Domination of Strategy

MAS Let $s,t\in S_i$ be strategies of player $i$. We say that

• $t$ is strictly dominated by s if $u_i(s,s_{-i})>u_i(t,{\mathbf{s}}_{-i})$ for every ${\mathbf{s}}_{-i}\in {\mathbf{S}}_{-i}$
• $t$ is weakly dominated by s if $u_i(s,s_{-i})\ge u_i(t,{\mathbf{s}}_{-i})$ for every ${\mathbf{s}}_{-i}\in {\mathbf{S}}_{-i},$

Examples

	L	M	R
U	4, 3	2, 1	3, 2
M	1, 4	3, 2	2, 3
D	2, 2	2, 1	2, 2

Column player:

• L vs M: L gives (3, 4, 2), M gives (1, 2, 1)
  • Against U: 3 > 1 ✓
  • Against M: 4 > 2 ✓
  • Against D: 2 > 1 ✓
  • M is strictly dominated by L
• L vs R: L gives (3, 4, 2), R gives (2, 3, 2)
  • Against U: 3 > 2 ✓
  • Against M: 4 > 3 ✓
  • Against D: 2 = 2 ✓
  • R is weakly dominated by L Row player:*
  • U vs D: U gives (4, 2, 3), D gives (2, 2, 2)
  • Against L: 4 > 2 ✓
  • Against M: 2 = 2 ✓
  • Against R: 3 > 2 ✓
  • D is weakly dominated by U