Polymer, method for producing polymer, electrolyte composition, and battery

A polymer comprising:

• a first structural unit which is at least one structural unit (A) represented by the following formula (A);
• and
• a second structural unit which is at least one of a structural unit (B1) represented by the following formula (B1) and a structural unit (B2) represented by the following formula (B2),
• wherein the polymer satisfies at least one of the following conditions (1) and (2),
• (1) a ratio m of the first structural unit to total structural units in the polymer is 0.2 to 0.8, and a ratio n of the second structural unit to the total structural units in the polymer is 0.2 to 0.8,
• (2) a content of the first structural unit is 25 to 95 mass % and a content of the second structural unit is 5 to 75 mass % based on the total mass of the polymer,
• (in formula (A), X is a divalent organic group having 1 to 20 carbon atoms, Y is a halogen atom or a monovalent organic group having 1 to 20 carbon atoms, M is an alkali metal element selected from Li, Na, and K, and * represents a position where the structural unit (A) is bound to another structural unit),
• (in formula (B1), R1 to R4 are each independently a hydrogen atom, a halogen atom, or a monovalent organic group having 1 to 20 carbon atoms, and * represents a position where the structural unit (B1) is bound to another structural unit), and
• (in formula (B2), R15 is a divalent organic group having 1 to 20 carbon atoms, and R16 and R17 are each a hydrogen atom, a halogen atom, or a monovalent organic group having 1 to 20 carbon atoms, with the proviso that a structural unit in which R15 is —C(═O)—O—C(═O)— and both R16 and R17 are hydrogen atoms, and a structural unit in the structural unit (A) are not in the structural unit (B2)).