. The study of strategic behaviors of firms in an oligopoly market has received little attention, even though real firms have been shown to compete in output and in price in a single industry. The purpose of this study is to propose a game-theoretic approach to studying strategic behaviors of firms in an oligopoly market structure.

This approach was developed to study market dynamics and pricing strategic behavior of firms that have the possibility of deciding to be one of the two types (price-maker or price-taker) and reconsider the choice overtime on the basis of their current insights and knowledge and their experience. Firms try to improve their performance in the competitive market in a strategic way, by considering their steady-state profits and choosing the best type given the other firms’ types, actions and interactions.

The results of the present study confirm the previous study that the Cournot market is a stable market, where each firm can be a price-maker and enjoy individual learning as well as social learning. On the contrary, the market with price-takers only is never stable, and, therefore, the Walrasian equilibrium may not be supported in some instances. The Cournot market loses its stability as the number of firms in the market increases due to the fact that it will be more profitable for a firm to switch to price-taking when the number of firms is high enough. In such a situation, when the number of price-takers increases, there are no stable markets and price dynamics are destabilized.

The study and modeling of real-world competitive strategies would enhance the understanding of oligopoly markets. The study of strategic behaviors of firms in an oligopoly market has received little attention, even though real firms have been shown to compete in output and in price in a single industry as price-takers and price-makers.

We model the interaction between a profit-maximizing firm and an activist using an infinite-horizon dynamic stochastic game. The firm enhances its reputation through “self-regulation”: voluntary provision of an abatement activity that reduces a negative externality. We show that in equilibrium the externality-reducing activity is subject to decreasing marginal returns, which can cause the firm to “coast on its reputation,” that is, decrease the level of externality-reducing activity as its reputation grows. The activist, which benefits from increases in the externality-reducing activity, can take two types of action that can harm the firm’s reputation: criticism, which can impair the firm’s reputation on the margin, and confrontation, which can trigger a crisis that may severely damage the firm’s reputation. The activist changes the reputational dynamics of the game by tending to keep the firm in reputational states in which it is highly motivated to invest in externality-reducing activity. Criticism and confrontational activity are shown to be imperfect substitutes. The more patient the activist or the more passionate it is about externality reduction, the more likely it is to rely on confrontation. The more patient the firm and the more important corporate citizenship is to firm’s brand equity, the more likely that it will be targeted by an activist that relies on confrontation.

Analyses the economic efficiency of innovation under different market conditions within the context of a formal model that represents competitive innovation as the closed loop solution of a dynamic stochastic game in the spirit of Reinganum’s analysis. Goes beyond Reingnaum’s model in its explicit treatment of the product market (following Spence), which permits a consistent analysis of competitive innovation in the absence of patent protection. Measures efficiency by the expected net present value of total surplus, and studies the effect on it of competitive structure, elasticity of demand, fixed costs, spillovers and subsidies.

The purpose of this paper is to study the advance selling strategies for oligopolists when considering the product diffusion effect.

The authors consider a market that composes of two competitive sellers who are different in their reputation. The two firms sell the same product in the market over two periods (i.e. the advance selling season and the regular selling season). Due to the effect of product diffusion, the demand of each firm in the regular selling season is dependent on the two firms’ advance demands.

For the firm with lower reputation, it is beneficial to decrease the advance selling price with the diffusion effect caused by its advance demand. For the firm with higher reputation, it is also beneficial to decrease the advance selling price with the diffusion effect caused by its advance demand if the consumers’ enthusiasm for the product in regular selling season is high enough; otherwise it should not decrease his advance selling price since this practice cannot greatly increase his demand.

The obtained results can provide operational managers in reality with valuable suggestions in making advance selling decisions.

The paper is among the first to investigate the impact of product diffusion effect on a firm’s advance selling strategy in a competitive setting.

We review the use of behavior from television game shows to infer risk attitudes. These shows provide evidence when contestants are making decisions over very large stakes, and in a replicated, structured way. Inferences are generally confounded by the subjective assessment of skill in some games, and the dynamic nature of the task in most games. We consider the game shows Card Sharks, Jeopardy!, Lingo, and finally Deal Or No Deal. We provide a detailed case study of the analyses of Deal Or No Deal, since it is suitable for inference about risk attitudes and has attracted considerable attention.

Introduction Operations research, i.e. the application of scientific methodology to operational problems in the search for improved understanding and control, can be said to have started with the application of mathematical tools to military problems of supply bombing and strategy, during the Second World War. Post‐war these tools were applied to business problems, particularly production scheduling, inventory control and physical distribution because of the acute shortages of goods and the numerical aspects of these problems.