Formulating a game in an economic setting I'm trying to teach myself Game Theory, and have come across the following question:

Suppose that a company, $L$, produces left shoes only, and a company $R$ produces right-shoes. If $L$ charges $p_{L}$ for a left shoe, and $R$ charges $p_{R}$ for a right-shoe, then the price of a pair of shoes is $p = p_{R} + p_{L}$. The quantity of pairs of shoes purchased is given by the formula $q = 100 - p$. The cost of production is $c>0$ per shoe. Both firms choose prices simultaneously and independently of each other. 
Formulate this situation as a game (specify the players, strategies and payoff functions).

So clearly the two players in the game are the two firms, $L$ and $R$. However, I am unsure how to identify the strategies, there are three possible scenarios:
$$\begin{cases}p_{L} < p_{R} \\
p_{L} = p_{R} \\
p_{L} > p_{R}\end{cases}$$
Are these the correct strategies? Moreover, I am confused by how to compute the payoff for each player? I'm quite new to game theory and economics, so any hint would be greatly appreciated!

Players: {L,R} Strategies {$p_L$,$p_R$}, $p_i$ $\in$[0,$\infty$], payoffs are
$(p_L -c_L) (100-(p_L+p_R))$ and similar for R. Slightly more complicated if firms can used a mixed strategy, putting a probability distribution over prices, but that usually isn't done in simple oligopoly games such as this.
