Corpus ID: 18202819

# Discrete All-Pay Bidding Games

@article{Menz2015DiscreteAB,
title={Discrete All-Pay Bidding Games},
author={Michael Menz and Justin Wang and J. Xie},
journal={ArXiv},
year={2015},
volume={abs/1504.02799}
}
• Published 2015
• Computer Science, Economics
• ArXiv
In an all-pay auction, only one bidder wins but all bidders must pay the auctioneer. All-pay bidding games arise from attaching a similar bidding structure to traditional combinatorial games to determine which player moves next. In contrast to the established theory of single-pay bidding games, optimal play involves choosing bids from some probability distribution that will guarantee a minimum probability of winning. In this manner, all-pay bidding games wed the underlying concepts of economic… Expand
7 Citations

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#### References

SHOWING 1-10 OF 10 REFERENCES
Combinatorial Games under Auction Play
• Mathematics
• 1999
Abstract A Richman game is a combinatorial game in which, rather than alternating moves, the two players bid for the privilege of making the next move. The theory of such games is a hybrid betweenExpand
Richman games
• Mathematics
• 1995
A Richman game is a combinatorial game in which, rather than alternating moves, the two players bid for the privilege of making the next move. We find optimal strategies for both the case where aExpand
Matching the Universal Barrier Without Paying the Costs : Solving Linear Programs with Õ(sqrt(rank)) Linear System Solves
• Mathematics, Computer Science
• ArXiv
• 2013
The method matches up to polylogarithmic factors a theoretical limit established by Nesterov and Nemirovski in 1994 regarding the use of a "universal barrier" for interior point methods, thereby resolving a long-standing open question regarding the running time of polynomial time interior point method methods for linear programming. Expand
Levinson and fast Choleski algorithms for Toeplitz and almost Toeplitz matrices
In this paper, we review Levinson and fast Choleski algorithms for solving sets of linear equations involving Toeplitz or almost Toeplitz matrices. The Levinson-Trench-Zohar algorithm is firstExpand
Matching the universal barrier without paying the costs : Solving linear programs withwith˜ with˜O(sqrt(rank)) linear system solves. CoRR, abs/1312
• Matching the universal barrier without paying the costs : Solving linear programs withwith˜ with˜O(sqrt(rank)) linear system solves. CoRR, abs/1312
• 2013
+ 1) · λ(0, s 0 , . . . , s −1 ) + (1 − λ)(s 0 , . . . , s −1 , 0) = v A 1
• + 1) · λ(0, s 0 , . . . , s −1 ) + (1 − λ)(s 0 , . . . , s −1 , 0) = v A 1
B's payoff x against against A bidding + 1 will be x = 1 − (α +1 s + α 1 s 0 )
• B's payoff x against against A bidding + 1 will be x = 1 − (α +1 s + α 1 s 0 )
By our assumption, v > v A so S is strictly better than S A against R(S A ). Thus S A cannot be a Nash Equilibrium strategy, which is a contradiction
• By our assumption, v > v A so S is strictly better than S A against R(S A ). Thus S A cannot be a Nash Equilibrium strategy, which is a contradiction
Note that because player A is winning ties, α +1 < α , . . . , α 1 < α 0 , as in each case A is winning by one more chip. Thus, α s + · · · + α 0 s 0 > α +1 s + α 1 s 0 which means
• Note that because player A is winning ties, α +1 < α , . . . , α 1 < α 0 , as in each case A is winning by one more chip. Thus, α s + · · · + α 0 s 0 > α +1 s + α 1 s 0 which means
Since B bids at most − 1, we only need to consider the first coordinates of
• Since B bids at most − 1, we only need to consider the first coordinates of