--- res: bibo_abstract: - In two-player games on graph, the players construct an infinite path through the game graph and get a reward computed by a payoff function over infinite paths. Over weighted graphs, the typical and most studied payoff functions compute the limit-average or the discounted sum of the rewards along the path. Besides their simple definition, these two payoff functions enjoy the property that memoryless optimal strategies always exist. In an attempt to construct other simple payoff functions, we define a class of payoff functions which compute an (infinite) weighted average of the rewards. This new class contains both the limit-average and the discounted sum functions, and we show that they are the only members of this class which induce memoryless optimal strategies, showing that there is essentially no other simple payoff functions.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Krishnendu foaf_name: Chatterjee, Krishnendu foaf_surname: Chatterjee foaf_workInfoHomepage: http://www.librecat.org/personId=2E5DCA20-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-4561-241X - foaf_Person: foaf_givenName: Laurent foaf_name: Doyen, Laurent foaf_surname: Doyen - foaf_Person: foaf_givenName: Rohit foaf_name: Singh, Rohit foaf_surname: Singh bibo_doi: 10.1007/978-3-642-22953-4_13 bibo_volume: 6914 dct_date: 2011^xs_gYear dct_language: eng dct_publisher: Springer@ dct_title: On memoryless quantitative objectives@ ...