{"id":{"repo_id":"usf","oai_identifier":"oai:digitalcommons.usf.edu:etd-1062"},"canonical_url":"https://search.dev.ndltd.org/etd/usf/oai:digitalcommons.usf.edu:etd-1062","repository":{"repo_id":"usf","name":"University of South Florida","base_url":"https://digitalcommons.usf.edu/do/oai/"},"display":{"title":"Algorithms for Simple Stochastic Games","abstract":"A simple stochastic game (SSG) is a game defined on a directed multigraph and played between players MAX and MIN. Both players have control over disjoint subsets of vertices: player MAX controls a subset VMAX and player MIN controls a subset VMIN of vertices. The remaining vertices fall into either VAVE, a subset of vertices that support stochastic transitions, or SINK, a subset of vertices that have zero outdegree and are associated with a payoff in the range [0, 1]. The game starts by placing a token on a designated start vertex. The token is moved from its current vertex position to a neighboring one according to certain rules. A fixed strategy σ of player MAX determines where to place the token when the token is at a vertex of VMAX. Likewise, a strategy τ of player MIN determines where to place the token when the token is at a vertex of VMIN. When the token is at a vertex of VAVE, the token is moved to a uniformly at random chosen neighbor. The game stops when the token arrives on a SINK vertex; at this point, player MAX gets the payoff associated with the SINK vertex. A fundamental question related to SSGs is the SSG value problem: Given a SSG G, is there a strategy of player MAX that gives him an expected payoff at least 1/2 regardless of the strategy of player MIN? This problem is among the rare natural combinatorial problems that belong to the class NP ∩ coNP but for which there is no known polynomial-time algorithm. In this thesis, we survey known algorithms for the SSG value problem and characterize them into four groups of algorithms: iterative approximation, strategy improvement, mathematical programming, and randomized algorithms. We obtain two new algorithmic results: Our first result is an improved worst-case, upper bound on the number of iterations required by the Homan-Karp strategy improvement algorithm. Our second result is a randomized Las Vegas strategy improvement algorithm whose expected running time is O(20:78n).","abstract_html":"A simple stochastic game (SSG) is a game defined on a directed multigraph and played between players MAX and MIN. Both players have control over disjoint subsets of vertices: player MAX controls a subset VMAX and player MIN controls a subset VMIN of vertices. The remaining vertices fall into either VAVE, a subset of vertices that support stochastic transitions, or SINK, a subset of vertices that have zero outdegree and are associated with a payoff in the range [0, 1]. The game starts by placing a token on a designated start vertex. The token is moved from its current vertex position to a neighboring one according to certain rules. A fixed strategy σ of player MAX determines where to place the token when the token is at a vertex of VMAX. Likewise, a strategy τ of player MIN determines where to place the token when the token is at a vertex of VMIN. When the token is at a vertex of VAVE, the token is moved to a uniformly at random chosen neighbor. The game stops when the token arrives on a SINK vertex; at this point, player MAX gets the payoff associated with the SINK vertex. A fundamental question related to SSGs is the SSG value problem: Given a SSG G, is there a strategy of player MAX that gives him an expected payoff at least 1/2 regardless of the strategy of player MIN? This problem is among the rare natural combinatorial problems that belong to the class NP ∩ coNP but for which there is no known polynomial-time algorithm. In this thesis, we survey known algorithms for the SSG value problem and characterize them into four groups of algorithms: iterative approximation, strategy improvement, mathematical programming, and randomized algorithms. We obtain two new algorithmic results: Our first result is an improved worst-case, upper bound on the number of iterations required by the Homan-Karp strategy improvement algorithm. Our second result is a randomized Las Vegas strategy improvement algorithm whose expected running time is O(20:78n).","abstract_has_math":false,"creators":["Valkanova, Elena"],"institution":"Digital Commons @ University of South Florida","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009-05-29T07:00:00Z","date_published":"2009-05-29T07:00:00Z","updated_at":"2026-07-24T05:42:11Z","subjects":["Game theory","Optimal strategies","Algorithms","Computational complexity","Computational equilibrium","American Studies","Arts and Humanities"],"languages":[],"rights":["default"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.usf.edu/etd/63","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Valkanova, Elena"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2009-05-29T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Digital Commons @ University of South Florida"]},{"key":"dc:type","label":"Dc Type","values":["thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Game theory","Optimal strategies","Algorithms","Computational complexity","Computational equilibrium","American Studies","Arts and Humanities"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["default"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.usf.edu/etd/63","https://digitalcommons.usf.edu/context/etd/article/1062/viewcontent/etd__63.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A simple stochastic game (SSG) is a game defined on a directed multigraph and played between players MAX and MIN. Both players have control over disjoint subsets of vertices: player MAX controls a subset VMAX and player MIN controls a subset VMIN of vertices. The remaining vertices fall into either VAVE, a subset of vertices that support stochastic transitions, or SINK, a subset of vertices that have zero outdegree and are associated with a payoff in the range [0, 1]. The game starts by placing a token on a designated start vertex. The token is moved from its current vertex position to a neighboring one according to certain rules. A fixed strategy σ of player MAX determines where to place the token when the token is at a vertex of VMAX. Likewise, a strategy τ of player MIN determines where to place the token when the token is at a vertex of VMIN. When the token is at a vertex of VAVE, the token is moved to a uniformly at random chosen neighbor. The game stops when the token arrives on a SINK vertex; at this point, player MAX gets the payoff associated with the SINK vertex. A fundamental question related to SSGs is the SSG value problem: Given a SSG G, is there a strategy of player MAX that gives him an expected payoff at least 1/2 regardless of the strategy of player MIN? This problem is among the rare natural combinatorial problems that belong to the class NP ∩ coNP but for which there is no known polynomial-time algorithm. In this thesis, we survey known algorithms for the SSG value problem and characterize them into four groups of algorithms: iterative approximation, strategy improvement, mathematical programming, and randomized algorithms. We obtain two new algorithmic results: Our first result is an improved worst-case, upper bound on the number of iterations required by the Homan-Karp strategy improvement algorithm. Our second result is a randomized Las Vegas strategy improvement algorithm whose expected running time is O(20:78n)."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:source","label":"Dc Source","values":["USF Tampa Graduate Theses and Dissertations"]},{"key":"dc:title","label":"Title","values":["Algorithms for Simple Stochastic Games"]}]}],"canonical_facts":{"dc:creator":["Valkanova, Elena"],"dc:date":["2009-05-29T07:00:00Z"],"dc:description":["A simple stochastic game (SSG) is a game defined on a directed multigraph and played between players MAX and MIN. Both players have control over disjoint subsets of vertices: player MAX controls a subset VMAX and player MIN controls a subset VMIN of vertices. The remaining vertices fall into either VAVE, a subset of vertices that support stochastic transitions, or SINK, a subset of vertices that have zero outdegree and are associated with a payoff in the range [0, 1]. The game starts by placing a token on a designated start vertex. The token is moved from its current vertex position to a neighboring one according to certain rules. A fixed strategy σ of player MAX determines where to place the token when the token is at a vertex of VMAX. Likewise, a strategy τ of player MIN determines where to place the token when the token is at a vertex of VMIN. When the token is at a vertex of VAVE, the token is moved to a uniformly at random chosen neighbor. The game stops when the token arrives on a SINK vertex; at this point, player MAX gets the payoff associated with the SINK vertex. A fundamental question related to SSGs is the SSG value problem: Given a SSG G, is there a strategy of player MAX that gives him an expected payoff at least 1/2 regardless of the strategy of player MIN? This problem is among the rare natural combinatorial problems that belong to the class NP ∩ coNP but for which there is no known polynomial-time algorithm. In this thesis, we survey known algorithms for the SSG value problem and characterize them into four groups of algorithms: iterative approximation, strategy improvement, mathematical programming, and randomized algorithms. We obtain two new algorithmic results: Our first result is an improved worst-case, upper bound on the number of iterations required by the Homan-Karp strategy improvement algorithm. Our second result is a randomized Las Vegas strategy improvement algorithm whose expected running time is O(20:78n)."],"dc:format":["application/pdf"],"dc:identifier":["https://digitalcommons.usf.edu/etd/63","https://digitalcommons.usf.edu/context/etd/article/1062/viewcontent/etd__63.pdf"],"dc:publisher":["Digital Commons @ University of South Florida"],"dc:rights":["default"],"dc:source":["USF Tampa Graduate Theses and Dissertations"],"dc:subject":["Game theory","Optimal strategies","Algorithms","Computational complexity","Computational equilibrium","American Studies","Arts and Humanities"],"dc:title":["Algorithms for Simple Stochastic Games"],"dc:type":["thesis"]},"updated_at":"2026-07-24T05:42:11Z"}