WE CLAIM:
1. An ink jet ink composition comprising:
water; and
particles including a chain polymer including Structural Unit (1), Structural Unit (2), and a hydrophilic group and a polymerizable group,
in Structural Units (1) and (2), Cy and Cy each independently represent a divalent organic group having 3 to 30 carbon atoms including a cyclic structure, Y1 and Y2 each independently represent an oxygen atom, a sulfur atom, or a -NR1- group, R1 represents a hydrogen atom or a hydrocarbon group having 1 to 10 carbon atoms,
*1 in Structural Unit (1) represents a bonding position to a structural unit other than Structural Unit (1), and *2 in Structural Unit (2) represents a bonding position to a structural unit other than Structural Unit (2).
2. The ink jet ink composition according to claim 1,
wherein a total content of Structural Units (1) and (2) is 60 mass% or greater with respect to a total amount of the chain polymer.
3. The ink jet ink composition according to claim 1 or 2,
wherein, in a case where a total millimolar number of the cyclic structure included in Structural Units (1) and (2) in 1 g of the chain polymer is defined as a ring value of the chain polymer, the ring value of the chain polymer is 3.00 mmol/g or greater.
4. The ink jet ink composition according to any one of claims 1 to 3,
wherein at least one of Cy1 or Cy2 includes an aliphatic ring as the cyclic structure.
5. The ink jet ink composition according to any one of claims 1 to 4,
wherein at least one of Cy1 or Cy2 includes two or more cyclic structures.

6. The ink jet ink composition according to any one of claims 1 to 5,
wherein at least one of Cy1 or Cy2 includes Bisaryl Structure (A),
in Bisaryl Structure (A), Ar1 and Ar2 each independently represent an arylene group, L represents a single bond or a divalent linking group, and two *’s each represent a bonding position.
7. The ink jet ink composition according to claim 6,
wherein at least one of Ar1 or Ar2 is an arylene group substituted with at least one halogen atom.
8. The ink jet ink composition according to claim 6 or 7,
wherein any one of Cy1 and Cy2 includes an aliphatic ring, and the other of Cy1 and Cy2 includes Bisaryl Structure (A).
9. The ink jet ink composition according to claim 8,
wherein, in the chain polymer, a molar ratio of the structural unit including Bisaryl Structure (A) to the structural unit including an aliphatic ring is 0.10 to 1.00.
10. The ink jet ink composition according to any one of claims 1 to 9,
wherein the hydrophilic group is at least one selected from the group consisting of a carboxy group and a salt of a carboxy group.
11. The ink jet ink composition according to claim 10,
wherein, in a case where a total millimolar number of the carboxy group and the salt of a carboxy group in 1 g of the chain polymer is defined as an acid value of the chain polymer, the acid value of the chain polymer is 0.30 mmol/g to 1.50 mmol/g.
12. The ink jet ink composition according to any one of claims 1 to 11,
wherein a weight-average molecular weight of the chain polymer is 10,000 to 100,000.

13. The ink jet ink composition according to any one of claims 1 to 12,
wherein the polymerizable group of the particles is a photopolymerizable group, and wherein the particles include a photopolymerizable compound as a compound having the photopolymerizable group.
14. The ink jet ink composition according to claim 13,
wherein at least one kind of the photopolymerizable compound includes one or more cyclic structures and two or more (meth)acryloyl groups in a molecule.
15. The ink jet ink composition according to claim 13 or 14,
wherein the chain polymer has a photopolymerizable group.
16. The ink jet ink composition according to any one of claims 1 to 15,
wherein the particles include an ethylenic double bond, and
wherein, in a case where a millimolar number of the ethylenic double bond in 1 g of a solid content of the particles is defined as the C=C value of the particles, a C=C value of the particles is 0.30 mmol/g or greater.
17. The ink jet ink composition according to any one of claims 1 to 12,
wherein the polymerizable group of the particles is a thermopolymerizable group, and wherein the particles include a thermopolymerizable compound as a compound including the thermopolymerizable group.
18. The ink jet ink composition according to any one of claims 1 to 17,
wherein a solid content amount of the particles is 50 mass% or greater with respect to a solid content amount of the ink jet ink composition.
19. The ink jet ink composition according to any one of claims 1 to 18,
wherein a content of the chain polymer is 20 mass% or greater with respect to a solid content amount of the particles.

20. An image forming method comprising:
applying the ink jet ink composition according to any one of claims 1 to 19 to a plastic base material by an ink jet method; and
curing the ink jet ink composition applied to the plastic base material.