The four conflict management styles are competing, avoiding, accommodating, and problem-solving. Competing, defined by high problem-solving needs and low relationship needs (also known as “my way or the highway”) is a type of conflict management that trends towards being very ineffective, though it has its place particularly when the conflict management is high-stakes and zero-sum (that is, any gain must be a loss for the other side). It tends towards being negatively oriented, confrontational, and non-cooperative. Someone using a competing style focuses on the culpability and faults of the other participants, is focused on problems rather than solutions, seeks out hostile questions, and tries to avoid responsibility; they are not likely to be willing to compromise and will want very close to what they came into the negotiation wanting.
Meanwhile, avoiding styles are the opposite: they try to avoid the conflict, not discuss it, not talk about it, and not solve it. They are also called “withdraw/run” strategies, and they are lose-lose: everyone will be worse off in an avoiding dynamic. They will tend to let the other person do what they want, which means they are likely to see a very bad deal emerge. This is also an extremely bad way of approaching conflict management on average because the other person in the conflict is likely to be willing to accommodate them if they were asked and because the person ducking the conflict is likely to see the problem get worse.
Accommodating people try to preserve the relationship. This is an effective style for the goal of preserving a friendship. It has a high need for relationships and a low need for problem-solving: it is also known as a “give in strategy”. It involves largely letting the other person have what they want as long as the relationship remains intact. Meanwhile, problem-solving conflict management tends to focus on solving the problem amicably and fairly, but the friendship or relationship could be ruined afterward. It involves both participants sitting down, expressing their feelings in a non-blaming way, and making compromises as to what they want and how it can be done. It is defined by both a high problem-solving need or orientation and a high relationship preservation orientation.