In a two-player zero-sum graph game the players move a token throughout a graph to produce an infinite path, 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, we hold an “auction” (bidding) to determine which player moves the token: both players simultaneously submit bids and the higher bidder moves the token. The bidding mechanisms differ in their payment schemes. Bidding games were largely studied with variants of first-price bidding in which only the higher bidder pays his bid. We focus on all-pay bidding, where both players pay their bids. Finite-duration all-pay bidding games were studied and shown to be technically more challenging than their first-price counterparts. We study for the first time, infinite-duration all-pay bidding games. Our most interesting results are for mean-payoff objectives: we portray a complete picture for games played on strongly-connected graphs. We study both pure (deterministic) and mixed (probabilistic) strategies and completely characterize the optimal and almost-sure (with probability 1) payoffs the players can respectively guarantee. We show that mean-payoff games under all-pay bidding exhibit the intriguing mathematical properties of their first-price counterparts; namely, an equivalence with random-turn games in which in each turn, the player who moves is selected according to a (biased) coin toss. The equivalences for all-pay bidding are more intricate and unexpected than for first-price bidding.
|Title of host publication||ACM-SIAM Symposium on Discrete Algorithms, SODA 2021|
|Publisher||Association for Computing Machinery|
|Number of pages||20|
|State||Published - 2021|
|Event||32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 - Alexandria, Virtual, United States|
Duration: 10 Jan 2021 → 13 Jan 2021
|Name||Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms|
|Conference||32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021|
|Period||10/01/21 → 13/01/21|
Bibliographical noteFunding Information:
This research was supported in part by the Austrian Science Fund (FWF) under grant Z211-N23 (Wittgenstein Award), ERC CoG 863818 (FoRM-SMArt), and by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385.
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ASJC Scopus subject areas
- Mathematics (all)