This study presents a novel exploration of the lottery Colonel Blotto game. This adaptation introduces the possibility of draws or ties, moving beyond the traditional winner-take-all framework. The inclusion of the possibility of a draw allows for a more realistic depiction of contests where players may arbitrarily split the value of a battlefield in the absence of a decisive victory. Our model is characterized by the number of battlefields, battlefield values that may vary across battlefields, but are symmetric across players, the distinct player shares of each battlefield value captured in the event of a draw, the potentially asymmetric budgets of the players and a parameter influencing the (endogenously determined) likelihood of a draw. Within this modified game structure, we derive the range of the underlying parameters for which there exists an interior solution and provide an analytic characterization of that solution. Additionally, we expand our analysis across the entire parameter space to determine the optimal resource allocation strategies when solutions are not interior (either some player’s complete budget is allocated to a battlefield, or a nonempty set of battlefields receives a zero allocation). Special cases corresponding to prominent models in the contest literature are examined and extensions explored.
","abstract_html":"<p>This study presents a novel exploration of the lottery Colonel Blotto game. This adaptation introduces the possibility of draws or ties, moving beyond the traditional winner-take-all framework. The inclusion of the possibility of a draw allows for a more realistic depiction of contests where players may arbitrarily split the value of a battlefield in the absence of a decisive victory. Our model is characterized by the number of battlefields, battlefield values that may vary across battlefields, but are symmetric across players, the distinct player shares of each battlefield value captured in the event of a draw, the potentially asymmetric budgets of the players and a parameter influencing the (endogenously determined) likelihood of a draw. Within this modified game structure, we derive the range of the underlying parameters for which there exists an interior solution and provide an analytic characterization of that solution. Additionally, we expand our analysis across the entire parameter space to determine the optimal resource allocation strategies when solutions are not interior (either some player’s complete budget is allocated to a battlefield, or a nonempty set of battlefields receives a zero allocation). Special cases corresponding to prominent models in the contest literature are examined and extensions explored.</p>","abstract_has_math":false,"creators":["Liu, Jingzhi"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Thesis","degree_discipline":"Behavioral and Computational Economics","degree_department":null,"school":null,"contributors":["Daniel Kovenock","David Porter","Stephen Rassenti"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-05-01T07:00:00Z","date_published":"2024-05-01T07:00:00Z","updated_at":"2026-07-24T01:38:37Z","subjects":["Game Theory","Lottery Colonel Blotto Games","Multi-Battlefield Contests with Draws","Economics","Economic Theory"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.chapman.edu/behavioral_and_computational_economics_theses/5","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Daniel Kovenock","David Porter","Stephen Rassenti"]},{"key":"dc:creator","label":"Author","values":["Liu, Jingzhi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2026-05-01T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Behavioral and Computational Economics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Game Theory","Lottery Colonel Blotto Games","Multi-Battlefield Contests with Draws","Economics","Economic Theory"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.chapman.edu/behavioral_and_computational_economics_theses/5"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This study presents a novel exploration of the lottery Colonel Blotto game. This adaptation introduces the possibility of draws or ties, moving beyond the traditional winner-take-all framework. The inclusion of the possibility of a draw allows for a more realistic depiction of contests where players may arbitrarily split the value of a battlefield in the absence of a decisive victory. Our model is characterized by the number of battlefields, battlefield values that may vary across battlefields, but are symmetric across players, the distinct player shares of each battlefield value captured in the event of a draw, the potentially asymmetric budgets of the players and a parameter influencing the (endogenously determined) likelihood of a draw. Within this modified game structure, we derive the range of the underlying parameters for which there exists an interior solution and provide an analytic characterization of that solution. Additionally, we expand our analysis across the entire parameter space to determine the optimal resource allocation strategies when solutions are not interior (either some player’s complete budget is allocated to a battlefield, or a nonempty set of battlefields receives a zero allocation). Special cases corresponding to prominent models in the contest literature are examined and extensions explored.
"]},{"key":"dc:source","label":"Dc Source","values":["Liu, J. (2024). The lottery Colonel Blotto game with draws [Master's thesis, Chapman University]. Chapman University Digital Commons. https://doi.org/10.36837/chapman.000599"]},{"key":"dc:title","label":"Title","values":["The Lottery Colonel Blotto Game with Draws"]}]}],"canonical_facts":{"dc:contributor":["Daniel Kovenock","David Porter","Stephen Rassenti"],"dc:creator":["Liu, Jingzhi"],"dc:date.available":["2026-05-01T07:00:00Z"],"dc:description.abstract":["This study presents a novel exploration of the lottery Colonel Blotto game. This adaptation introduces the possibility of draws or ties, moving beyond the traditional winner-take-all framework. The inclusion of the possibility of a draw allows for a more realistic depiction of contests where players may arbitrarily split the value of a battlefield in the absence of a decisive victory. Our model is characterized by the number of battlefields, battlefield values that may vary across battlefields, but are symmetric across players, the distinct player shares of each battlefield value captured in the event of a draw, the potentially asymmetric budgets of the players and a parameter influencing the (endogenously determined) likelihood of a draw. Within this modified game structure, we derive the range of the underlying parameters for which there exists an interior solution and provide an analytic characterization of that solution. Additionally, we expand our analysis across the entire parameter space to determine the optimal resource allocation strategies when solutions are not interior (either some player’s complete budget is allocated to a battlefield, or a nonempty set of battlefields receives a zero allocation). Special cases corresponding to prominent models in the contest literature are examined and extensions explored.
"],"dc:identifier":["https://digitalcommons.chapman.edu/behavioral_and_computational_economics_theses/5"],"dc:source":["Liu, J. (2024). The lottery Colonel Blotto game with draws [Master's thesis, Chapman University]. Chapman University Digital Commons. https://doi.org/10.36837/chapman.000599"],"dc:subject":["Game Theory","Lottery Colonel Blotto Games","Multi-Battlefield Contests with Draws","Economics","Economic Theory"],"dc:title":["The Lottery Colonel Blotto Game with Draws"],"thesis:degree_discipline":["Behavioral and Computational Economics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T01:38:37Z"}