000060407 001__ 60407 000060407 005__ 20190709135533.0 000060407 0247_ $$2doi$$a10.3390/g8010001 000060407 0248_ $$2sideral$$a97866 000060407 037__ $$aART-2017-97866 000060407 041__ $$aeng 000060407 100__ $$0(orcid)0000-0002-9769-8796$$aGracia-Lázaro, C. 000060407 245__ $$aCognitive hierarchy theory and two-person games 000060407 260__ $$c2017 000060407 5060_ $$aAccess copy available to the general public$$fUnrestricted 000060407 5203_ $$aThe outcome of many social and economic interactions, such as stock-market transactions, is strongly determined by the predictions that agents make about the behavior of other individuals. Cognitive hierarchy theory provides a framework to model the consequences of forecasting accuracy that has proven to fit data from certain types of game theory experiments, such as Keynesian beauty contests and entry games. Here, we focus on symmetric two-player-two-action games and establish an algorithm to find the players’ strategies according to the cognitive hierarchy approach. We show that the snowdrift game exhibits a pattern of behavior whose complexity grows as the cognitive levels of players increases. In addition to finding the solutions up to the third cognitive level, we demonstrate, in this theoretical frame, two new properties of snowdrift games: (i) any snowdrift game can be characterized by only a parameter, its class; (ii) they are anti-symmetric with respect to the diagonal of the pay-off’s space. Finally, we propose a model based on an evolutionary dynamics that captures the main features of the cognitive hierarchy theory. 000060407 536__ $$9info:eu-repo/grantAgreement/ES/MINECO/FIS2014-55867-P$$9info:eu-repo/grantAgreement/EC/FP7/317532/EU/Foundational Research on MULTIlevel comPLEX networks and systems/MULTIPLEX$$9info:eu-repo/grantAgreement/ES/DGA/E19 000060407 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000060407 592__ $$a0.242$$b2017 000060407 593__ $$aApplied Mathematics$$c2017$$dQ4 000060407 593__ $$aStatistics, Probability and Uncertainty$$c2017$$dQ4 000060407 593__ $$aStatistics and Probability$$c2017$$dQ4 000060407 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000060407 700__ $$0(orcid)0000-0002-1406-8810$$aFloría, L.M.$$uUniversidad de Zaragoza 000060407 700__ $$0(orcid)0000-0002-0895-1893$$aMoreno, Y.$$uUniversidad de Zaragoza 000060407 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000060407 7102_ $$12003$$2395$$aUniversidad de Zaragoza$$bDpto. Física Materia Condensa.$$cÁrea Física Materia Condensada 000060407 773__ $$g8, 1 (2017), [18 pp.]$$pGames$$tGames$$x2073-4336 000060407 8564_ $$s1836224$$uhttps://zaguan.unizar.es/record/60407/files/texto_completo.pdf$$yVersión publicada 000060407 8564_ $$s111661$$uhttps://zaguan.unizar.es/record/60407/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000060407 909CO $$ooai:zaguan.unizar.es:60407$$particulos$$pdriver 000060407 951__ $$a2019-07-09-12:03:34 000060407 980__ $$aARTICLE