Degenerate feedback and time consistency in dynamic games

This paper analyses the time consistency of open-loop equilibria, in the cases of Nash and Stackelberg behaviour. We define a class of games where the strong time-consistency of the open-loop Nash equilibrium associates with the time consistency of the open-loop Stackelberg equilibrium. We label these games as `perfect uncontrollable' and provide two examples based on (i) a model where firms invest so as to increase consumers' reservation prices, based upon Cellini and Lambertini (CEJOR, 2003); and (ii) a model where firms compete to increase their respective market shares, based upon Leit- mann and Schmitendorf (IEEE Transactions on Automatic Control, 1978)

R&D incentives under Bertrand competition: a differential game

We investigate dynamic R&D for process innovation in an oligopoly where firms invest in cost-reducing activities. We focus on the relationship between R&D intensity and market structure, proving that the industry R&D investment monotonically increases in the number of firms. This result contradicts the established wisdom acquired from static games on the same topic. We also prove that, if competition is sufficiently tough, any increase in product substitutability reduces R&D efforts

Endogenous Royalty Factor in a Licensing Contract

The owner of a well known fashion brand grants a manufacturer the rights to produce and sell a second-line brand against a percentage of the sales called royalty. To this end, the brand owner and the manufacturer sign a licensing contract which assigns the owner, who has already determined his advertising campaign, the right of determining the royalty factor. The manufacturer will plan her advertising campaign for the licenced product in order to maximize her profit. The brand owner's objective is twofold: on one hand he wants to maximize the profit coming from the contract, on the other hand he wants to improve the value of the brand at the end of a given planning period. We model this interaction between the two agents using a Stackelberg game, where the brand owner is the leader and the manufacturer is the follower. We characterise the royalty percentage and the licensee's advertising effort which constitute the unique Stackelberg equilibrium of the game

Advertising in a Differential Oligopoly Game

We illustrate a differential oligopoly game where firms compete à la Cournot in homogeneous goods in the market phase, and invest in advertising activities aimed at increasing consumers’ reservation price. Such investments produce external effects, characterizing the advertising activity as a public good. We derive the open-loop and the closed-loop Nash equilibria, and show that the properties of the equilibria depend on the curvature of the market demand function. The comparative assessment of these equilibria shows that firms’ advertising efforts are larger in the open-loop than in the closed-loop equilibrium. We also show that a cartel involving all firms, setting both quantities and advertising efforts so as to maximize joint profits, may produce a steady state where social welfare is higher than the social welfare levels associated with both the non-cooperative settings

Harvesting of a Transboundary Replenishable Fish Stock: A Noncooperative Game Solution

In this study we use a N-person differential game structure to represent a renewable resource industry in which the decision agents are few in number and noncooperative (as would be the case, for example, in international fishing wars). As an illustration we assume an environment similar to that presented by Levhari and Mirman (1980) to derive a set of tractable strategies. Although there is no guarantee that the stock size would always be positive with human harvesting in the Levhari and Mirman case, our model provides growth dynamics that rule out negative stocks. Explicit solutions of equilibrium game strategies and a steady-state level of stock are derived. Finally, we demonstrate that in situations when stock size enters the production function, combined maximization such as an international treaty is more "conservative" than individual maximization.Environmental Economics and Policy, Institutional and Behavioral Economics, International Relations/Trade, Resource /Energy Economics and Policy,

A Class of Differential Games Where the Closed-Loop and Open-Loop Nash Equilibria Coincide

It is well known that, in general, Nash equilibria in open-loop strategies do not coincide with those in closed-loop strategies. This note identifies a class of differential games in which the Nash equilibrium in closed-loop strategies is degenerate in the sense that it depends on time (t) only. Consequently, the closed-loop equilibrium is also an equilibrium in open-loop strategies