Consistent conjectures are optimal Cournot-Nash strategies in the meta-game

Special Issue on Variational Inequalities: Consistent Conjectural Variations Coincide with the Nash Solution in the Meta-Model

“…, n, coincides with the classical Cournot-Nash equilibrium in the meta-game. Similar results were claimed (without proof) in our previous paper (Kalashnykova et al 2012) but only for quadratic cost functions.…”

“…In the same manner as in Bulavsky andKalashnikov (1994, 1995), the authors considered a conjectural variations oligopoly model, in which the degree of influence upon the general situation by each agent is modeled by special parameters (influence coefficients). However, in contrast to the models defined in Bulavsky andKalashnikov (1994, 1995) and Kalashnikov et al (2009Kalashnikov et al ( , 2010, the papers Kalashnikov et al (2011) and Kalashnikov et al (2017) follows the pattern proposed in Bulavsky (1997) selecting the market clearing price p, rather than the producers' total output G, as an observable variable. Because of that, the players' conjectures are denoted by letters v i instead of the previously employed w i , with an evident relationship valid for these pairs of parameters:…”

“…All the above-mentioned papers deal in various modes with games with conjectural variations equilibrium (CVE). A more detailed story of the "highs and lows" of the CVE can be found in Kalashnikov et al (2011Kalashnikov et al ( , 2017 . However, for the sake of a complete list of the predecessors, we briefly repeat the short survey presented in Kalashnikov et al (2017).…”

“…The consistency (a.k.a., sometimes, "rationality") of the equilibrium is defined as the coincidence of the conjectural best response by each agent and the conjectured reaction function of the same agent. A conceptual difficulty arises when one considers consistency in the case of many (i.e., more than 2) agents (see, again, Kalashnikov et al (2017) and Figuières et al (2004)). Interesting discussions of the concept of consistency of predictions can be also found in the papers Ben-Akiva et al (2001) and Zerrahn and Huppmann (2017).…”

“…The consistency criterion, its verification procedure, and the existence theorems for the interior equilibrium are formulated in the same Section 4. Even though the short Sections 2 to 4 mainly are the same as in our recent paper (Kalashnikov et al 2017), we insert them to make this paper somewhat self-contained. Finally, Section 5 establishes the main (and the only new) results of this manuscript asserting that the consistent conjectural equilibrium in the original oligopoly provides the classical Cournot-Nash equilibrium in the meta-model and vice versa.…”