Equilibria Under Passive Beliefs for Multi-leader-follower Games with Vertical Information: Existence Results

Maria Carmela Ceparano and Jacqueline Morgan

CSEF Working Papers from Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy

Abstract: We consider two-stage multi-leader-follower games, called multi-leader-follower games with vertical information, where leaders in the first stage and followers in the second stage choose simultaneously an action but those chosen by any leader are observed by only one “exclusive” follower. This partial unobservability leads to extensive form games that have no proper subgames but may have an infinity of Nash equilibria. So it is not possible to refine using the concept of subgame perfect Nash equilibrium and, moreover, the concept of weak perfect Bayesian equilibrium could be not useful since it does not prescribe limitations on the beliefs out of the equilibrium path. This has motivated the introduction of a selection concept for Nash equilibria based on a specific class of beliefs, called passive beliefs, that each follower has about the actions chosen by the leaders rivals of his own leader. In this paper, we illustrate the effectiveness of this concept and we investigate the existence of such a selection for significant classes of problems satisfying generalized concavity properties and conditions of minimal character on possibly discontinuous data.

Keywords: multi-leader-follower game; selection of equilibria; passive belief; discontinuous function; fixed point; generalized concavity (search for similar items in EconPapers)
Date: 2015-10-13, Revised 2017-01-09
New Economics Papers: this item is included in nep-com, nep-cta, nep-gth and nep-mic
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Published in TOP with the title "Equilibria Selection for Multi-leader-follower Games with Vertical Information", 2017, 25(3), pp. 526-543

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