These notes provide a brief introduction to the theory of noncooperative differential games. After the Introduction, Section 2 reviews the theory of static games. Different concepts of solution are discussed, including Pareto optima, Nash and Stackelberg equilibria, and the co-co (cooperative-competitive) solutions. Section 3 introduces the basic framework of differential games for two players....

The paper is concerned with Stackelberg solutions for a differential game with deterministic dynamics but random initial data, where the leading player can adopt a strategy in feedback form: u1 = u1(t, x). The first main result provides the existence of a Stackelberg equilibrium solution, assuming that the family of feedback controls u1(t, ·) available to the leading player are constrained to a...

We consider situations in which a principal tries to induce an agent to spend effort on accumulating a state variable that affects the well-being of both parties. The only incentive mechanism that the principal can use is a state-dependent transfer of her own utility to the agent. Formally, the model is a Stackelberg differential game in which the players use feedback strategies. Whereas in gen...

We describe a method for an agent playing a generalsum normal form game to balance the rewards of exploiting a prediction of opponent behavior with the risks of being exploited by a self-interested opponent while guaranteeing a worst-case safety margin. Our algorithm, Restricted Stackelberg Response with Safety, calculates a probability distribution over the agent’s moves that balances those co...

H IERARCHICAL and large scale systems have received considerable attention during the last few years; firstly because of their importance in engineering, economics, and other areas, and secondly because of the increased capability of computer facilities [13], [14]. An important characteristic of many large scale systems is the presence of many decision makers with different and usually confl...

In this paper, we introduce the concept of dynamic pricing within the context of our previous Stackelberg network game model and view the ISP’s policy as an incentive policy, and the underlying game as a reverse Stackelberg game. We study this incentive-design problem under complete information as well as incomplete information. In both cases, we show that the game is not generally incentive co...

in this paper, the competition between two supply chains and their elements is studied. each chain consisted of a manufacturer and a distributor and the two chains compete in a market with single type of customer sensitive to price and delivery time. therefore, this is a two-supply chain game and during the competition between two supply chains, elements of each supply chain (manufacturer and/o...

many studies have been conducted to determine the efficiency of two-stage network structures in the recent years. the two-stage network with additional inputs to the second stage, in which the second stage is independent of the first stage are one of these structures. thus, there is a need for a model capable of calculating the efficiency of two-stage structures as well as efficiency of each st...

This paper demonstrates that in a duopoly model with firms being concerned about profit as well as corporate social responsibility (CSR), the outcome of game may coincide with the Stackelberg outcome. We argue that owner of the firm may use CSR orientation as a strategy to become Stackelberg leader in the quantity competition game.