{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T04:28:48Z","timestamp":1761280128046,"version":"build-2065373602"},"reference-count":56,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T00:00:00Z","timestamp":1761091200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"crossref","award":["64015"],"award-info":[{"award-number":["64015"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>Classifying games according to their strategic properties provides meaningful insights into the motivations driving the interacting parties, suggests possible future trajectories, and in some cases also points to potential interventions aiming to influence the interactions\u2019 outcomes. Here, we present a new classification that merges two perspectives: (i) a revised version of Rapoport and Guyer\u2019s taxonomy, which extends beyond the original 78 games they describe by classifying all two-by-two games according to fundamental strategic properties, and (ii) a novel classification grounded in the theory of subjective expected relative similarity, which addresses not only the games\u2019 payoffs but also the players\u2019 strategic perceptions of their opponents. While Rapoport and Guyer\u2019s original taxonomy classifies only strictly-ordinal games, the revised classification addresses all two-by-two games. It comprises eleven categories that are further grouped into five super-categories that focus on the game\u2019s expected outcome and its strategic stability. The second, similarity-based, classification comprises four main categories, specifying whether players\u2019 perceptions of their opponents have the potential to influence strategic decision-making. The merged classification comprises 14 game types, offering a holistic account of the strategic interaction, the players\u2019 underlying motivations, and the expected outcome. It combines the fixed strategic properties with the variable social aspects of the interaction. Moreover, the novel classification points to the potential of social interventions that may influence the game\u2019s outcome by altering strategic similarity perceptions. Therefore, the present work is relevant for both theoretical and experimental research, providing insights into actual choices expected inside and outside of the laboratory.<\/jats:p>","DOI":"10.3390\/g16060056","type":"journal-article","created":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T05:20:44Z","timestamp":1761196844000},"page":"56","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Integrating Strategic Properties with Social Perspectives: A Bipartite Classification of Two-by-Two Games"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-6535-4819","authenticated-orcid":false,"given":"Shacked","family":"Avrashi","sequence":"first","affiliation":[{"name":"Department of Psychology, University of Haifa, Haifa 3103301, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2102-4530","authenticated-orcid":false,"given":"Lior","family":"Givon","sequence":"additional","affiliation":[{"name":"Department of Psychology, University of Haifa, Haifa 3103301, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2622-7743","authenticated-orcid":false,"given":"Ilan","family":"Fischer","sequence":"additional","affiliation":[{"name":"Department of Psychology, University of Haifa, Haifa 3103301, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,22]]},"reference":[{"key":"ref_1","unstructured":"Axelrod, R. M. (1984). The evolution of cooperation, Basic Books."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1006\/jesp.1994.1003","article-title":"Cooperation in intergroup and single-group social dilemmas","volume":"30","author":"Bornstein","year":"1994","journal-title":"Journal of Experimental Social Psychology"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1007\/s11238-021-09850-z","article-title":"Classification by decomposition: A novel approach to classification of symmetric 2 \u00d7 2 games","volume":"93","author":"Everitt","year":"2022","journal-title":"Theory and Decision"},{"key":"ref_4","first-page":"562","article-title":"Theory of moves","volume":"81","author":"Brams","year":"1993","journal-title":"American Scientist"},{"key":"ref_5","unstructured":"Brams, S. J. (2001). Game theory and the Cuban missile crisis. Plus, 13, Available online: http:\/\/plus.maths.org\/issue13\/features\/brams\/index.html."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s11238-021-09824-1","article-title":"Every normal-form game has a Pareto-optimal nonmyopic equilibrium","volume":"92","author":"Brams","year":"2022","journal-title":"Theory and Decision"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1177\/073889429301200201","article-title":"Theory of moves: Overview and examples","volume":"12","author":"Brams","year":"1993","journal-title":"Conflict Management and Peace Science"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"495","DOI":"10.3390\/g6040495","article-title":"Names for games: Locating 2 \u00d7 2 games","volume":"6","author":"Bruns","year":"2015","journal-title":"Games"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1002\/bdm.3960070404","article-title":"Subjective randomization in one-and two-person games","volume":"7","author":"Budescu","year":"1994","journal-title":"Journal of Behavioral Decision Making"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Chierchia, G., and Coricelli, G. (2015). The impact of perceived similarity on tacit coordination: Propensity for matching and aversion to decoupling choices. Frontiers in Behavioral Neuroscience, 9.","DOI":"10.3389\/fnbeh.2015.00202"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"23441","DOI":"10.1525\/collabra.23441","article-title":"The influence of similarity and mimicry on decisions to trust","volume":"7","author":"Clerke","year":"2021","journal-title":"Collabra: Psychology"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1177\/1043463195007002008","article-title":"Leadership games in collective action","volume":"7","author":"Colomer","year":"1995","journal-title":"Rationality and Society"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1080\/13594321003630055","article-title":"Birds of a feather: Leader-follower similarity and procedural fairness effects on cooperation","volume":"20","author":"Cornelis","year":"2011","journal-title":"European Journal of Work and Organizational Psychology"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1177\/00223433231186446","article-title":"Leader similarity and international conflict","volume":"62","author":"DiLorenzo","year":"2025","journal-title":"Journal of Peace Research"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1162\/003355399556151","article-title":"A theory of fairness, competition, and cooperation","volume":"114","author":"Fehr","year":"1999","journal-title":"The Quarterly Journal of Economics"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Fehr, E., and Schmidt, K. M. (2005). The economics of fairness, reciprocity and altruism\u2014Experimental evidence and new theories. Handbook of the economics of giving, altruism and reciprocity, Elsevier. [1st ed.].","DOI":"10.1016\/S1574-0714(06)01008-6"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1037\/a0016073","article-title":"Friend or foe: Subjective expected relative similarity as a determinant of cooperation","volume":"138","author":"Fischer","year":"2009","journal-title":"Journal of Experimental Psychology: General"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1080\/1047840X.2012.658004","article-title":"Similarity or reciprocity? On the determinants of cooperation in similarity-sensitive games","volume":"23","author":"Fischer","year":"2012","journal-title":"Psychological Inquiry"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"e21","DOI":"10.1017\/S1473550424000144","article-title":"Identifying optimal decision-making strategies and determining effective messaging to maximize the expected outcomes of potential human\u2013extraterrestrial encounters","volume":"23","author":"Fischer","year":"2024","journal-title":"International Journal of Astrobiology"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"922","DOI":"10.1007\/s10683-024-09828-y","article-title":"Subjective game structures: Eliciting alternatives and payoffs to study the properties of social interactions","volume":"27","author":"Fischer","year":"2024","journal-title":"Experimental Economics"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Fischer, I., Avrashi, S., and Givon, L. (2025). Subjective game structures: A behavioral game theoretic analysis of hidden perceptions and strategic properties underlying the Israeli\u2013Palestinian conflict. Games, 16, (1).","DOI":"10.3390\/g16010003"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"201131","DOI":"10.1098\/rsos.201131","article-title":"The behavioural challenge of the COVID-19 pandemic: Indirect measurements and personalized attitude changing treatments (IMPACT)","volume":"7","author":"Fischer","year":"2020","journal-title":"Royal Society Open Science"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"e106","DOI":"10.1017\/S0140525X21001291","article-title":"Interacting with others while reacting to the environment","volume":"45","author":"Fischer","year":"2022a","journal-title":"Behavioral and Brain Sciences"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"211515","DOI":"10.1098\/rsos.211515","article-title":"Vaccination-hesitancy and global warming: Distinct social challenges with similar behavioural solutions","volume":"9","author":"Fischer","year":"2022b","journal-title":"Royal Society Open Science"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"19849","DOI":"10.1038\/s41598-023-46609-8","article-title":"The effect of similarity perceptions on human cooperation and confrontation","volume":"13","author":"Fischer","year":"2023","journal-title":"Scientific Reports"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1287\/mnsc.5.1.5","article-title":"Some experimental games","volume":"5","author":"Flood","year":"1958","journal-title":"Management Science"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/BF00135087","article-title":"Non-strict ordinal 2 \u00d7 2 games: A comprehensive computer-assisted analysis of the 726 possibilities","volume":"20","author":"Fraser","year":"1986","journal-title":"Theory and Decision"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"104753","DOI":"10.1016\/j.euroecorev.2024.104753","article-title":"The role of payoff parameters for cooperation in the one-shot Prisoner\u2019s Dilemma","volume":"166","author":"Lee","year":"2024","journal-title":"European Economic Review"},{"key":"ref_29","first-page":"205","article-title":"A note on \u201cA taxonomy of 2 \u00d7 2 games\u201d","volume":"13","author":"Guyer","year":"1968","journal-title":"General Systems"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/0022-1031(70)90073-9","article-title":"Threat in a two-person game","volume":"6","author":"Guyer","year":"1970","journal-title":"Journal of Experimental Social Psychology"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1177\/002200277201600310","article-title":"2 \u00d7 2 games played once","volume":"16","author":"Guyer","year":"1972","journal-title":"Journal of Conflict Resolution"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1002\/bs.3830140207","article-title":"A geometric classification system for 2 \u00d7 2 interval-symmetric games","volume":"14","author":"Harris","year":"1969","journal-title":"Behavioral Science"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1002\/bs.3830170405","article-title":"An interval-scale classification system for all 2 \u00d7 2 games","volume":"17","author":"Harris","year":"1972","journal-title":"Behavioral Science"},{"key":"ref_34","unstructured":"Huertas-Rosero, A. F. (2003). A cartography for 2 \u00d7 2 symmetric games. arXiv."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"73","DOI":"10.3758\/BF03330765","article-title":"Similarity and cooperation received as determinants of cooperation rendered","volume":"9","author":"Kaufmann","year":"1967","journal-title":"Psychonomic Science"},{"key":"ref_36","unstructured":"Kelley, H. H., and Thibaut, J. W. (1978). Interpersonal relations: A theory of interdependence, John Wiley & Sons Inc.. Available online: https:\/\/cir.nii.ac.jp\/crid\/1130000798116531328."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/BF00132457","article-title":"A taxonomy of all ordinal 2 \u00d7 2 games","volume":"24","author":"Kilgour","year":"1988","journal-title":"Theory and Decision"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1177\/0963721413481352","article-title":"Social projection as a source of cooperation","volume":"22","author":"Krueger","year":"2013","journal-title":"Current Directions in Psychological Science"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1111\/1467-9280.14481","article-title":"Using nonconscious behavioral mimicry to create affiliation and rapport","volume":"14","author":"Lakin","year":"2003","journal-title":"Psychological Science"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"10838","DOI":"10.1073\/pnas.1400830111","article-title":"Public goods in relation to competition, cooperation, and spite","volume":"111","author":"Levin","year":"2014","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"805","DOI":"10.2307\/2232669","article-title":"Regret theory: An alternative theory of rational choice under uncertainty","volume":"92","author":"Loomes","year":"1982","journal-title":"The Economic Journal"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"3182","DOI":"10.1111\/ecoj.12548","article-title":"Risk and temptation: A meta-study on prisoner\u2019s dilemma games","volume":"128","author":"Mengel","year":"2018","journal-title":"The Economic Journal"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1073\/pnas.36.1.48","article-title":"Equilibrium points in n-person games","volume":"36","author":"Nash","year":"1950","journal-title":"Proceedings of the National Academy of Sciences USA"},{"key":"ref_44","unstructured":"Osborne, M. J., and Rubinstein, A. (1994). A course in game theory, MIT Press."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1002\/bs.3830120202","article-title":"Exploiter, leader, hero, and martyr: The four archetypes of the 2 \u00d7 2 game","volume":"12","author":"Rapoport","year":"1967","journal-title":"Behavioral Science"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Rapoport, A., and Chammah, A. M. (1965). Prisoner\u2019s dilemma: A study in conflict and cooperation, University of Michigan Press.","DOI":"10.3998\/mpub.20269"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1177\/000276426601000303","article-title":"The game of chicken","volume":"10","author":"Rapoport","year":"1966","journal-title":"American Behavioral Scientist"},{"key":"ref_48","first-page":"203","article-title":"A taxonomy of 2 \u00d7 2 games","volume":"11","author":"Rapoport","year":"1966","journal-title":"General Systems"},{"key":"ref_49","unstructured":"Rapoport, A., Guyer, M., and Gordon, D. G. (1976). The 2 \u00d7 2 game, University of Michigan Press. Available online: https:\/\/openlibrary.org\/works\/OL57409W\/The_2_X_2_game?edition=2x2game0000rapo."},{"key":"ref_50","unstructured":"Robinson, D., and Goforth, D. (2004). Topology of 2 \u00d7 2 games, Routledge."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1177\/1043463195007001004","article-title":"Conversation and cooperation in social dilemmas","volume":"7","author":"Sally","year":"1995","journal-title":"Rationality and Society"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/01621459.1951.10500768","article-title":"The theory of statistical decision","volume":"46","author":"Savage","year":"1951","journal-title":"Journal of the American Statistical Association"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"31","DOI":"10.2307\/3218711","article-title":"The stag hunt","volume":"75","author":"Skyrms","year":"2001","journal-title":"Proceedings and Addresses of the American Philosophical Association"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1037\/0022-3514.77.2.337","article-title":"The pursuit of joint outcomes and equality in outcomes: An integrative model of social value orientation","volume":"77","year":"1999","journal-title":"Journal of Personality and Social Psychology"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"von Neumann, J., and Morgenstern, O. (2007). Theory of games and economic behavior (60th anniversary commemorative edition), Princeton University Press.","DOI":"10.1515\/9781400829460"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1037\/h0028279","article-title":"Prediction of behavior in two-person games","volume":"13","author":"Wyer","year":"1969","journal-title":"Journal of Personality and Social Psychology"}],"container-title":["Games"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4336\/16\/6\/56\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T04:25:59Z","timestamp":1761279959000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4336\/16\/6\/56"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,22]]},"references-count":56,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["g16060056"],"URL":"https:\/\/doi.org\/10.3390\/g16060056","relation":{},"ISSN":["2073-4336"],"issn-type":[{"type":"electronic","value":"2073-4336"}],"subject":[],"published":{"date-parts":[[2025,10,22]]}}}