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Nikolai S. Kukushkin and Pierre von Mouche
''Cournot tatonnement and Nash equilibrium in binary status games''
( 2018, Vol. 38 No.2 )
We study a rather simplified game model of competition for status. Each player chooses a scalar variable (say, the level of conspicuous consumption), and then those who chose the highest level obtain the "high" status, while everybody else remains with the "low" status. Each player strictly prefers the high status, but they also have intrinsic preferences over their choices. The set of all feasible choices may be continuous or discrete, whereas the strategy sets of different players can only differ in their upper and lower bounds. The resulting strategic game with discontinuous utilities does not satisfy the assumptions of any general theorem known as of today. Nonetheless, the existence of a (pure strategy) Nash equilibrium, as well as the "finite best response improvement property," are established.
Keywords: status game, Cournot tatonnement, Nash equilibrium
JEL: C7 - Game Theory and Bargaining Theory:General
D1 - Household Behavior: General
Manuscript Received : Jan 29 2018 Manuscript Accepted : May 25 2018

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