On the effects of conjectures in a symmetric strategic setting

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 superior outcoumes.