Bidding mechanisms in graph games

A graph game proceeds as follows: two players move a token through a graph to produce a finite or infinite path, which determines the payoff of the game. We study bidding games in which in each turn, an auction determines which player moves the token. Bidding games were largely studied in combination with two variants of first-price auctions called “Richman” and “poorman” bidding. We study taxman bidding, which span the spectrum between the two. The game is parameterized by a constant τ∈[0,1]: portion τ of the winning bid is paid to the other player, and portion 1−τ to the bank. While finite-duration (reachability) taxman games have been studied before, we present, for the first time, results on infinite-duration taxman games: we unify, generalize, and simplify previous equivalences between bidding games and a class of stochastic games called random-turn games.