Implementation in Strong Nash Equilibrium

1991 ◽  
pp. 93-122
Author(s):  
J. Abdou ◽  
H. Keiding
Keyword(s):  
Nash Equilibrium ◽  
Strong Nash Equilibrium

Markets versus Negotiations: The Predominance of Centralized Markets

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Zvika Neeman ◽  
Nir Vulkan
Keyword(s):  
Nash Equilibrium ◽  
Exchange Mechanism ◽  
Future Period ◽  
Strong Nash Equilibrium ◽  
Heterogenous Group ◽  
Informed Traders ◽  
Decentralized Bargaining

The paper considers the consequences of competition between two widely used exchange mechanisms, a “decentralized bargaining'' market, and a “centralized'' market. In every period, members of a large heterogenous group of privately-informed traders who each wish to buy or sell one unit of some homogenous good may opt for trading through one exchange mechanism. Traders may also postpone their trade to a future period. It is shown that trade outside the centralized market completely unravels. In every strong Nash equilibrium, all trade takes place in the centralized market. No trade ever occurs through direct negotiations.

scholarly journals Pure Nash Equilibria: Hard and Easy Games

2005 ◽  
Vol 24 ◽  
pp. 357-406 ◽  
Author(s):  
G. Gottlob ◽  
G. Greco ◽  
F. Scarcello
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Equilibrium Problems ◽  
Small Neighborhood ◽  
Constraint Satisfaction Problems ◽  
Pure Nash Equilibrium ◽  
Bounded Treewidth ◽  
Dependency Structure ◽  
Strong Nash Equilibrium ◽  
Restrictive Settings

We investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NP-hard, while deciding whether a game has a strong Nash equilibrium is SigmaP2-complete. We then study practically relevant restrictions that lower the complexity. In particular, we are interested in quantitative and qualitative restrictions of the way each player's payoff depends on moves of other players. We say that a game has small neighborhood if the utility function for each player depends only on (the actions of) a logarithmically small number of other players. The dependency structure of a game G can be expressed by a graph DG(G) or by a hypergraph H(G). By relating Nash equilibrium problems to constraint satisfaction problems (CSPs), we show that if G has small neighborhood and if H(G) has bounded hypertree width (or if DG(G) has bounded treewidth), then finding pure Nash and Pareto equilibria is feasible in polynomial time. If the game is graphical, then these problems are LOGCFL-complete and thus in the class NC2 of highly parallelizable problems.

Prices of Anarchy of Selfish 2D Bin Packing Games

2019 ◽  
Vol 30 (03) ◽  
pp. 355-374
Author(s):  
Cristina G. Fernandes ◽  
Carlos E. Ferreira ◽  
Flávio K. Miyazawa ◽  
Yoshiko Wakabayashi
Keyword(s):  
Nash Equilibrium ◽  
Bin Packing ◽  
Price Of Anarchy ◽  
Dimensional Case ◽  
Theoretical Problem ◽  
Single Item ◽  
Strong Nash Equilibrium ◽  
Square Packing ◽  
The Cost

We consider a game-theoretical problem called selfish 2-dimensional bin packing game, a generalization of the 1-dimensional case already treated in the literature. In this game, the items to be packed are rectangles, and the bins are unit squares. The game starts with a set of items arbitrarily packed in bins. The cost of an item is defined as the ratio between its area and the total occupied area of the respective bin. Each item is a selfish player that wants to minimize its cost. A migration of an item to another bin is allowed only when its cost is decreased. We show that this game always converges to a Nash equilibrium (a stable packing where no single item can decrease its cost by migrating to another bin). We show that the pure price of anarchy of this game is unbounded, so we address the particular case where all items are squares. We show that the pure price of anarchy of the selfish square packing game is at least [Formula: see text] and at most [Formula: see text]. We also present analogous results for the strong Nash equilibrium (a stable packing where no nonempty set of items can simultaneously migrate to another common bin and decrease the cost of each item in the set). We show that the strong price of anarchy when all items are squares is at least [Formula: see text] and at most [Formula: see text].

Computing the strong Nash equilibrium for Markov chains games

2015 ◽  
Vol 265 ◽  
pp. 911-927 ◽  
Author(s):  
Julio B. Clempner ◽  
Alexander S. Poznyak
Keyword(s):  
Nash Equilibrium ◽  
Markov Chains ◽  
Strong Nash Equilibrium
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