On the Commitment Value and Commitment Optimal Strategies in Bimatrix Games
Stefanos Leonardos () and
Costis Melolidakis ()
Additional contact information
Stefanos Leonardos: Department of Mathematics, National & Kapodistrian University of Athens, Panepistimioupolis GR — 157 84, Athens, Greece
Costis Melolidakis: Department of Mathematics, National & Kapodistrian University of Athens, Panepistimioupolis GR — 157 84, Athens, Greece
International Game Theory Review (IGTR), 2018, vol. 20, issue 03, 1-28
Abstract:
Given a bimatrix game, the associated leadership or commitment games are defined as the games at which one player, the leader, commits to a (possibly mixed) strategy and the other player, the follower, chooses his strategy after being informed of the irrevocable commitment of the leader (but not of its realization in case it is mixed). Based on a result by Von Stengel and Zamir [2010], the notions of commitment value and commitment optimal strategies for each player are discussed as a possible solution concept. It is shown that in nondegenerate bimatrix games (a) pure commitment optimal strategies together with the follower’s best response constitute Nash equilibria, and (b) strategies that participate in a completely mixed Nash equilibrium are strictly worse than commitment optimal strategies, provided they are not matrix game optimal. For various classes of bimatrix games that generalize zero-sum games, the relationship between the maximin value of the leader’s payoff matrix, the Nash equilibrium payoff and the commitment optimal value are discussed. For the Traveler’s Dilemma, the commitment optimal strategy and commitment value for the leader are evaluated and seem more acceptable as a solution than the unique Nash equilibrium. Finally, the relationship between commitment optimal strategies and Nash equilibria in 2 × 2 bimatrix games is thoroughly examined and in addition, necessary and sufficient conditions for the follower to be worse off at the equilibrium of the leadership game than at any Nash equilibrium of the simultaneous move game are provided.
Keywords: Bimatrix game; Nash equilibrium; subgame perfect; commitment optimal; commitment value; weakly unilaterally competitive games; pure strategy equilibrium; commitment advantageous games (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations:
Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219198918400017
Access to full text is restricted to subscribers
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:wsi:igtrxx:v:20:y:2018:i:03:n:s0219198918400017
Ordering information: This journal article can be ordered from
DOI: 10.1142/S0219198918400017
Access Statistics for this article
International Game Theory Review (IGTR) is currently edited by David W K Yeung
More articles in International Game Theory Review (IGTR) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().