Complementarity Enhanced Nash’s Mappings and Differentiable Homotopy Methods to Select Perfect Equilibria

2021 ◽  
Author(s):  
Yiyin Cao ◽  
Chuangyin Dang ◽  
Yabin Sun
Keyword(s):  
Homotopy Methods ◽  
Perfect Equilibria

scholarly journals Search for a moving target in a competitive environment

2021 ◽  
Author(s):  
Benoit Duvocelle ◽  
János Flesch ◽  
Hui Min Shi ◽  
Dries Vermeulen
Keyword(s):  
Markov Chain ◽  
Discrete Time ◽  
Competitive Environment ◽  
Moving Target ◽  
Time Varying ◽  
Greedy Strategy ◽  
Time Dynamic ◽  
Dynamic Search ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

AbstractWe consider a discrete-time dynamic search game in which a number of players compete to find an invisible object that is moving according to a time-varying Markov chain. We examine the subgame perfect equilibria of these games. The main result of the paper is that the set of subgame perfect equilibria is exactly the set of greedy strategy profiles, i.e. those strategy profiles in which the players always choose an action that maximizes their probability of immediately finding the object. We discuss various variations and extensions of the model.

UNIQUENESS IN RANDOM-PROPOSER MULTILATERAL BARGAINING

2009 ◽  
Vol 11 (04) ◽  
pp. 407-417 ◽  
Author(s):  
HUIBIN YAN
Keyword(s):  
Subgame Perfect Equilibrium ◽  
Characteristic Functions ◽  
Bargaining Model ◽  
Equilibrium Outcome ◽  
Multilateral Bargaining ◽  
Legislative Bargaining ◽  
Uniqueness Results ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria ◽  
Special Case

Solution uniqueness is an important property for a bargaining model. Rubinstein's (1982) seminal 2-person alternating-offer bargaining game has a unique Subgame Perfect Equilibrium outcome. Is it possible to obtain uniqueness results in the much enlarged setting of multilateral bargaining with a characteristic function? This paper investigates a random-proposer model first studied in Okada (1993) in which each period players have equal probabilities of being selected to make a proposal and bargaining ends after one coalition forms. Focusing on transferable utility environments and Stationary Subgame Perfect Equilibria (SSPE), we find ex ante SSPE payoff uniqueness for symmetric and convex characteristic functions, considerably expanding the conditions under which this model is known to exhibit SSPE payoff uniqueness. Our model includes as a special case a variant of the legislative bargaining model in Baron and Ferejohn (1989), and our results imply (unrestricted) SSPE payoff uniqueness in this case.

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