Records 
Author 
Cominetti, R.; Quattropani, M.; Scarsini, M. 
Title 
The BuckPassing Game 
Type 

Year 
2022 
Publication 
Mathematics Operations Research 
Abbreviated Journal 
Math. Oper. Res. 
Volume 
Early Access 
Issue 

Pages 

Keywords 
priorfree equilibrium; generalized ordinal potential game; finite improvement property; fairness of equilibria; price of anarchy; price of stability; Markov chain tree theorem; PageRank; PageRank game 
Abstract 
We consider two classes of games in which players are the vertices of a directed graph. Initially, nature chooses one player according to some fixed distribution and gives the player a buck. This player passes the buck to one of the player's outneighbors in the graph. The procedure is repeated indefinitely. In one class of games, each player wants to minimize the asymptotic expected frequency of times that the player receives the buck. In the other class of games, the player wants to maximize it. The PageRank game is a particular case of these maximizing games. We consider deterministic and stochastic versions of the game, depending on how players select the neighbor to which to pass the buck. In both cases, we prove the existence of pure equilibria that do not depend on the initial distribution; this is achieved by showing the existence of a generalized ordinal potential. If the graph on which the game is played admits a Hamiltonian cycle, then this is the outcome of priorfive Nash equilibrium in the minimizing game. For the minimizing game, we then use the price of anarchy and stability to measure fairness of these equilibria. 
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ISSN 
0364765X 
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Notes 
WOS:000731930100001 
Approved 

Call Number 
UAI @ alexi.delcanto @ 
Serial 
1502 
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Author 
Cominetti, R.; Scarsini, M.; Schroder, M.; StierMoses, N. 
Title 
Approximation and Convergence of Large Atomic Congestion Games 
Type 

Year 
2022 
Publication 
Mathematics of Operations Research 
Abbreviated Journal 
Math. Oper. Res. 
Volume 
Early Access 
Issue 

Pages 

Keywords 
unsplittable atomic congestion games; nonatomic congestion games; Wardrop equilibrium; Poisson games; symmetric equilibrium; price of anarchy; price of stability; total variation 
Abstract 
We consider the question of whether and in what sense, Wardrop equilibria provide a good approximation for Nash equilibria in atomic unsplittable congestion games with a large number of small players. We examine two different definitions of small players. In the first setting, we consider games in which each player's weight is small. We prove that when the number of players goes to infinity and their weights to zero, the random flows in all (mixed) Nash equilibria for the finite games converge in distribution to the set of Wardrop equilibria of the corresponding nonatomic limit game. In the second setting, we consider an increasing number of players with a unit weight that participate in the game with a decreasingly small probability. In this case, the Nash equilibrium flows converge in total variation toward Poisson random variables whose expected values are War drop equilibria of a different nonatomic game with suitably defined costs. The latter can be viewed as symmetric equilibria in a Poisson game in the sense of Myerson, establishing a plausible connection between the Wardrop model for routing games and the stochastic fluctuations observed in real traffic. In both settings, we provide explicit approximation bounds, and we study the convergence of the price of anarchy. Beyond the case of congestion games, we prove a general result on the convergence of large games with random players toward Poisson games. 
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ISSN 
0364765X 
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Notes 
WOS:000850694300001 
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Call Number 
UAI @ alexi.delcanto @ 
Serial 
1647 
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