Uniqueness of Normalized Nash Equilibrium for a Class of Games With Strategies in Banach Spaces

2002 ◽  
pp. 333-348 ◽  
Author(s):  
Dean A. Carlson
Keyword(s):  
Nash Equilibrium ◽  
Banach Spaces ◽  
Normalized Nash Equilibrium

scholarly journals Gamification Based Blockchain Tournaments Between Miners

2021 ◽  
Vol 3 (1) ◽  
pp. 91-114
Author(s):  
Hiroshi Kenta ◽  
Yamato Shino ◽  
Dewi Immaniar ◽  
Eka Purnama Harahap ◽  
Alfian Dimas Ahsanul Rizki Ahmad
Keyword(s):  
Nash Equilibrium ◽  
Cooperative Game ◽  
Traffic Congestion ◽  
Nash Equilibria ◽  
Allocation Of Resources ◽  
Complexity Level ◽  
System Models ◽  
Short Algorithm ◽  
Normalized Nash Equilibrium

We have modelled mining resource and cryptocurrency-related relationships into a non-cooperative game. Then we took advantage of the traffic congestion results, set a native convention for the Nash equilibria, and created a short algorithm to find the equilibria. Next, we will make calculations for several system models whose variations follow the existing mining resources and have appropriately allocated according to the details of the mining complexity level that has defeated. In the included resources, the game's result is the allocation of resources as a feature of a normalized Nash equilibrium. In the model that has proposed, we provide a property structure of the type of equilibrium that exists, such as a condition where there are two or more mining infrastructures that will be active and another state that explains that no Miners get results in wanting a specific cryptocurrency, like bitcoin.

Split Equilibrium Problems for Related Games and Applications to Economic Theory

2018 ◽  
Vol 20 (04) ◽  
pp. 1850005
Author(s):  
Jinlu Li
Keyword(s):  
Economic Theory ◽  
Nash Equilibrium ◽  
Banach Spaces ◽  
Price Competition ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Strategic Games ◽  
Kkm Theorem ◽  
Duopoly Model ◽  
Convex Subsets

In this paper we introduce the concept of split Nash equilibrium problems associated with two related noncooperative strategic games. Then we apply the Fan–KKM theorem to prove the existence of solutions to split Nash equilibrium problems of related noncooperative strategic games, in which the strategy sets of the players are nonempty closed and convex subsets in Banach spaces. As an application of this existence to economics, an example is provided that studies the existence of split Nash equilibrium of utilities of two related economies. As applications, we study the existence of split Nash equilibrium in the dual (playing twice) extended Bertrand duopoly model of price competition.

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