We have witnessed in recent years a revival of Conjectural Variations in Game Theory. This reincarnation of an old idea, using a dynamic point of view, aims at combining the adequacy with facts to the requirements of a firmly grounded theory. This book presents, for the first time, a comprehensive account of conjectural variations equilibria in their static inceptions, featuring new comparative results of equilibria with regard to efficiency. It then describes several advances in Dynamic Game Theory, allowing to understand Conjectural Variations Equilibria as dynamic equilibria. The question of how conjectures evolve in strategic and learning situations with boundedly rational agents is also discussed.

This paper deals with the effect of conjectures in a strategic setting.To do this it focuses on the so-called Conjectural Variation Equilibrium (CVE).According to this concept, each agent chooses his most favorable action taking into account that rival strategies are a conjectured function of his own strategy. In the existing literature, a central role is played by the comparison between the CVE and the NASH Equilibrium (NE). The purpose of such a comparison is to appraise the impact of non zero conjectures on agents'behaviors.The existing results suggest that it is not possible to know, in advance, the consequences of non zero conjectures on behaviors. Our aim is: i) to identify situations where it is indeed possible, a priori, to know which kind of non cooperative concept Pareto dominates the other, ii) to provide out the corresponding theoretical explanations. The economic situations can be divided into two families, depending on whether they admit a stable Nash equilibrium and an interior Pareto situation (family 1) or not (family 2). Within each family it is shown that the sign of the externalities (positives or negative effect of the rival actions on a player's payoffs) together with the properties of conjectures (their sign and their absolute value): i) indicates how to rank the action levels associated with the NE and the CVE, ii) allows one to predict which kind of behavior leads the players to the most favorable outcome. It turns out that the qualitative results prevailing for family 1 are reversed for the family 2. This classification is useful in that outcomes and payoffs need not be calculated to assess the impact of conjectures on players'payoffs; the only relevant pieces of information are the sign of second order derivatives of the payoff function and the properties of conjectures, i.e. the description of the game. We then study in which kind of game reasonable conjectures, i.e. consistent conjectures, belongs to the set of conjectures that produces

This article provides a theoretical contribution on the issue of under-investment of public capitals. In a differential game of accumulation of capital between two jurisdictions, the open loop Nash equilibrium and the centralized solution converge towards their respective steady states. In the long run we characterize the inefficiency of the Nash equilibrium using as a benchmark case the utilitarian centralized outcome. When the stocks of infrastructures are strategic complements, the jurisdictions under-invest (over-invest) in situations with negative (positive) externalities. When the stocks are strategic substitutes the same results hold for similar jurisdictions. On the contrary when the cost structures of the jurisdictions are different enough, it is shown within an example that the low-cost jurisdiction under-invests whereas the high-cost jurisdiction over-invests. We then broach briefly the economic policy implications of these results. Cet article apporte une contribution théorique au débat sur le sous-investissement en capitaux publics. Il utilise pour cela un jeu différentiel d’accumulation de capitaux entre deux collectivités. Dans ce jeu l’équilibre de Nash en boucle ouverte et la solution centralisée du jeu convergent à long terme vers un régime stationnaire. Dans le long terme nous étudions la nature de l’inefficacité de l’équilibre de Nash en prenant comme référence la solution centralisée utilitariste. Lorsque les stocks d’infrastructures sont des compléments stratégiques, les collectivités surinvestissent (sous-investissent) en présence d’externalités négatives (positives). Lorsque les stocks d’infrastructures sont des substituts stratégiques, les mêmes résultats restent vrais si les collectivités sont similaires. En revanche, nous montrons dans un exemple que lorsque les collectivités ont des structures de coûts assez différentes, la collectivité qui a le coût le plus faible sous-investit tandis que la collectivité qui a le coût le plus fort surinv

The preemptive role of capital is analyzed in a class of differential games of capital accumulation with reversible investment for two symmetric players. Two dynamic concepts of interaction are defined: feedback substitutability and feedback complementarity. These concepts are useful for exploring the dynamic properties of the stocks. In particular it is proved that if the equilibrium of the game is characterized by feedback substitutability, the firm with the higher initial condition overshoots his long-run level of capital.