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I propose a differential oligopoly game of resource extraction under (quasi-static) open-loop and nonlinear feedback strategies, where firms are managerial and two alternative types of delegation contract are considered. Under open-loop information, delegation expands the residual steady state resource stock. Conversely, under nonlinear feedback information the outcome depends on the structure of managerial incentives. If sales are used, once again delegation favours resource preservation. On the contrary, if market shares are included in the delegation contract, this combines with an underlying voracity effect in shrinking the steady state volume of the resource.

This paper offers an overview of the literature discussing oligopoly games in which polluti ng emissions are generated by the supply of goods requiring a natural resource as an input. An analytical summary of the main features of the interplay between pollution and resource extraction is then given using a differential game based on the Cournot oligopoly model, in which (i) the bearings on resource preservation of Pigouvian tax rate tailored on emissions are singled out and (ii) the issue of the optimal number of firms in the commons is also addressed.

Zaccour (2008) investigates the behaviour of a marketing channel where firms invest in advertising to increase brand equity, showing that an exogenous twopart tariff cannot be used to replicate the vertically integrated monopolist's performance. I revisit the same model proving the existence of a multiplicity of franchising contracts taht can do the job. In particular, I set out by illustrating an optimal two-part tariff specified as a linear function of the upstream firm's advertising effort, performing this task both in the static and in the dynamic game. then, I show that an analogous result emerges (i) in the static game by writing the fixed component of the two-part tariff as a non-linear function of the manufacturer's advertising effort; and (ii) by using a contract which is linear in the brand equity, in the dynamic case.

I investigate two versions of a differential Cournot oligopoly game with nonrenewable resource exploitation, in which each firm may either exploit its own private pool or exploit a common pool jointly with the rivals. Firms use a deterministic technology to invest in exploration activities. In both models, there emerges that (i) the individual exploration effort is higher when each firms has exclusive rights on a pool of its own, and (ii) depending on the assumptions on technology and demand, the aggregate exploration effort is either constant or increasing in the number of firms.

I investigate a two-country non cooperative game where the status quo ante is asymmetric as one country is endowed with nuclear weapons while the other is not and is evaluating the opportunity of build up a nuclear arsenal. After identifying the conditions on payoffs such that the resulting reduced form is a coordination game with two symmetric equilibria, I resort to forward induction to show that the implicit signaling mechanism in it may lead countries to select the peaceful equilibrium in a symmetric environment where both are endowed with analogous arsenals.

I characterise the subgame perfect equilibrium of a differential market game with hyperbolic demand where firms are quantity-setters and accumulate capacity over time à la Ramsey. I show that the open-loop solution is subgame perfect. Then, I analyse the feasibility of horizontal mergers, and compare the result generated by the dynamic setup with the merger incentive associated with the static model. It appears that allowing for the role of time makes mergers more likely to occur than they would on the basis of the static setting.

A dynamic approach is proposed for the analysis of the Cournot oligopoly game with hyperbolic demand, showing that the adoption of capital accumulation dynamics either `a la Solow-Swan or `a la Ramsey eliminate the indeterminacy problem characterising the static model when marginal costs are nil. It is proved that the steady state equilibria produced by both models are stable in the saddle point sense. Finally, it is also shown that the solutions of the corresponding feedback problems share analogous properties, although they cannot be fully characterised from an analytical standpoint.

The issue of technical progress under uncertainty is nested into the debate on vertical integration vs outsourcing, to show that, in general, the former is preferable to the latter in terms of both expected profits and technological efficiency. It is then shown that there exist (i) an optimal two part tariff where the unit price set by the upstream firm is conditional upon its R&D effort, and (ii) an optimal contract specifying the input price in terms of the initial capabilities of the sub-contractor, whereby the industry replicates the same performance as the vertically integrated firm as for both profits and R&D efforts.

The monopolist's incentives towards product proliferation are evaluated in an optimal control model considering three alternative regimes: profit-seeking; social planning; and a hybrid case with monopoly pricing and a regulator setting product innovation to maximise welfare. In equilibtium, the profitseeking firm supplies a socially suboptimal number of varieties to reduce cannibalisation while the social planner exploits the same effect to satisfy consumers' love for variety and decrease the market price of all products. In terms of the Schumpeter vs Arrow debate on the relationship between market structure and innovation incentives, the results obtained in this model have a definite Arrovian flavor.