Bidding Graph Games with Partially-Observable Budgets

TL;DR

This paper explores the novel area of bidding graph games with partial information, analyzing how uncertainty in budgets affects strategies and game outcomes, especially for mean-payoff objectives with poorman bidding.

Contribution

It introduces the study of partial-information bidding games, develops techniques for analyzing them, and constructs optimal strategies in complex scenarios with incomplete budget knowledge.

Findings

Optimal strategies are constructed for partially-informed players.

The game value may not exist under pure strategies.

Partial information significantly complicates the analysis.

Abstract

Two-player zero-sum "graph games" are a central model, which proceeds as follows. A token is placed on a vertex of a graph, and the two players move it to produce an infinite "play", which determines the winner or payoff of the game. Traditionally, the players alternate turns in moving the token. In "bidding games", however, the players have budgets and in each turn, an auction (bidding) determines which player moves the token. So far, bidding games have only been studied as full-information games. In this work we initiate the study of partial-information bidding games: we study bidding games in which a player's initial budget is drawn from a known probability distribution. We show that while for some bidding mechanisms and objectives, it is straightforward to adapt the results from the full-information setting to the partial-information setting, for others, the analysis is significantly more challenging, requires new techniques, and gives rise to interesting results. Specifically, we study games with "mean-payoff" objectives in combination with "poorman" bidding. We construct optimal strategies for a partially-informed player who plays against a fully-informed adversary. We show that, somewhat surprisingly, the "value" under pure strategies does not necessarily exist in such games.