First, a few tips on cleaning up your text.
1. Delete the redundant information or excessive use of clauses to make yourself across at the least cost of words. Instead of writing “the technology of the firms in the economy is convex”, trim it to “technology is convex” because it is obvious that the firms are the adopters of technology and they exist in the economy (p80 in the book).
2. Do not be obsessed with the word “assume” (or “is/are assumed”). It’s better to state “assumptions” once and list all of them. But when you want to emphasize some aspects of your model that are different from the existing literature, you may start a separate sentence of paragraph highlighting these.
3. Stick with plain words if you can deliver your message. Instead of writing “the set of Nash Equilibrium is nonempty”, write “Nash Equilibrium exists”. The latter expression gets rid of the nerdy feel in the text and makes your writing more accessible.
Then, Thomson talks about how to present a model effectively. I have found the following most useful.
1. When you are introducing your model, go from the infrastructure to the superstructure. For example, when describing a multi-stage game, introduce and describe each of the players separately before bringing them together. Follow the logical steps of defining actors -> relationship -> concepts based on actors and relationship.
2. A good yet under appreciated (in my opinion) way to prevent ambiguity is to avoid using multiple clauses. This is especially true for non-native speakers. Adding clauses will dramatically increase your chance of making grammatical errors. Moreover, badly placed and imbalanced clauses will disorient the reader.
3. When stating a difficult definition, assist the reader by giving an informal and intuitive explanation preceding the formal explanation.
4. Use one enumeration for each object category. Combining different categories into a single list saves your time at the cost of your reader.
5. When specifying your assumptions, make sure there is at least one example satisfying them. If you cannot think of an example, then your assumptions are likely to be practically useless even though they are mathematically meaningful.