{"type":"ScholarlyArticle","title":"Discrete Two Player All-Pay Auction with Complete Information","authors":[{"name":"Marcin Dziubiński","slug":"marcin-dziubinski","given":"Marcin","family":"Dziubiński","affiliation":"Institute of Informatics , University of Warsaw , Banacha 2 , 02-097 Warsaw , Poland"},{"name":"Krzysztof Jahn","slug":"krzysztof-jahn","given":"Krzysztof","family":"Jahn","affiliation":"Faculty of Mathematics and Information Science , Warsaw University of Technology , Warsaw , Poland"}],"abstract":"We study discrete two player all-pay auction with complete information. We provide full characterization of mixed strategy Nash equilibria and show that they constitute a subset of Nash equilibria of discrete General Lotto game. We show that equilibria are not unique in general but they are interchangeable and sets of equilibrium strategies are convex. We also show that equilibrium payoffs are unique, unless valuation of at least one of the players is an even integer number. If equilibrium payoffs are not unique, continuum of equilibrium payoffs are possible.","doi":"10.24963/ijcai.2023/296","url":"https://ijcai.org/proceedings/2023/296","pdf":"https://ijcai.org/proceedings/2023/0296.pdf","markdown":"https://ijcai.org/proceedings/2023/296.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/296","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":296,"pages":{"first":2659,"last":2666},"keywords":["Game Theory and Economic Paradigms: GTEP: Auctions and market-based systems","Game Theory and Economic Paradigms: GTEP: Noncooperative games"],"videos":[],"references":[{"position":1,"raw":"[Baye et al., 1993] M. Baye, D. Kovenock, and C. de Vries. Rigging the lobbying process: An application of the all- pay auction. The American Economic Review, 83(1):289- 294, 1993.","title":"Rigging the lobbying process: An application of the allpay auction","authors":"M Baye, D Kovenock, C De Vries","year":"1993","venue":"The American Economic Review","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Baye et al., 1996] M. R. Baye, D. Kovenock, and C. G. de Vries. The all-pay auction with complete information. Economic Theory, 8(2):291-305, 1996.","title":"The all-pay auction with complete information","authors":"M R Baye, D Kovenock, C G De Vries","year":"1996","venue":"Economic Theory","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bell and Cover, 1980] R. Bell and T. Cover. Competitive optimality of logarithmic investment. Mathematics of Op- erations Research, 5(2):161-166, 1980.","title":"Competitive optimality of logarithmic investment","authors":"R Bell, T Cover","year":"1980","venue":"Mathematics of Operations Research","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Chawla et al., 2019] S. Chawla, J. Hartline, and B. Sivan. Optimal crowdsourcing contests. Games and Economic Behavior, 113:80-96, 2019.","title":"Optimal crowdsourcing contests","authors":"S Chawla, J Hartline, B Sivan","year":"2019","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Cohen and Sela, 2007] C. Cohen and A. Sela. Contests with ties. The B.E. Journal of Theoretical Economics, 7(1 (Con- tributions)):Article 43, 2007.","title":"Contests with ties. The B","authors":"C Cohen, A Sela","year":"2007","venue":".E. Journal of Theoretical Economics","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Dasgupta, 1986] P. Dasgupta. The theory of technological competition. In J. Stiglitz and G. Mathewson, editors, New Developments in the Analysis of Market Structure, pages 519-547. MIT press, Cambridge, 1986.","title":"The theory of technological competition","authors":"P Dasgupta","year":"1986","venue":"New Developments in the Analysis of Market Structure","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Dimitri, 2017] N. Dimitri. Bitcoin mining as a contest. Ledger, 2:31-37, 2017.","title":"Bitcoin mining as a contest","authors":"N Dimitri","year":"2017","venue":"Ledger","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[DiPalantino and Vojnovic, 2009] D. DiPalantino and M. Vojnovic. Crowdsourcing and all-pay auctions. In Proceedings of the 10th ACM Conference on Electronic Commerce, EC '09, page 119-128, New York, NY, USA, 2009. Association for Computing Machinery.","title":"Crowdsourcing and all-pay auctions","authors":"D Dipalantino, M Vojnovic","year":"2009","venue":"Proceedings of the 10th ACM Conference on Electronic Commerce, EC '09","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Dziubiński, 2012] M. Dziubiński. Non-symmetric discrete General Lotto games. International Journal of Game The- ory, 42(4):1-33, 2012.","title":"Non-symmetric discrete General Lotto games","authors":"M Dziubiński","year":"2012","venue":"International Journal of Game Theory","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Ellingsen, 1991] T. Ellingsen. Strategic buyers and the social cost of monopoly. American Economic Review, 81(3):648-657, 1991.","title":"Strategic buyers and the social cost of monopoly","authors":"T Ellingsen","year":"1991","venue":"American Economic Review","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Hart, 2008] S. Hart. Discrete Colonel Blotto and General Lotto games. International Journal of Game Theory, 36:441-460, 2008.","title":"Discrete Colonel Blotto and General Lotto games","authors":"S Hart","year":"2008","venue":"International Journal of Game Theory","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Hillman and Riley, 1989] A. Hillman and J. Riley. Politi- cally contestable rents and transfers. Economics and Poli- tics, 1:17-39, 1989.","title":"Politically contestable rents and transfers","authors":"A Hillman, J Riley","year":"1989","venue":"Economics and Politics","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Hillman and Samet, 1987] A. Hillman and D. Samet. Dis- sipation of contestable rents by small numbers of con- tenders. Public Choice, 54(1):63-82, 1987.","title":"Dissipation of contestable rents by small numbers of contenders","authors":"Samet Hillman, A Hillman, D Samet","year":"1987","venue":"Public Choice","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Hillman, 1988] A. Hillman. The Political Economy of Pro- tectionism. Harwood, New York, 1988.","title":"The Political Economy of Protectionism","authors":"A Hillman","year":"1988","venue":null,"doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Lev et al., 2013] O. Lev, M. Polukarov, Y. Bachrach, and J. Rosenschein. Mergers and collusion in all-pay auc- tions and crowdsourcing contests. In Proceedings of the 2013 International Conference on Autonomous Agents and Multi-Agent Systems, AAMAS '13, page 675-682, Rich- land, SC, 2013. International Foundation for Autonomous Agents and Multiagent Systems.","title":"Mergers and collusion in all-pay auctions and crowdsourcing contests","authors":"O Lev, M Polukarov, Y Bachrach, J Rosenschein","year":"2013","venue":"Proceedings of the 2013 International Conference on Autonomous Agents and Multi-Agent Systems, AAMAS '13","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Lewenberg et al., 2017] Y. Lewenberg, O. Lev, Y. Bachrach, and J. Rosenschein. Agent failures in all-pay auctions. IEEE Intelligent Systems, 32(1):8-16, 2017.","title":"Agent failures in all-pay auctions","authors":"Y Lewenberg, O Lev, Y Bachrach, J Rosenschein","year":"2017","venue":"IEEE Intelligent Systems","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Moulin, 1986] H. Moulin. Game theory of the social sci- ences. NYU Press, New York, 1986.","title":"Game theory of the social sciences","authors":"H Moulin","year":"1986","venue":null,"doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Myerson, 1993] R. Myerson. Incentives to cultivate favored minorities under alternative electoral systems. The Ameri- can Political Science Review, 87(4):856-869, 1993.","title":"Incentives to cultivate favored minorities under alternative electoral systems","authors":"R Myerson","year":"1993","venue":"The American Political Science Review","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Sahuguet and Persico, 2006] N. Sahuguet and N. Persico. Campaign spending regulation in a model of redistributive politics. Economic Theory, 28(1):95-124, 2006.","title":"Campaign spending regulation in a model of redistributive politics","authors":"N Sahuguet, N Persico","year":"2006","venue":"Economic Theory","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Snyder, 1989] J. Snyder. Election goals and the allocation of campaign resources. Econometrica, 57(3):637-660, 1989.","title":"Election goals and the allocation of campaign resources","authors":"J Snyder","year":"1989","venue":"Econometrica","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Szymanski, 2003] S. Szymanski. The economic design of sporting contests. Journal of Economic Literature, 41(4):1137-1187, 2003.","title":"The economic design of sporting contests","authors":"S Szymanski","year":"2003","venue":"Journal of Economic Literature","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}