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On the Effects of Conjectures in a Strategic Setting

Charles Figuieres 1 Alain Jean-Marie 2 Mabel Tidball 1 
2 APR - Algorithmes et Performance des Réseaux
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Recent papers have provided a justification for the so-called conjectural variation equilibrium (CVE) as a shortcut to capture long run interactions. According to this concept, each agent chooses her most favorable action taking into account that rival strategies are a conjectured function of her own strategy. Our aim is to compare the CVE and the Nash Equilibrium (NE), and thus to appraise the impact on agents' behaviors of the underlying intertemporal forces that yield the conjectures. 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 the corresponding theoretical explanations. It turns out that the economic situations can be divided into two families, depending on whether they admit a stable NE and an interior Pareto solution (family 1) or not (family 2). Within each family it is shown that the sign of the externalities 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 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 consistent conjectures belongs to the set of conjectures that produces superior outcomes.
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Submitted on : Monday, October 23, 2006 - 7:43:12 AM
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Charles Figuieres, Alain Jean-Marie, Mabel Tidball. On the Effects of Conjectures in a Strategic Setting. Research in Economics, Elsevier, 2004, 58 (1), pp.75-102. ⟨10.1016/j.rie.2003.11.002⟩. ⟨lirmm-00108560⟩



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