Bidding Games with Charging
Guy Avni, Ehsan Kafshdar Goharshady, Thomas A. Henzinger, Kaushik, Mallik

TL;DR
This paper introduces bidding games with charging, where players can collect vertex-dependent charges to improve budgets, leading to complex behaviors and new computational challenges in infinite-duration game objectives.
Contribution
It extends traditional bidding games by allowing budget improvements through charges, analyzing the resulting non-unique fixed points and providing complexity bounds for key objectives.
Findings
Existence of threshold ratios for winning strategies.
Non-uniqueness of fixed points in charging games.
Lower bounds for Rabin and Streett objectives.
Abstract
Graph games lie at the algorithmic core of many automated design problems in computer science. These are games usually played between two players on a given graph, where the players keep moving a token along the edges according to pre-determined rules, and the winner is decided based on the infinite path traversed by the token from a given initial position. In bidding games, the players initially get some monetary budgets which they need to use to bid for the privilege of moving the token at each step. Each round of bidding affects the players' available budgets, which is the only form of update that the budgets experience. We introduce bidding games with charging where the players can additionally improve their budgets during the game by collecting vertex-dependent charges. Unlike traditional bidding games (where all charges are zero), bidding games with charging allow non-trivial…
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