SHRI RAM COLLEGE OF COMMERCE
BA (HONS.) ECONOMICS – SEM 4C SESSION 2019-2020
INTERMEDIATE MICROECONOMICS -2
Game Theory – Definitions -1
Note:
Put these definitions to work with the help of examples done in class and from the readings. You may
also create your own examples in order to better grasp the definitions. This is rigorous work and should be taken
seriously.
• A strategy is a complete contingent plan of action.
• A game in strategic form or normal form is a triple Γ ≡ (N, {Si}i∈N , {ui}i∈N ) in which:
- N = {1, 2, ..., n} is a finite set of players
- Si is the set of strategies of player i, for every player i ∈ N - the set of strategy profiles is denoted
as S ≡ S1 × ... × Sn,
- ui : S → R is a utility function that associates with each profile of strategies s ≡ (s1, ..., sn), a
payoff ui(s) for every player i ∈ N.
When the Si is finite for each i
∈
N, we will refer to Γ as a finite game.
A strategy profile of all the players will be denoted as s ≡ (s1, ..., sn) ∈ S. A strategy profile of
all the players excluding a Player i will be denoted by s−i. The set of all strategy profiles of
players other than a Player i will be denoted by S−i.
• A strategy si of player i
strictly dominates
her strategy s’i if for all s-i ∈ S-i,
ui(si, s-i) > ui(s’i, s-i)
• A strategy si ∈ Si for Player i is
strictly dominant
if it strictly dominates every s’i ∈ Si\{si}.
• A strategy si
weakly dominates
strategy s’i if for every s−i ∈ S−i,
ui(si, s−i) ≥ ui(s’i, s−i),
with strict inequality holding for some s−i.
• A strategy si is
weakly dominant
if it weakly dominates every other strategy s’i ∈ Si\{si}.
• A strategy si ∈ Si for Player i is
strictly dominated
if there exists s’i ∈ Si such that s’i strictly
dominates si, i.e., for every s−i
∈
S−i, we have
ui(si, s−i) < ui(s’i, s−i).
• A strategy si ∈ Si for Player i is
weakly dominated
if there exists s’i ∈ Si such that s’i weakly
dominates si, i.e., for every s−i
∈
S−i, we have
ui(si, s−i) ≤ ui(s’i, s−i)
with strict inequality holding for some s−i.
