All-pay bidding games on graphs

Guy Avni, Rasmus Ibsen-Jensen, Josef Tkadlec

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publicationAAAI 2020 - 34th AAAI Conference on Artificial Intelligence
PublisherAAAI Press
Pages1798-1805
Number of pages8
ISBN (Electronic)9781577358350
StatePublished - 2020
Externally publishedYes
Event34th AAAI Conference on Artificial Intelligence, AAAI 2020 - New York, United States
Duration: 7 Feb 202012 Feb 2020

Publication series

NameAAAI 2020 - 34th AAAI Conference on Artificial Intelligence

Conference

Conference34th AAAI Conference on Artificial Intelligence, AAAI 2020
Country/TerritoryUnited States
CityNew York
Period7/02/2012/02/20

Bibliographical note

Publisher Copyright:
Copyright © 2020, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.

ASJC Scopus subject areas

  • Artificial Intelligence

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