{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:48:13Z","timestamp":1760150893538,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,31]],"date-time":"2023-12-31T00:00:00Z","timestamp":1703980800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"CINELDI\u2014Centre for intelligent electricity distribution","award":["257626\/E20"],"award-info":[{"award-number":["257626\/E20"]}]},{"DOI":"10.13039\/501100005416","name":"FME-scheme (Centre for Environment-friendly Energy Research","doi-asserted-by":"publisher","award":["257626\/E20"],"award-info":[{"award-number":["257626\/E20"]}],"id":[{"id":"10.13039\/501100005416","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Research Council of Norway","award":["257626\/E20"],"award-info":[{"award-number":["257626\/E20"]}]},{"name":"CINELDI partners","award":["257626\/E20"],"award-info":[{"award-number":["257626\/E20"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>We apply three equilibrium selection techniques to study which equilibrium is selected in a hawk\u2013dove game with a multiplicity of equilibria. By using a uniform-price auction as an illustrative example, we find that when the demand in the auction is low or intermediate, the tracing procedure method of Harsanyi and Selten (1988) and the quantal response method of McKelvey and Palfrey (1998) select the same equilibrium. When the demand is high, the tracing procedure method does not select any equilibrium, but the quantal response method still selects the same equilibrium as when the demand is low or intermediate. The robustness to strategic uncertainty method of Andersson, Argenton and Weibull (2014) selects two of the multiple equilibria irrespective of the demand size. We also analyze the impact of an increase in the minimum bid allowed by the auctioneer in the equilibrium selection.<\/jats:p>","DOI":"10.3390\/g15010002","type":"journal-article","created":{"date-parts":[[2023,12,31]],"date-time":"2023-12-31T04:51:51Z","timestamp":1703998311000},"page":"2","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Equilibrium Selection in Hawk\u2013Dove Games"],"prefix":"10.3390","volume":"15","author":[{"given":"Mario","family":"Bl\u00e1zquez de Paz","sequence":"first","affiliation":[{"name":"Department of Business and Management Science, Norwegian School of Economics, 5045 Bergen, Norway"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nikita","family":"Koptyug","sequence":"additional","affiliation":[{"name":"Research Institute of Industrial Economics, SE-102 15 Stockholm, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,31]]},"reference":[{"key":"ref_1","unstructured":"Harsanyi, J., and Selten, R. (1988). A General Theory of Equilibrium Selection in Games, The MIT Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1016\/j.geb.2014.01.018","article-title":"Robustness to Strategic Uncertainty","volume":"85","author":"Andersson","year":"2014","journal-title":"Games Econ. Behav."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1006\/game.1995.1023","article-title":"Quantal Response Equilibria for Normal Form Games","volume":"10","author":"McKelvey","year":"1998","journal-title":"Games Econ. Behav."},{"key":"ref_4","unstructured":"de Paz, M., Bigoni, M., and Le Coq, C. (2022). Beyond Hawks and Doves: Can Inequality Ease Coordination?, CEPR."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"39","DOI":"10.2307\/2526949","article-title":"Bertrand-Edgeworth Duopoly with Proportional Residual Demand","volume":"34","author":"Allen","year":"1993","journal-title":"Int. Econ. Rev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"404","DOI":"10.2307\/2555720","article-title":"Long-Run Competition in Capacity, Short-Run Competition in Price, and the Cournot Model","volume":"17","author":"Davidson","year":"1986","journal-title":"Rand J. Econ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1016\/j.jet.2016.06.003","article-title":"Equilibrium Selection with Couple Populations in hawk\u2013dove Games: Theory and Experiment in Continuous Time","volume":"165","author":"Benndorf","year":"2016","journal-title":"J. Econ. Theory"},{"key":"ref_8","unstructured":"Boom, A. (2008). Equilibrium Selection with Risk Dominance in a Multiple-Unit Unit Price Auction, Available online: https:\/\/ideas.repec.org\/p\/hhs\/cbsnow\/2008_002.html."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1006\/game.1998.0687","article-title":"Endogenous Stackelberg Leadership","volume":"28","author":"Hurkens","year":"1999","journal-title":"Games Econ. Behav."},{"key":"ref_10","unstructured":"(1990). Endogenous timing in duopoly games: Stackelberg or cournot equilibria. Games Econ. Behav., 1, 29\u201346."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1016\/j.geb.2004.01.003","article-title":"Endogenous Price Leadership","volume":"47","author":"Hurkens","year":"2004","journal-title":"Games Econ. Behav."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1006\/jeth.1996.0080","article-title":"Product Differentiation in a Bertrand\u2014Edgeworth Duopoly","volume":"70","author":"Canoy","year":"1996","journal-title":"J. Econ. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"143","DOI":"10.2307\/2297930","article-title":"Price Leadership","volume":"59","author":"Deneckere","year":"1992","journal-title":"Rev. Econ. Stud."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1016\/0022-0531(86)90117-1","article-title":"Price Competition in a Capacity-Constrained Duopoly","volume":"38","author":"Osborne","year":"1986","journal-title":"J. Econ. Theory"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/S0167-7187(99)00037-5","article-title":"Risk Dominance Selects the Leader: An Experimental Analysis","volume":"18","author":"Cabrales","year":"2000","journal-title":"Int. J. Ind. Organ."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1177\/0305829818781690","article-title":"Social Action in Quantum Social Science","volume":"47","author":"Allan","year":"2018","journal-title":"Millenn. J. Int. Stud."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1111\/j.1756-2171.2006.tb00002.x","article-title":"Designing Electricity Auctions","volume":"37","author":"Fabra","year":"2006","journal-title":"Rand J. Econ."},{"key":"ref_18","unstructured":"Luce, R., and Raiffa, H. (1957). Games and Decisions, Wiley."},{"key":"ref_19","unstructured":"Binmore, K. (1992). Fun and Games, D.C. Health."},{"key":"ref_20","unstructured":"Belleflamme, P., and Peitz, M. (2015). Markets and Strategies, Cambridge University Press."},{"key":"ref_21","unstructured":"Gao, B., and Pavel, L. (2018). On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning. Working Paper. arXiv, Available online: https:\/\/arxiv.org\/abs\/1704.00805."},{"key":"ref_22","unstructured":"Tirole, J., and Fudenberg, D. (1991). Game Theory, MIT Press."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1016\/j.eneco.2018.07.001","article-title":"Electricity Auctions in the Presence of Transmission Constraints and Transmission Costs","volume":"74","year":"2018","journal-title":"Energy Econ."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"27","DOI":"10.2307\/2297589","article-title":"The Existence of Equilibrium in Discontinuous Economic Games, II: Applications","volume":"53","author":"Dasgupta","year":"1986","journal-title":"Rev. Econ. Stud."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01212009","article-title":"Bertramd-Edgeworth Duopoly with Unit Cost Asymmetry","volume":"8","author":"Deneckere","year":"1996","journal-title":"Econ. Theory"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Bigoni, M., and Le Coq, C. (2023, October 25). Beyond Hawks and Doves: Can Inequality Ease Coordination?. Available online: https:\/\/cepr.org\/publications\/dp17867.","DOI":"10.1007\/s00199-024-01603-7"}],"container-title":["Games"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4336\/15\/1\/2\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:45:16Z","timestamp":1760132716000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4336\/15\/1\/2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,31]]},"references-count":26,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,2]]}},"alternative-id":["g15010002"],"URL":"https:\/\/doi.org\/10.3390\/g15010002","relation":{},"ISSN":["2073-4336"],"issn-type":[{"type":"electronic","value":"2073-4336"}],"subject":[],"published":{"date-parts":[[2023,12,31]]}}}