Pure-strategy Nash equilibria in an advertising game with interference

Two manufacturers produce substitutable goods for a homogeneous market. The advertising efforts of the two manufacturers determine the demand for the goods and interfere negatively with each other. The demand of each good is a piecewise linear function of the product goodwill, and the latter is a linear function of advertising efforts. In a game with two competing profit-maximizing manufacturers who have access to a set of several advertising media, the pure-strategy Nash equilibria are characterized and their existence is shown.     

The Leitmann-Schmitendorf advertising differential game

The paper revisits the advertising differential game suggested by Leitmann and Schmitendorf [1]. We put the model into perspective and discuss the related issues of (i) state separable (or linear-state) games and (ii) open-loop equilibria that are feedback equilibria which are constant with respect to state.     

New product advertising in dynamic oligopolies

The success of the introduction of a new product in a market is very sensitive to the marketing decision variables adopted by the firm. In the present paper we are concerned with the question of new product advertising in a heterogeneous oligopoly market consisting of N firms. A dynamic game is formulated to model strategic as well as sales interactions in such a market. Optimal advertising strategies are identified as open-loop Nash solutions.The comments of two anonymous referees are appreciated. The first author wishes to acknowledge support from NSERC (Grant No. OGP0037342).     

Retail competition and cooperative advertising

We consider a cooperative advertising channel consisting of a manufacturer selling its product through a retailer in competition with another independent retailer. The manufacturer subsidizes its retailer’s advertising only when a certain threshold is positive. Moreover, the manufacturer’s support for its retailer is higher under competition than in its absence.     

Reductions of interval noncooperative games

Noncooperative games of a finite number of persons with interval-valued payoff functions are considered. The concept of an equilibrium situation is introduced. A reduction of such games to deterministic noncooperative games is proposed. Properties of the reduced games are discussed. Interval antagonistic and bimatrix games are examined, and illustrative examples are considered.     

An empirical study on the Lanchester model of combat for competitive advertising decisions

This paper presents an empirical study on the Lanchester model of combat for competitive advertising decisions. Three issues are evaluated: (i) the specification of the market share response model; (ii) the effect of inflation on the estimation of the response model; and (iii) the performance of competitive strategies. It is shown that (a) the square root function that is used in previous studies is often inappropriate to characterize the market share response model; (b) market share variations are more responsive to current advertising expenditures; (c) closed-loop Nash equilibrium strategies are better competitive advertising strategies for firms to maximize profits than open-loop Nash equilibrium strategies; and (d), finally, general perfect equilibria Nash equilibrium strategies developed by Case are usually not good competitive advertising strategies for firms to maximize profits.     

A differential game of industrial pollution management

This paper explores a differential game between a policy maker and a profit maximizing entrepreneur in which production generates pollution. The government levies a pollution tax on output and uses the tax received for pollution abatement. The entrepreneur determines the level of output. A feedback Nash equilibrium is derived. Using more specific functional forms, the game is extended to cover the multiple firm case.     

Persuasive advertising under Bertrand competition: A differential game

We investigate a linear state differential game of advertising, under Cournot and Bertrand competition. A unique saddlepoint equilibrium exists if the marginal cost of advertising is sufficiently low. Bertrand competition entails more intense advertising than Cournot competition, since increasing market size is more important to firms when competition is tough.     

The Leitmann-Schmitendorf advertising game with n players and time discounting

The extension of the Leitmann-Schmitendorf advertising game to n players and positive time discounting is investigated. We show that the strong time consistency of the open-loop Nash equilibrium is preserved. As to optimal controls, while the boundary solution is unaffected by the number of firms as well as discounting, the inner solution depends on industry structure. The fully symmetric version of the game allows us to identify the parameter regions wherein both solutions are sustainable.     

Differential game approach to pricing and advertising decisions

This study proposes a model to make concurrent decisions on dynamic pricing and advertising to maximise firms' profitability over an infinite time horizon in a duopoly market. To this end, the Nerlove-Arrow pricing and advertising model is designed in the presence of shifting costs in a dynamic duopolistic competition as a differential game. The Nash equilibrium solution is defined based upon a set of Hamilton–Jacobi–Bellman. Four scenarios are applied for economic interpretations and the efficacy of the model.     

Vendor Management Inventory with consignment contracts and the benefits of cooperative advertising

Most of the cooperative advertising literature has focused on studying the effects of such programs considering marketing variables. This paper integrates production and inventory management with pricing and advertising considerations to assess the effects of cooperative advertising programs in bilateral monopolies. We consider a supply chain where a Vendor Managed Inventory (VMI) along with a consignment contract is implemented to coordinate the chain. We develop and solve a differential model for two games. The first one is a benchmark scenario where no cooperative advertising is offered, while the manufacturer offers the cooperative program in the second game. The main results show that cooperative advertising programs, usually considered as successful marketing initiatives, can be very difficult to implement in a supply chain undertaking a VMI policy with a consignment contract, in which operations and marketing interface is taken into account. A cooperative program mainly hurts the manufacturer’s profits, and can be profit-Pareto-improving only in a few cases. Although the retailer is generally willing to receive a support from the manufacturer, she can opt for a non-cooperative program when the largest part of the supply chain profits goes to the manufacturer. We developed several special cases to strengthen our findings.     

单主多从博弈中中级社会Nash均衡的存在性与应用

对单主多从博弈进行分析,给出跟随者反应函数的相关性质.进一步,针对跟随者反应函数是集值映射的情形,定义出中级社会Nash均衡,讨论该均衡的存在性,并把该均衡应用到非线性反需求函数的单主多从寡头竞争,得出该模型的中级社会Nash均衡解.     

具有产品质量差异的扩展Hotelling模型

假定两家厂商生产的同种产品具有质量差异,及消费者对产品质量偏好服从[d,e]区间上的均匀分布情况,研究了二次运输成本Hotelling模型:两家厂商首先沿[0,1]线性城市同时选址,然后进行价格竞争.运用后退归纳法得到了子博弈精炼Nash均衡,此时厂商将选址于城市中心。     

Learning Equilibrium Play: A Myopic Approach

We model repeated play of noncooperative stage games in terms of approximate gradient steps. That simple format requires little information and no optimization. Moreover, it allows players to evaluate marginal cost or profit inexactly and to move with different velocities. Uncertainty can also be accommodated. Granted some crucial stability, we show that play converges to Nash equilibrium.     

On the existence of equilibria in discontinuous games: three counterexamples

We study whether we can weaken the conditions given in Reny [4] and still obtain existence of pure strategy Nash equilibria in quasiconcave normal form games, or, at least, existence of pure strategy ɛ-equilibria for all ɛ>0. We show by examples that there are:1. quasiconcave, payoff secure games without pure strategy ɛ-equilibria for small enough ɛ>0 (and hence, without pure strategy Nash equilibria),2. quasiconcave, reciprocally upper semicontinuous games without pure strategy ɛ-equilibria for small enough ɛ>0, and3. payoff secure games whose mixed extension is not payoff secure.The last example, due to Sion and Wolfe [6], also shows that non-quasiconcave games that are payoff secure and reciprocally upper semicontinuous may fail to have mixed strategy equilibria.I wish to thank the editor, an associate editor and an anonymous referee for very helpful comments. I thank also John Huffstot for editorial assistance. Any remaining error is, of course, mine     

Network games; adaptations to Nash-Cournot equilibrium

We consider nonlinear flow problems involving noncooperative agents, all active in the same network. To find Nash equilibria, we develop an algorithm that lends itself to decentralized computation and parallel processing. The algorithm, which proceeds in terms of iterative strategy adjustments, is, in essence, of subgradient type. One advantage of that type is the ease with which stochastic and nonsmooth data can be accommodated.This paper was written while the first author was visiting the Université de Perpignan. Support from Elf Petroleum, Université de Perpignan and NFR project Quantec 111039/410 is gratefully acknowledged.     

Interactive economic dynamics and differential games

This survey reviews the applications of differential game theory in analyzing issues in the economic literature. The needs of the economic discipline are juxtaposed with the merits of various existing types of differential games. Suggestions are also made as to areas holding great promise for future research.The authors are grateful to Prof. George Leitmann for suggestions to their final draft, which improved the clarity of certain assumptions in keeping with the literature.     

Stochastic dominance equilibria in two-person noncooperative games

Two-person noncooperative games with finitely many pure strategies are considered, in which the players have linear orderings over sure outcomes but incomplete preferences over probability distributions resulting from mixed strategies. These probability distributions are evaluated according to t-degree stochastic dominance. A t-best reply is a strategy that induces a t-degree stochastically undominated distribution, and a t-equilibrium is a pair of t-best replies. The paper provides a characterization and an existence proof of t-equilibria in terms of representing utility functions, and shows that for large t behavior converges to a form of max–min play. Specifically, increased aversion to bad outcomes makes each player put all weight on a strategy that maximizes the worst outcome for the opponent, within the supports of the strategies in the limiting sequence of t-equilibria.The paper has benefitted from the comments of four referees and an associate editor.     

Pricing game of online display advertisement publishers

We consider online display advertisement publishers who maximize the revenue by optimal pricing in an oligopoly setting. Each publisher interacts with others through setting cost-per-impression (CPM) that affects the demand for everyone. Using the pseudoconcavity of the objective function, we prove that a unique best response Nash equilibrium exists for each publisher. We also consider the sensitivity of the publisher while other publishers changes their CPM. In both cases, the best response of the publisher depends entirely on her current best response CPM. We provide an algorithm for finding the equilibrium and illustrate by numerical examples.     

A basic searchlight game

A searchlight game is a two-person zero-sum dynamic game of the pursuit-evasion type in which at least one of the two players has a searchlight. A searchlight can be flashed a given number of times within a fixed time period and the objective is to catch the opponent in the region illuminated by the flash. Olsder and Papavassilopoulos instituted the study of these games and, in this paper, we supplement their results, obtaining a closed formula for the value and optimal strategies for the players in their basic game.