TY - JOUR

T1 - The Buck-Passing Game

AU - Cominetti, Roberto

AU - Quattropani, Matteo

AU - Scarsini, Marco

N1 - Funding Information:
Funding: Roberto Cominetti’s research was partially supported by the Complex Engineering Systems Institute [Grant ICM-FIC: P05-004-F, CONICYT: FB0816]. Marco Scarsini’s research was partially supported by Fondo Nacional de Desarrollo Científico y Tecnológico [Grant 1130564] and Núcleo Milenio “Información y Coordinación en Redes” [Grant RC130003]. This research project received partial support from the COST action GAMENET, the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni, Istituto Nazionale di Alta Matematica 2020 “Random walks on random games,” the European Cooperation in Science and Technology Action European Network for Game Theory, and the Progetti di Rilevante Interesse Nazionale 2017 “Algorithms, Games, and Digital Markets.”
Funding Information:
The authors thank two anonymous referees, the associate editor, and the area editor for their insightful comments and for pointing out several relevant references. M. Quattropani gratefully thanks Pietro Caputo for several interesting discussions. M. Quattropani and M. Scarsini are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni, Istituto Nazionale di Alta Matematica. R. Cominetti gratefully acknowledges the support of Luiss University during a visit in which this research was initiated. M. Scarsini gratefully acknowledges the support and hospitality of Universidad Adolfo Ibáñez.
Publisher Copyright:
Copyright: © 2021 INFORMS.

PY - 2022/8

Y1 - 2022/8

N2 - 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 out-neighbors 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 prior-free 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.

AB - 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 out-neighbors 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 prior-free 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.

KW - Markov chain tree theorem

KW - PageRank

KW - PageRank game

KW - fairness of equilibria

KW - finite improvement property

KW - generalized ordinal potential game

KW - price of anarchy

KW - price of stability

KW - prior-free equilibrium

UR - http://www.scopus.com/inward/record.url?scp=85140012775&partnerID=8YFLogxK

U2 - 10.1287/moor.2021.1186

DO - 10.1287/moor.2021.1186

M3 - Article

AN - SCOPUS:85140012775

SN - 0364-765X

VL - 47

SP - 1731

EP - 1766

JO - Mathematics of Operations Research

JF - Mathematics of Operations Research

IS - 3

ER -