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Discrete All-Pay Bidding Games [article]

Michael Menz, Justin Wang, Jiyang Xie
2015 arXiv   pre-print
All-pay bidding games arise from attaching a similar bidding structure to traditional combinatorial games to determine which player moves next.  ...  We then give a fast algorithm for computing such strategies for a large class of all-pay bidding games.  ...  Acknowledgements We would like to thank Michael Landry and Sam Payne for exposing to us the research potential surrounding all-pay bidding games and giving guidance in the research process.  ... 
arXiv:1504.02799v2 fatcat:xmyimgswkvfobb73nyk35jc5wy

A Survey of Bidding Games on Graphs (Invited Paper)

Guy Avni, Thomas A. Henzinger, Laura Kovács, Igor Konnov
2020 International Conference on Concurrency Theory  
Specifically, bidding games, and in particular bidding games of infinite duration, have an intriguing equivalence with random-turn games in which in each turn, the player who moves is chosen randomly.  ...  In bidding games, both players have budgets, and in each turn, we hold an "auction" (bidding) to determine which player moves the token.  ...  All-Pay Bidding Games Before describing the theoretical properties of all-pay bidding games, we illustrate applications of the model.  ... 
doi:10.4230/lipics.concur.2020.2 dblp:conf/concur/AvniH20 fatcat:ngem4jljbfey5hg24lpsi54fsq

A note on the wallet game with discrete bid levels

Ricardo Gonçalves, Indrajit Ray
2017 Economics Letters  
there is a discontinuity in the equilibrium set from discrete to continuous. a b s t r a c t It is well-known that in the wallet game with two bidders, bidding twice the (individual) signal is an equilibrium  ...  h i g h l i g h t s • We analyse a Japanese-English auction with fixed bid levels for the wallet game. • We prove that bidding twice the value of the private signal is never an equilibrium. • We show that  ...  bid levels are discrete for the wallet game.  ... 
doi:10.1016/j.econlet.2017.07.032 fatcat:6g4fcxkhbfc23opsuyy2dzsg3m

All-Pay Bidding Games on Graphs

Guy Avni, Rasmus Ibsen-Jensen, Josef Tkadlec
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
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.  ...  A central quantity in bidding games is the ratio of the players budgets.  ...  Let G be an all-pay bidding game.  ... 
doi:10.1609/aaai.v34i02.5546 fatcat:qyoqlblfdvdytcrjignyyjkojm

The importance of being discrete: on the inaccuracy of continuous approximations in auction theory [article]

Itzhak Rasooly, Carlos Gavidia-Calderon
2021 arXiv   pre-print
For instance, introducing an arbitrarily small amount of discreteness into the all-pay auction makes its symmetric, pure-strategy equilibrium disappear; and appears (based on computational experiments)  ...  While auction theory views bids and valuations as continuous variables, real-world auctions are necessarily discrete.  ...  As it turns out, however, their games have no SE at all -and therefore cannot have the particular SE that they identify. The All-Pay Auction We now turn to the all-pay auction.  ... 
arXiv:2006.03016v2 fatcat:ooucgyqzsnhedf7edlr7ag65ne

Cheating in evolutionary games

Michael R. Rose
1978 Journal of Theoretical Biology  
Thus, the Scotch Auction is a transient evolutionary game, being the initial point of a seemingly orthogenetic game evolutionary process.  ...  The analysis of models of evolutionary games requires explicit consideration of both evolutionary game rules and mutants which infinitesimally break these rules.  ...  The player making the largest bid wins the pay-off item, paying the full cost of its bid, irrespective of the size of the opponent's bid. The loser pays its full bid too.  ... 
doi:10.1016/0022-5193(78)90200-x pmid:745430 fatcat:26v6fylqond5bbxwfjifehw6tm

All-Pay Bidding Games on Graphs [article]

Guy Avni, Rasmus Ibsen-Jensen, Josef Tkadlec
2019 arXiv   pre-print
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.  ...  A central quantity in bidding games is the ratio of the players budgets.  ...  Player 1's ratio is B 1 /B 2 . 3 Let G be an all-pay bidding game.  ... 
arXiv:1911.08360v1 fatcat:dei3z7mosvfbrdkagw5b6nooj4

Discrete Strategies in Keyword Auctions and Their Inefficiency for Locally Aware Bidders [chapter]

Evangelos Markakis, Orestis Telelis
2010 Lecture Notes in Computer Science  
We study formally discrete bidding strategies for the game induced by the Generalized Second Price keyword auction mechanism.  ...  We give a detailed definition of iterative best response under these strategies and, under appropriate discretization of the players' strategy spaces we find that the discretized configurations space contains  ...  We give experimental results in figure 1, for the inefficiency of "reverse" assignments of players to slots, in games with k = n slots, n = 2, 3, . . . , 20.  ... 
doi:10.1007/978-3-642-17572-5_46 fatcat:z3jyzlenezenbbi5a56tptnkb4

Determinacy in Discrete-Bidding Infinite-Duration Games

Milad Aghajohari, Guy Avni, Thomas A. Henzinger, Michael Wagner
2019 International Conference on Concurrency Theory  
In particular, we show that, in contrast to non-discrete bidding games, the mechanism with which tied bids are resolved plays an important role in discrete-bidding games.  ...  In bidding games the players bid for the right to move the token: in each round, the players simultaneously submit bids, and the higher bidder moves the token and pays the other player.  ...  Discrete-bidding has previously been studied in combination with all-pay bidding [30] in which both players pay their bid to the other player.  ... 
doi:10.4230/lipics.concur.2019.20 dblp:conf/concur/AghajohariAH19 fatcat:lb6idby55vh2pisnz6k24fazii

Computational analysis of perfect-information position auctions

David R.M. Thompson, Kevin Leyton-Brown
2017 Games and Economic Behavior  
, one-shot game.  ...  These auctions have all been subjected to theoretical analysis under a variety of models, typically with the assumption that bidders will converge, in repeated play, to an equilibrium of the full-information  ...  We assume that bidders report the discrete value nearest to their true value. (All bidders bidding in this way is an -Nash equilibrium, where is equal to half of one bid increment.)  ... 
doi:10.1016/j.geb.2017.02.009 fatcat:3mwq34g24jcvbh3onwrzqyvhqi

Computational analysis of perfect-information position auctions

David Robert Martin Thompson, Kevin Leyton-Brown
2009 Proceedings of the tenth ACM conference on Electronic commerce - EC '09  
, one-shot game.  ...  These auctions have all been subjected to theoretical analysis under a variety of models, typically with the assumption that bidders will converge, in repeated play, to an equilibrium of the full-information  ...  We assume that bidders report the discrete value nearest to their true value. (All bidders bidding in this way is an -Nash equilibrium, where is equal to half of one bid increment.)  ... 
doi:10.1145/1566374.1566382 dblp:conf/sigecom/ThompsonL09 fatcat:wg2melwcx5hc5ku6lpj4r2fsmm

All-Pay Auction Equilibria in Contests

José Alcalde, Matthias Dahm
2008 Social Science Research Network  
We provide intuitive and easily verifiable conditions for the existence of an equilibrium with properties similar to the one of the (deterministic) all-pay auction.  ...  An application of this result contributes to fill a gap in the analysis of the popular Tullock rentseeking game because it characterizes properties of an equilibrium for increasing returns to scale larger  ...  Moreover, the expected bid -even of the discrete all-pay auction -is strictly lower than :5 (but larger than 0:44).  ... 
doi:10.2139/ssrn.1120292 fatcat:cyuaouyp2fcljbvwl3e7qwxwta

Determinacy in Discrete-Bidding Infinite-Duration Games [article]

Milad Aghajohari and Guy Avni and Thomas A. Henzinger
2021 arXiv   pre-print
In particular, we show that, in contrast to non-discrete bidding games, the mechanism with which tied bids are resolved plays an important role in discrete-bidding games.  ...  In bidding games the players bid for the right to move the token: in each round, the players simultaneously submit bids, and the higher bidder moves the token and pays the other player.  ...  Bidding reachability games with all-pay bidding in which both players pay their bid to the bank were studied with continuous bidding [11] as well as with discrete Richman-all-pay bidding [32] in which  ... 
arXiv:1905.03588v6 fatcat:zaqrfja2nbdltamit5g4bif5au

Mixed Equilibria in Tullock Contests

Christian Ewerhart
2014 Social Science Research Network  
Numerical bid distributions are generally negatively skewed, and exhibit, for some parameter values, a higher probability of expost overdissipation than the all-pay auction.  ...  All probability weight is concentrated on those mass points, which have the zero bid as their sole point of accumulation.  ...  Numerical bid distributions As the right-upper panel illustrates, the skewness of the bid distribution is generally negative for R > 2, in contrast to the corresponding case of the all-pay auction.  ... 
doi:10.2139/ssrn.2407509 fatcat:figfc2h2dfcmtnggicflakkm3u

Mixed equilibria in Tullock contests

Christian Ewerhart
2014 Economic Theory  
Numerical bid distributions are generally negatively skewed and exhibit, for some parameter values, a higher probability of ex-post overdissipation than the all-pay auction.  ...  All probability weight is concentrated on those mass points, which have the zero bid as their sole point of accumulation.  ...  As the right-upper panel illustrates, the skewness of the bid distribution is generally negative for R > 2, in contrast to the corresponding case of the all-pay auction.  ... 
doi:10.1007/s00199-014-0835-x fatcat:euixaenyn5hshmjaq2jvlssydy
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