2016/12/28 by Stefanos Leonardos, Leonardos, Stefanos, Costis Melolidakis +1
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #91A40 #Best response #Computer Science and Game Theory (cs.GT) #Correlated equilibrium #Economic theories and models #Economics #Epsilon-equilibrium #Equilibrium selection #Evolutionary Game Theory and Cooperation #Experimental Behavioral Economics Studies #FOS: Computer and information sciences #Game Theory and Applications #Game theory #Mathematical economics #Mathematics #Microeconomics #Minimax #Nash equilibrium #Normal-form game #Primary: 91A05 #Repeated game #Risk dominance #Secondary: 91A10 #Statistics #Stochastic game #Strategy #Traveler's dilemma #Value (mathematics) #cs.GT #msc:91A05 #msc:91A10 #msc:91A40
paper · pdf · doi:10.48550/arxiv.1612.08888
arxiv created 2016/12/28 · openalex publication_date 2016/12/28 · arxiv updated 2016/12/30 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Given a bimatrix game, the associated leadership or commitment games are\ndefined as the games at which one player, the leader, commits to a (possibly\nmixed) strategy and the other player, the follower, chooses his strategy after\nhaving observed the irrevocable commitment of the leader. Based on a result by\nvon Stengel and Zamir [2010], the notions of commitment value and commitment\noptimal strategies for each player are discussed as a possible solution\nconcept. It is shown that in non-degenerate bimatrix games (a) pure commitment\noptimal strategies together with the follower's best response constitute Nash\nequilibria, and (b) strategies that participate in a completely mixed Nash\nequilibrium are strictly worse than commitment optimal strategies, provided\nthey are not matrix game optimal. For various classes of bimatrix games that\ngeneralize zero sum games, the relationship between the maximin value of the\nleader's payoff matrix, the Nash equilibrium payoff and the commitment optimal\nvalue is discussed. For the Traveler's Dilemma, the commitment optimal strategy\nand commitment value for the leader are evaluated and seem more acceptable as a\nsolution than the unique Nash equilibrium. Finally, the relationship between\ncommitment optimal strategies and Nash equilibria in 2 \× 2 bimatrix\ngames is thoroughly examined and in addition, necessary and sufficient\nconditions for the follower to be worse off at the equilibrium of the\nleadership game than at any Nash equilibrium of the simultaneous move game are\nprovided.\n