I have the following equation:
T = total times the game is repeated t = current period delta = discount rate u_i(a_i^t...) = the state payoff to player i
I'm attempting to understand the subscript of the second a, the -i. i'm not sure whether it is an indication of the other player in the game or something else. Unfortunately, I'm relatively new to finite repetition.
The link to the powerpoint I found it on follows this post. I'm working on finite repeated games and finding SPNE. I need to solve for my twice-repeated game.
As you correctly guessed, the subscript denotes the action of the other players. It is a standard notation in game theory which applies outside repeated games too.
In your case $a_{-i}^t := (a_1^t,a_2^t,\dots, a_{i-1}^t,a_{i+1}^t, \dots,a_n^t\}$ is the vector of actions of all agents but $i$ in time $t$, where $n$ is the total number of players.