Negative Rewards in Reinforcement Learning

Question

I'm using self play to teach a model to play games (e.g. board games). Basically the model is playing against itself. When playing as player 2 I switch the perspective as if it is player 1 to train the model on this data too.

In the end one player wins and gets the reward. There is no other reward. Do I need to add a negative reward (in retrospect) for the action the loosing player took one step before the winning player made his action?

An example since this sentences was quite long and disturbing: Assume a model learning tic tac toe. Player 1 wins with the last move witch was taken in this game. He gets a reward. Player 2 lost obviously. Would it be beneficial to give a penalty for the move he took (the second last move)? If so why?

Answer 1

4 months later I cans say negativ rewards are very crucial. Without them both players seemed to play for them self. No sign of competition. But with negativ rewards for a lose, agents started competing.

In the case of board games you have to store the two last played moves. This way you can reward the last move with a positiv reward (because the last move lead to a win). The second last move was the losing player's move which gets a negativ reward.