The Buck-Passing Game

Roberto Cominetti (), Matteo Quattropani () and Marco Scarsini
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Roberto Cominetti: Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Santiago 7941169, Chile
Matteo Quattropani: Dipartimento di Economia e Finanza, Luiss University, Roma 00197, Italy

Mathematics of Operations Research, 2022, vol. 47, issue 3, 1731-1756

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 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.

Keywords: Primary: 91A43; secondary: 91A06; 60J10; 91A14; prior-free equilibrium; generalized ordinal potential game; finite improvement property; fairness of equilibria; price of anarchy; price of stability; Markov chain tree theorem; PageRank; PageRank game (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:3:p:1731-1756

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