All-pay bidding games on graphs

Avni G, Ibsen-Jensen R, Tkadlec J. 2020. All-pay bidding games on graphs. Proceedings of the AAAI Conference on Artificial Intelligence. 34(02), 1798–1805.

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Abstract
In this paper we introduce and study all-pay bidding games, a class of two player, zero-sum games on graphs. The game proceeds as follows. We place a token on some vertex in the graph and assign budgets to the two players. Each turn, each player submits a sealed legal bid (non-negative and below their remaining budget), which is deducted from their budget and the highest bidder moves the token onto an adjacent vertex. The game ends once a sink is reached, and Player 1 pays Player 2 the outcome that is associated with the sink. The players attempt to maximize their expected outcome. Our games model settings where effort (of no inherent value) needs to be invested in an ongoing and stateful manner. On the negative side, we show that even in simple games on DAGs, optimal strategies may require a distribution over bids with infinite support. A central quantity in bidding games is the ratio of the players budgets. On the positive side, we show a simple FPTAS for DAGs, that, for each budget ratio, outputs an approximation for the optimal strategy for that ratio. We also implement it, show that it performs well, and suggests interesting properties of these games. Then, given an outcome c, we show an algorithm for finding the necessary and sufficient initial ratio for guaranteeing outcome c with probability 1 and a strategy ensuring such. Finally, while the general case has not previously been studied, solving the specific game in which Player 1 wins iff he wins the first two auctions, has been long stated as an open question, which we solve.
Publishing Year
Date Published
2020-04-03
Journal Title
Proceedings of the AAAI Conference on Artificial Intelligence
Acknowledgement
This research was supported by the Austrian Science Fund (FWF) under grants S11402-N23 (RiSE/SHiNE), Z211-N23 (Wittgenstein Award), and M 2369-N33 (Meitner fellowship).
Volume
34
Issue
02
Page
1798-1805
Conference
AAAI: Conference on Artificial Intelligence
Conference Location
New York, NY, United States
Conference Date
2020-02-07 – 2020-02-12
IST-REx-ID

Cite this

Avni G, Ibsen-Jensen R, Tkadlec J. All-pay bidding games on graphs. Proceedings of the AAAI Conference on Artificial Intelligence. 2020;34(02):1798-1805. doi:10.1609/aaai.v34i02.5546
Avni, G., Ibsen-Jensen, R., & Tkadlec, J. (2020). All-pay bidding games on graphs. Proceedings of the AAAI Conference on Artificial Intelligence. New York, NY, United States: Association for the Advancement of Artificial Intelligence. https://doi.org/10.1609/aaai.v34i02.5546
Avni, Guy, Rasmus Ibsen-Jensen, and Josef Tkadlec. “All-Pay Bidding Games on Graphs.” Proceedings of the AAAI Conference on Artificial Intelligence. Association for the Advancement of Artificial Intelligence, 2020. https://doi.org/10.1609/aaai.v34i02.5546.
G. Avni, R. Ibsen-Jensen, and J. Tkadlec, “All-pay bidding games on graphs,” Proceedings of the AAAI Conference on Artificial Intelligence, vol. 34, no. 02. Association for the Advancement of Artificial Intelligence, pp. 1798–1805, 2020.
Avni G, Ibsen-Jensen R, Tkadlec J. 2020. All-pay bidding games on graphs. Proceedings of the AAAI Conference on Artificial Intelligence. 34(02), 1798–1805.
Avni, Guy, et al. “All-Pay Bidding Games on Graphs.” Proceedings of the AAAI Conference on Artificial Intelligence, vol. 34, no. 02, Association for the Advancement of Artificial Intelligence, 2020, pp. 1798–805, doi:10.1609/aaai.v34i02.5546.

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arXiv 1911.08360

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