scholarly journals Monotone Operator Methods for Nash Equilibria in Non-potential Games

Author(s):  
Luis M. Briceño-Arias ◽  
Patrick L. Combettes
Author(s):  
João P. Hespanha

This chapter discusses several classes of potential games that are common in the literature and how to derive the Nash equilibrium for such games. It first considers identical interests games and dummy games before turning to decoupled games and bilateral symmetric games. It then describes congestion games, in which all players are equal, in the sense that the cost associated with each resource only depends on the total number of players using that resource and not on which players use it. It also presents other potential games, including the Sudoku puzzle, and goes on to analyze the distributed resource allocation problem, the computation of Nash equilibria for potential games, and fictitious play. It concludes with practice exercises and their corresponding solutions, along with additional exercises.


2014 ◽  
Vol 39 (4) ◽  
pp. 1252-1296 ◽  
Author(s):  
Ragavendran Gopalakrishnan ◽  
Jason R. Marden ◽  
Adam Wierman

1999 ◽  
Vol 01 (03n04) ◽  
pp. 283-299 ◽  
Author(s):  
MARK VOORNEVELD ◽  
PETER BORM ◽  
FREEK VAN MEGEN ◽  
STEF TIJS ◽  
GIOVANNI FACCHINI

In congestion games, players use facilities from a common pool. The benefit that a player derives from using a facility depends, possibly among other things, on the number of users of this facility. The paper gives an easy alternative proof of the isomorphism between exact potential games and the set of congestion games introduced by Rosenthal (1973). It clarifies the relations between existing models on congestion games, and studies a class of congestion games where the sets of Nash equilibria, strong Nash equilibria and potential-maximising strategies coincide. Particular emphasis is on the computation of potential-maximising strategies.


2011 ◽  
pp. 65-87 ◽  
Author(s):  
A. Rubinstein

The article considers some aspects of the patronized goods theory with respect to efficient and inefficient equilibria. The author analyzes specific features of patronized goods as well as their connection with market failures, and conjectures that they are related to the emergence of Pareto-inefficient Nash equilibria. The key problem is the analysis of the opportunities for transforming inefficient Nash equilibrium into Pareto-optimal Nash equilibrium for patronized goods by modifying the institutional environment. The paper analyzes social motivation for institutional modernization and equilibrium conditions in the generalized Wicksell-Lindahl model for patronized goods. The author also considers some applications of patronized goods theory to social policy issues.


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