Georges Zaccour

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• Ph.D. in management science
• Professor (Full) at HEC Montréal

The objective of this paper is to assess the impact of disclosing environmental information and price fairness on the strategies and outcomes of a supply chain in a dynamic framework. The relevance of our work stems from the ample empirical evidence that consumers are indeed sensitive to the green reputation of a manufacturer and perceive a transac...

Governments are motivated to subsidize profit-driven firms that manufacture zero-emission vehicles to ensure they become price-competitive. This paper introduces a dynamic Stackelberg game to determine the government's optimal subsidy strategy for zero-emission vehicles, taking into account the pricing decisions of a profit-maximizing firm. While f...

We consider a finite-horizon discrete-time dynamic model of oligopolistic competition, with uncertain supply. The firms (retailers) make their decisions on quantities (sales) and orders of goods from a nonstrategic manufacturer taking into account uncertainty in demand parameters and available supply capacity. The retailers need to satisfy the join...

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-o...

Reconciling food security, economic development and biodiversity conservation in the face of global changes is a major challenge. The sustainable uses of marine biodiversity in the context of climate change, invasive species, water pollution and demographic growth is an example of this bio-economic challenge. There is a need for quantitative method...

We consider the problem of a government that wishes to promote replacing old cars with new ones via a vehicle scrappage program. Since these programs increase consumer’s willingness to pay for a new car, manufacturers (or dealers) could respond strategically by raising their prices. In a two-period game between a government and a manufacturer, we f...

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-o...

In this chapter, we provide a brief introduction to the theory of multistage games. We recall some properties of dynamical systems described in state-space formalism, and introduce the idea of information structure, which defines what the players know when they make their decisions.

This chapter deals with the node consistency of the core in cooperative dynamic games played over event trees. Being a set-valued solution, the core does not (in general) uniquely define the profile of payoffs to the players. This is the first major difference from the single-valued solutions discussed in the previous chapter. The second difference...

In this chapter, we review the main ingredients of cooperative games, which will be needed in the following chapters.

In this chapter, we review the basic concepts of noncooperative game theory. In Sect. 1.1, we deal with finite games in strategic form and, in Sect. 1.2, with continuous games in strategic form. In Sect. 1.3, games in extensive form are introduced, and the Stackelberg equilibrium is defined in Sect. 1.4. The chapter ends with a series of exercises.

In this chapter, we extend to the class of dynamic games played over event trees (DGPETs) the concepts of subgame perfect ε-equilibrium and incentive equilibrium discussed in a deterministic framework in Chap. 4.

In this chapter, we examine the problem of the sustainability of cooperative solutions in dynamic games played over event trees (DGPETs). We introduce a cooperative version of the noncooperative DGPET defined in Chap. 5. We describe the problem of node inconsistency of cooperative solutions, which is a key issue in sustainable cooperation. We propo...

In this chapter, we introduce a class of dynamic games played over event trees (DGPETs). We define the elements of the game, in particular the S-adapted information structure, and the corresponding concepts. We state the existence and uniqueness of the equilibrium results and a maximum principle for this class of games. Also, we extend the formalis...

This chapter introduces the concepts of time consistency and cooperative equilibrium in cooperative dynamic games. To simplify the exposition, we retain a deterministic setup. In the next chapters, we extend the results to dynamic games played over event trees (DGPETs).

We model a closed-loop supply chain, made up of one manufacturer and one retailer, as a stochastic dynamic game. This paradigm allows us to simultaneously capture the strategic interactions between the agents, the intertemporal nature of the return of past-sold products for remanufacturing, and the uncertainty in the parameter values. We characteri...

We consider a discrete-time version of the fish war model, where a regulator imposes a moratorium on fishing activities whenever the stock reaches a predetermined critical low value. The moratorium will be in place until the fish stock recovers, that is, attains a desirable value. We obtain conditions on the parameter values such that a moratorium...

In this paper, we study the time consistency of cooperative agreements in dynamic games with non-transferable utility. An agreement designed at the outset of a game is time-consistent (or sustainable) if it remains in place for the entire duration of the game, that is, if the players would not benefit from switching to their non-cooperative strateg...

An essential ingredient to net-zero-emissions policies is to regionally integrate electricity markets. But electricity cross-border trades are often assessed as inefficient. We explain this inefficiency by the presence of a dichotomous regulation: producers are highly regulated with regard to their local activities, but weakly regulated when it com...

We consider a firm offering an opaque good over one selling season, that is, a product whose full characteristics are only revealed after the consumer completes the transaction. In our model, the consumer can choose between buying either of two transparent goods offered on the market at given high- and low-price, respectively, or paying a price in...

To satisfy a rising demand, agricultural practices have shifted from the organic fertilization of soils to intensive and highly specialized farming that uses chemical fertilization. The resulting short-term increase in soil productivity has lead to serious ecological drawbacks over time, e.g., degradation of soil quality, pollution of water and air...

Product recalls are often consequences of quality failures. While such failures are related to a manufacturer’s or supplier’s design quality, the perceived quality of products may be severely damaged when a product harm crisis occurs. However, most often, such a crisis will not last forever, and a firm at fault eventually recovers. Considering an o...

This paper surveys two key issues in Closed-loop Supply Chain (CLSC) research: return functions and coordination mechanisms. The return function provides the rule according to which end-of-life/use products are returned to a collector. The coordination mechanisms consist of the adoption of a certain mechanism (e.g., a contract) to align the closed-...

We built a time-consistent cooperative solution for the class of dynamic games played over event trees in the context where the tree structure is given, but the players have different beliefs about the transition probabilities between nodes. Our three-step approach is as follows. First, we consider three alternative methods for aggregating the play...

We review dynamic quality models both in single-agent setup and in a competitive framework. Our objectives are: (1) to give the reader a vantage point on the state of the art in this area, (2) to identify the boundaries between the different concepts of quality to help build a bridge between the various communities interested in the management of q...

It is a challenge to sustain cooperation in a finite-horizon dynamic game. Since players generally have an incentive to deviate to their noncooperative strategies in the last stage, a backward induction argument leads them to defect from cooperation in all stages. In this paper, we propose two payment schemes having some desirable properties, namel...

The use of space through satellites is more and more important for nations, companies, and individuals. However, since the first satellite was sent up in 1957, mankind has been polluting space with debris (i.e., artificial objects with no function), especially in low orbits (between 100 and 2000 km). The current situation is such that: 1/ space age...

In this paper, we introduce a framework for new product diffusion that integrates consumer heterogeneity and strategic social influences at individual level. Forward-looking consumers belong to two mutually exclusive segments: individualists, whose adoption decision is influenced by the price and reputation of the innovation, and conformists, whose...

We study a class of deterministic finite-horizon two-player nonzero-sum differential games where players are endowed with different kinds of controls. We assume that Player 1 uses piecewise-continuous controls, while Player 2 uses impulse controls. For this class of games, we seek to derive conditions for the existence of feedback Nash equilibrium...

An essential ingredient to net-zero-emissions policies is to regionally integrate electricity markets. But electricity cross-border trades are often assessed as inefficient. We explain this inefficiency by the presence of a dichotomous regulation: producers are highly regulated with regard to their local activities, but weakly regulated when it com...

Proofs and GAMS codes of the article published in The Energy Journal

Consumers are increasingly concerned about pollution and are, at least in part, making their purchases accordingly. In this paper, we consider a supply chain where demand depends on the manufacturer’s environmental reputation, an asset that can only be built over time. We assume that this reputation depends on information emanating from the manufac...

We study a class of deterministic two-player nonzero-sum differential games where one player uses piecewise-continuous controls to affect the continuously evolving state, while the other player uses impulse controls at certain discrete instants of time to shift the state from one level to another. The state measurements are made at some given insta...

We consider a large group of consumers who decide whether or not to buy a durable good offered by a firm. Without previous experience with the product, consumers rely on the ratings of past purchasers to evaluate the product goodwill and make optimal decisions. The consumers have heterogeneous intrinsic rating behaviors and preferences. For example...

We study a class of deterministic finite-horizon two-player nonzero-sum differential games where players are endowed with different kinds of controls. We assume that Player 1 uses piecewise-continuous controls, while Player 2 uses impulse controls. For this class of games, we seek to derive conditions for the existence of feedback Nash equilibrium...

In this paper, we introduce a class of deterministic finite-horizon two-player nonzero-sum differential games where one player uses ordinaryWe use the word ‘ordinary’ to mean that Player 1 uses control strategies that are piecewise continuous functions of time. controls while the other player uses impulse controls. We formulate the necessary and su...

In this exploratory study, we consider an extended producer responsibility (EPR) regulation in the context where a firm can be penalized by a municipality for each uncollected unit of past sold products. A starting point is that the return rate of used products depends on the available infrastructure and on consumers’ environmental awareness. These...

Counterfeiting, which is defined as illegally copying genuine goods with a brand name, is a widespread phenomenon and is imposing a huge cost on owners of trademarks. As a consequence, to deter counterfeiting authorities fine anyone producing or trading (in) fake goods. Yet, consuming counterfeit products is not prosecuted in certain countries, lik...

We study the strategic behavior of firms competing in the exploitation of a common-access productive asset, in the presence of pollution externalities. We consider a differential game with two state variables (asset stock and pollution stock), and by using a piecewise-linear approximation of the nonlinear asset growth function, we provide a tractab...

We consider a firm producing and selling experience products over two periods with private quality information. Consumers strategically decide their purchasing timing driven by the imitation effect, and the firm chooses pricing policy (dynamic or preannounced) and equilibrium type (separating or pooling, through which true quality information is re...

To cope with ever-increasing demand and ensure food security, agronomic systems have shifted over time from traditional agriculture, based on the organic fertilization of soils, to intensive and specialized farming that use chemical fertilization. This resulted in increased soil productivity in the short term, but caused serious ecological drawback...

In this paper, we revisit the problem of existence of an optimal dynamic pricing strategy when the demand depends on a reference price. Using alternative assumptions and technique to those typically used in the literature, we show the existence of a unique pricing policy parametrized in the initial value of the reference price. Our main results are...

Many countries have introduced vehicle scrappage programs to motivate consumers to replace their old cars earlier. Since these programs are generally offered over a given period of time, policy makers need to plan for inter-temporal subsidies. Considering a two-period game between strategic consumers and the government, we determine the optimal scr...

We determine optimal pricing and order quantity of two substitute products in two markets, one of them is seasonal, with a decreasing market potential over time, and the other is nonseasonal. The two markets are sealed, that is, the prices in one market are irrelevant to consumers in the other market. Still, the two markets are linked through inven...

We consider a two-player linear-state differential game, where one player intervenes continuously in the game, while the other implements an impulse control. When the impulse instants are exogenous, we obtain the classical result in linear-state differential games that open-loop and feedback Nash equilibria coincide. When the impulse instants are e...

The technological developments observed in the last two decades contributed to the digitalization of products and the introduction of various mobile devices designed for the consumption of this digital content. Many online retailers launched their own mobile devices, which had a direct effect on their multi-product pricing strategies, but also an e...

Nonprofit organizations play an important role in providing goods and services in all countries. The objective of this paper is to determine optimal policies for a charity when its managers are imperfectly altruistic. The starting point of our analysis is that the donations a charity receives are a function of its reputation, which is an asset that...

We consider a luxury supply chain in which one Stackelberg manufacturer sells products to consumers through a retailer. Driven by exclusivity or conformity, consumers are classified as either snobs or conformists, with uncertain preferences about the product. The manufacturer can obtain a private signal on this preference, while the retailer cannot...

In this paper, we suggest a new approach called the return function to deal with the determination of Bayesian–Nash equilibria in games of incomplete information. Whereas in the traditional approach players reply to each others’ strategies, here each player replies to his own return function. In short, given a player’s choice of action and the othe...

We consider two charities whose revenues are used on advertising to attract market share, on administrative expenditures to manage the charity, and on program expenditures. Assuming a finite planning horizon, we seek to answer the following research question: are there any circumstances under which the charities devote less funds to their programs...

We consider a fishery described by two state variables, namely, the stock of fish and its marine environmental quality, operationalized as an index of habitat extent and quality, which influences the growth rate and the carrying capacity (MEQ). Assuming that myopic fishing agents exploit the fishery, we characterize and contrast the steady‐state va...

This paper studies pricing strategies of competing retailers offering substitutable products in multiple product categories. For such retailers, in addition to accounting for within-category pricing effects, cross-category effects can also influence consumers’ purchase decisions and thereby impact the retailers’ optimal pricing strategies. We model...

We characterize open-loop and feedback Nash equilibria for a class of constrained linear–quadratic multistage games having the following features: (a) The control variables are of two types, namely, control variables that enter the dynamics, but are not constrained, and control variables that are part of state-control constraints, but do not enter...

This work considers a dual-channel supply chain in which a manufacturer sells an experience product through its retailer and directly to consumers. The market potential is stochastic, and the two agents receive different signals about its value. The manufacturer invests in product's quality, and this investment cannot be observed by the retailer. W...

In this paper, we study the problem of responsibility sharing for product recovery, and its relation to the design of Extended Producer Responsibility (EPR) regulations. By defining several scenarios for responsibility sharing policies, we show that designing an EPR regulation and allocating the responsibilities within the supply chain must be done...

We consider the problem of efficiently managing a fishery where pollution externalities are present. The open‐access bionomic model is analyzed in an equation/nrm12216-math-0001.png‐player differential game framework with two‐state variables, that is, the fish stock and the pollution stock. We characterize the noncooperative feedback‐Nash equilibri...

We consider the problem of pricing and advertising a one-time entertainment event. Three pricing policies are characterized and contrasted, namely, dynamic price (DP), constant price (CP) and two-market price (TMP). In this last scenario, the selling season is composed of a regular price period and a last-minute price period, with the switching dat...

This paper surveys two key issues in closed-loop supply chain (CLSC) research: return functions and coordination mechanisms. The return function provides the rule according to which end-of-life/use products are returned to a collector. The coordination mechanisms consist of the adoption of a certain mechanism (e.g., a contract) to align the closed-...

A private bad is a commodity that causes its owner disutility. We study the bilateral exchange of a bad for a good that provides utility. Considering the exchange price to be fixed, we determine the first-best choice of a single agent and study its properties, then investigate the equilibrium strategies of the two-player game. We characterize the n...

Vehicle scrappage subsidy programs have been widely applied by governments to replace old cars by newer, more fuel-efficient ones. While these programs have been implemented to provide motivation for replacing vehicles earlier, they may not be as effective as expected. From a cost-benefit perspective, the consumers who would have replaced anyway, e...

This work studies the strategic impact of a region’s investment in adaptation measures on the equilibrium outcomes of a transboundary pollution dynamic game played in finite horizon. We incorporate adaptation as a region-specific capital stock that decreases local damages and study the feedback (subgame perfect) equilibrium of the non-cooperative g...

To address the problem of the effectiveness and efficiency of environmental protection regulations, we propose a general functional form for regulations to provide a decision support system for social planners designing new regulations. Thanks to the proposed functional form, we are able to compare a variety of different regulations within a single...

We study the impact of collective effort in R&D in adaptation technologies, and also spillover effects on formation and size of stable international environmental agreements (IEAs). Our results suggest that it is possible to have more than one size of stable IEA. We can achieve a superior equilibrium, i.e., the grand coalition, if countries manage...

Brand imitation is a common practice that can take different forms, i.e., legal copying, as in the case of clones and knockoffs, or illegal, in the case of counterfeiting. We consider a scenario in which a producer enters the market with a “similar” product to the incumbent's and we assess the impact of this entry on the incumbent's strategies. A d...

A manufacturer invests in product quality to encourage consumers who have purchased in the past to substitute their current product version with a new release. Since price deters the adoption of an upgraded quality product, consumers evaluate both the quality improvements and the new release price before deciding whether to return a good. The retur...

We characterize the domestic production and imports of food by a country under two scenarios, namely: food security and welfare maximization, in a model with an exogenously given probability of occurrence of an embargo or other sources of supply disruption on the international grain market, e.g., a natural catastrophe. In our framework, food securi...

This will be a two-part handbook on Dynamic Game Theory and part of the Springer Reference program. Part I will be on the fundamentals and theory of dynamic games. It will serve as a quick reference and a source of detailed exposure to topics in dynamic games for a broad community of researchers, educators, practitioners, and students. Each topic w...

In this chapter, we expose a full theory for infinite-horizon concave differential games with coupled state-constraints. Concave games provide an attractive setting for many applications of differential games in economics, management science and engineering, and state coupling constraints happen to be quite natural features in many of these applica...

In many instances, players find it individually and collectively rational to sign a long-term cooperative agreement. A major concern in such a setting is how to ensure that each player will abide by her commitment as time goes by. This will occur if each player still finds it individually rational at any intermediate instant of time to continue to...

This chapter provides an overview of the theory of nonzero-sum differential games, describing the general framework for their formulation, the importance of information structures, and noncooperative solution concepts. Several special structures of such games are identified, which lead to closed-form solutions. © Springer International Publishing A...

It is well known that strategic consumers can harm firms’ profits by delaying their purchases, to buy at discounted price. A retailer can induce consumers to purchase at the right price and time by acting on the two components of the consumer’s surplus in each period, that is, the willingness to pay (WTP) and the selling price. We develop a multi-p...

We analyze the impact of social externalities (SEs) on the stability of an international environmental agreement (IEA). We consider a framework in which players are divided into two homogeneous groups, namely, developed and developing countries. We assume that members of an IEA get some additional benefits, to which we refer as SEs. One main result...

In this paper, we survey the literature applying viability theory to the sustainable management of renewable resources. After a refresher on the main concepts of viability theory, we provide a general map of the contributions and next discuss them by area of application, including ecosystems and population biology, climate change, forestry and othe...

We consider a pricing and advertising dynamic-optimization problem where the goodwill dynamics evolve à la Nerlove–Arrow. The firm maximizes its profit over a finite-planning horizon corresponding to the product's lifespan, and it turns out that the Hamiltonian is non-concave. We show the existence and uniqueness of an optimal solution under some m...

Vehicle scrappage subsidy programs have been widely applied by governments to replace old cars by newer, more fuel-efficient ones. While these programs have been implemented to motivate earlier replacement, they may not be as effective as expected. From a cost-benefit perspective, the consumers who would have replaced anyway, even without the progr...

This paper deals with R&D investment and technology licensing in a supply chain formed of an original equipment manufacturer (OEM) and a contract manufacturer (CM). The R&D is conducted by the CM and the OEM agrees to pay a share of the cost. At the R&D stage, we assume that there are some uncertainties both in terms of performance of the developed...

We consider a dynamic marketing channel comprising of one manufacturer and one retailer, where consumer demand depends on price and on brand reputation. We investigate two scenarios. In the first one, the retailer may also invest in brand advertising, while in the second, it does not. Comparing the results of the two scenarios yields interesting in...

Why do private labels (PLs) enjoy a large market in some countries while hardly penetrating others? What makes a market favorable to PL-product development? Can we identify drivers that explain differences between countries in terms of PL performance? This study aims at addressing these relatively less-researched questions in international marketin...

We consider a class of dynamic games played over an event tree, with random terminal time. We assume that the players wish to jointly optimize their payoffs throughout the whole planning horizon and adopt the Shapley value to share the joint cooperative outcome. We devise a node-consistent decomposition of the Shapley value, which means that in any...

In this tutorial, we recall the main ingredients of the theory of dynamic games played over event trees and show step-by-step how to build a sustainable cooperative solution.

Abstract Purpose – The starting conjecture is that the market share of a brand in one category benefits from its performance in another category, and vice versa. The purpose of this paper is to assess the umbrella-branding spillovers by investigating the presence of synergy effect between categories when a retailer and/or a manufacturer decide to a...

In this paper, we propose a diffusion model for a subscription service. The evolution over time of the number of subscribers is governed by a differential equation combining two processes, namely, a customer acquisition process and a customer attrition process. Assuming profit-maximization behavior of the firm, we use dynamic programming to optimiz...