--- _id: '5440' abstract: - lang: eng text: 'Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom for payoff in the context of evolution. The replacement graph specifies who competes with whom for reproduction. The vertices of the two graphs are the same, and each vertex corresponds to an individual of the population. The fitness (or the reproductive rate) is a non-negative number, and depends on the payoff. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability. Our main results are as follows: First, we consider a special case of the general problem, where the residents do not reproduce. We show that the qualitative question is NP-complete, and the quantitative approximation question is #P-complete, and the hardness results hold even in the special case where the interaction and the replacement graphs coincide. Second, we show that in general both the qualitative and the quantitative approximation questions are PSPACE-complete. The PSPACE-hardness result for quantitative approximation holds even when the fitness is always positive.' alternative_title: - IST Austria Technical Report author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Rasmus full_name: Ibsen-Jensen, Rasmus id: 3B699956-F248-11E8-B48F-1D18A9856A87 last_name: Ibsen-Jensen orcid: 0000-0003-4783-0389 - first_name: Martin full_name: Nowak, Martin last_name: Nowak citation: ama: Chatterjee K, Ibsen-Jensen R, Nowak M. The Complexity of Evolutionary Games on Graphs. IST Austria; 2015. doi:10.15479/AT:IST-2015-323-v2-2 apa: Chatterjee, K., Ibsen-Jensen, R., & Nowak, M. (2015). The complexity of evolutionary games on graphs. IST Austria. https://doi.org/10.15479/AT:IST-2015-323-v2-2 chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Martin Nowak. The Complexity of Evolutionary Games on Graphs. IST Austria, 2015. https://doi.org/10.15479/AT:IST-2015-323-v2-2. ieee: K. Chatterjee, R. Ibsen-Jensen, and M. Nowak, The complexity of evolutionary games on graphs. IST Austria, 2015. ista: Chatterjee K, Ibsen-Jensen R, Nowak M. 2015. The complexity of evolutionary games on graphs, IST Austria, 18p. mla: Chatterjee, Krishnendu, et al. The Complexity of Evolutionary Games on Graphs. IST Austria, 2015, doi:10.15479/AT:IST-2015-323-v2-2. short: K. Chatterjee, R. Ibsen-Jensen, M. Nowak, The Complexity of Evolutionary Games on Graphs, IST Austria, 2015. date_created: 2018-12-12T11:39:21Z date_published: 2015-06-16T00:00:00Z date_updated: 2023-02-23T12:26:10Z day: '16' ddc: - '005' - '576' department: - _id: KrCh doi: 10.15479/AT:IST-2015-323-v2-2 file: - access_level: open_access checksum: 66aace7d367032af97c15e35c9be9636 content_type: application/pdf creator: system date_created: 2018-12-12T11:53:23Z date_updated: 2020-07-14T12:46:56Z file_id: '5484' file_name: IST-2015-323-v2+2_main.pdf file_size: 466161 relation: main_file file_date_updated: 2020-07-14T12:46:56Z has_accepted_license: '1' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: '18' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '338' related_material: record: - id: '5421' relation: earlier_version status: public - id: '5432' relation: earlier_version status: public status: public title: The complexity of evolutionary games on graphs type: technical_report user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2015' ...