Reachability Poorman Discrete-Bidding Games.

Avni, Guy and Meggendorfer, Tobias and Sadhukhan, Suman and Tkadlec, Josef and Žikelić, Đorđe (2023) Reachability Poorman Discrete-Bidding Games. In: ECAI 2023 - 26th European Conference on Artificial Intelligence, including 12th Conference on Prestigious Applications of Intelligent Systems, PAIS 2023 - Proceedings :. Frontiers in Artificial Intelligence and Applications . UNSPECIFIED, pp. 141-148. ISBN 9781643684369

Abstract

We consider bidding games, a class of two-player zero-sum graph games. The game proceeds as follows. Both players have bounded budgets. A token is placed on a vertex of a graph, in each turn the players simultaneously submit bids, and the higher bidder moves the token, where we break bidding ties in favor of Player 1. Player 1 wins the game iff the token visits a designated target vertex. We consider, for the first time, poorman discrete-bidding in which the granularity of the bids is restricted and the higher bid is paid to the bank. Previous work either did not impose granularity restrictions or considered Richman bidding (bids are paid to the opponent). While the latter mechanisms are technically more accessible, the former is more appealing from a practical standpoint. Our study focuses on threshold budgets, which is the necessary and sufficient initial budget required for Player 1 to ensure winning against a given Player 2 budget. We first show existence of thresholds. In DAGs, we show that threshold budgets can be approximated with error bounds by thresholds under continuous-bidding and that they exhibit a periodic behavior. We identify closed-form solutions in special cases. We implement and experiment with an algorithm to find threshold budgets.