Bidding Graph Games with Partially-Observable Budgets.

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.