The Buck-Passing Game
Cominetti
R
author
Quattropani
M
author
Scarsini
M
author
2022
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-five 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.
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
WOS:000731930100001
exported from refbase (show.php?record=1502), last updated on Thu, 30 Dec 2021 09:27:51 -0300
text
10.1287/moor.2021.1186
Cominetti_etal2022
Mathematics Operations Research
Math. Oper. Res.
2022
continuing
periodical
academic journal
Early Access
0364-765X