# Infinite-duration all-pay bidding games

Avni G, Jecker IR, Zikelic D. 2021. Infinite-duration all-pay bidding games. Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 617–636.

Conference Paper | Published | English

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Author
Editor
Marx, Dániel
Department
Abstract
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.
Publishing Year
Date Published
2021-01-01
Proceedings Title
Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms
Acknowledgement
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.
Page
617-636
Conference
SODA: Symposium on Discrete Algorithms
Conference Location
Virtual
Conference Date
2021-01-10 – 2021-01-13
IST-REx-ID

### Cite this

Avni G, Jecker IR, Zikelic D. Infinite-duration all-pay bidding games. In: Marx D, ed. Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics; 2021:617-636. doi:10.1137/1.9781611976465.38
Avni, G., Jecker, I. R., & Zikelic, D. (2021). Infinite-duration all-pay bidding games. In D. Marx (Ed.), Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (pp. 617–636). Virtual: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611976465.38
Avni, Guy, Ismael R Jecker, and Dorde Zikelic. “Infinite-Duration All-Pay Bidding Games.” In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms, edited by Dániel Marx, 617–36. Society for Industrial and Applied Mathematics, 2021. https://doi.org/10.1137/1.9781611976465.38.
G. Avni, I. R. Jecker, and D. Zikelic, “Infinite-duration all-pay bidding games,” in Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms, Virtual, 2021, pp. 617–636.
Avni G, Jecker IR, Zikelic D. 2021. Infinite-duration all-pay bidding games. Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 617–636.
Avni, Guy, et al. “Infinite-Duration All-Pay Bidding Games.” Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms, edited by Dániel Marx, Society for Industrial and Applied Mathematics, 2021, pp. 617–36, doi:10.1137/1.9781611976465.38.
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arXiv 2005.06636