Продавец согласился торговаться.

Because the subject, продавец (seller), is grammatically masculine.

In the Russian past tense, verbs usually agree with the subject in gender and number:

• согласился = masculine singular
• согласилась = feminine singular
• согласилось = neuter singular
• согласились = plural

So with продавец, you use согласился.

For example:

• Продавец согласился торговаться.
• Продавщица согласилась торговаться.

The ending -ся (or -сь) is the reflexive marker, but in Russian it does not always mean a literal oneself idea.

In these two verbs, it is simply part of the dictionary form:

• согласиться = to agree
• торговаться = to bargain / haggle

So you should learn them as whole verbs, not try to translate them word-for-word as agree oneself or bargain oneself.

A useful point:

• Some Russian reflexive verbs are truly reflexive.
• Others are just standard verbs that happen to use -ся.

Here, both verbs belong to that second group.

Because after согласиться you can use an infinitive to say what someone agreed to do.

Pattern:

• согласиться + infinitive

So:

• согласился торговаться = agreed to bargain / agreed to haggle

Other examples:

• Он согласился помочь. = He agreed to help.
• Она согласилась подождать. = She agreed to wait.

This is very natural Russian.

Because торговаться and торговать mean different things.

• торговать = to trade, to sell, to do business
• торговаться = to bargain, haggle, negotiate over a price

So in this sentence, the idea is that the seller agreed to negotiate the price, not simply to sell.

Compare:

• Он торгует фруктами. = He sells fruit.
• Он торгуется с покупателем. = He is bargaining with the buyer.

Продавец is in the nominative case because it is the subject of the sentence.

It is the person performing the action:

• the seller agreed

So nominative is exactly what you would expect here.

No. Согласиться can be used in several patterns.

Common ones include:

• согласиться + infinitive
  Он согласился помочь.
  He agreed to help.

• согласиться с + instrumental
  Я согласен с тобой.
  I agree with you.

• согласиться на + accusative
  Она согласилась на сделку.
  She agreed to the deal.

In your sentence, it uses the infinitive pattern: the seller agreed to bargain.

This is a very common question.

• согласился is a verb in the past tense:
  agreed
• согласен is a short-form adjective meaning:
  is willing / is in agreement / agrees

So:

• Продавец согласился торговаться.
  The seller agreed to bargain.
  This describes a completed action or decision.

• Продавец согласен торговаться.
  The seller is willing to bargain.
  This describes the seller’s current state or attitude.

The difference is similar to:

• He agreed vs
• He is willing

Yes, the word order can change.

Russian word order is more flexible than English because case endings show grammatical roles. The neutral, straightforward order here is:

• Продавец согласился торговаться.

But you could also hear:

• Согласился торговаться продавец.
• Торговаться продавец согласился.

These alternative orders change the emphasis, not the core meaning.

For a learner, the given order is the safest and most neutral.

Согласился comes from согласиться, which is perfective.

That means it presents the action as a completed event:

• the seller agreed
• a decision was reached

The imperfective partner is:

• соглашаться = to be agreeing / to agree repeatedly / to agree in process

Compare:

• Он согласился торговаться.
  He agreed to bargain.
  A completed decision.

• Он долго соглашался торговаться.
  He was agreeing only after a long time / It took him a while to agree to bargain.
  Focus on the process.

Торговаться is usually the imperfective verb.

Here that makes sense because the sentence refers to the activity of bargaining in general, not one single completed bargaining event.

You may also encounter a perfective form such as поторговаться, which can mean to bargain for a while / to have a bargaining exchange.

Compare the nuance:

• согласился торговаться
  agreed to bargain / was willing to negotiate

• согласился поторговаться
  agreed to have a bargaining session / agreed to do some bargaining

In many contexts, торговаться is the more natural default choice.

Yes. The verb often appears with с + instrumental to show who the bargaining is with.

For example:

• Продавец согласился торговаться с покупателем.
  The seller agreed to bargain with the buyer.

So in your sentence, the other side is simply not mentioned, because it is either obvious or not important.

The stress is:

• продавЕц
• согласИлся
• торговАться

A rough pronunciation guide:

• продавЕц = pra-da-VYETS
• согласИлся = sa-gla-SEEL-sya
• торговАться = tar-ga-VAT-sya

A useful pronunciation note: The ending -ться in infinitives is pronounced roughly like -ца.

So торговаться sounds approximately like:

• таргавАцца

That is pronunciation only; the spelling remains -ться.

Yes, it is completely natural.

It is a normal way to say that the seller agreed to negotiate the price. The grammar is standard, and the verb choice is appropriate.

A native speaker might also say similar things like:

• Продавец согласился на торг.
• Продавец был готов торговаться.
• Продавец согласился немного уступить в цене.

But your original sentence is simple, correct, and natural.