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}
}
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

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  • 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