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.
|Title of host publication||AAAI 2020 - 34th AAAI Conference on Artificial Intelligence|
|Number of pages||8|
|State||Published - 2020|
|Event||34th AAAI Conference on Artificial Intelligence, AAAI 2020 - New York, United States|
Duration: 7 Feb 2020 → 12 Feb 2020
|Name||AAAI 2020 - 34th AAAI Conference on Artificial Intelligence|
|Conference||34th AAAI Conference on Artificial Intelligence, AAAI 2020|
|Period||7/02/20 → 12/02/20|
Bibliographical noteFunding Information:
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).
Copyright © 2020, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
ASJC Scopus subject areas
- Artificial Intelligence