Any time a group of children play a game together, whether indoors or out, the issue of rules is likely to arise. Younger children argue about who gets to be the mommy when they play dolls, for example, while older kids often disagree on what constitutes an out in kickball. A parent or playground monitor can always step in and set specific rules, but ideally, the kids will work together to resolve the issues on their own. Work with your children to teach them about compromises, and help them identify specific approaches that might work next time a disagreement about rules comes up.
Read the rules for board games out loud with your kids before they start to play. Ask them if there are any questions or any aspects of the rules they don't understand. If anyone wants to change a rule, or you have a family adaptation of the rules, make sure all the players understand and agree to these changes before they start the game. Keep the rules handy for reference in case disputes arise.
Talk to the kids who are disagreeing over the rules for either indoor or outdoor games to determine what the problem is. Ask them how they think they could resolve the problem and provide suggestions if necessary. Perhaps they can play one game under Susie's rules and the second game using Johnny's alternate rules. When kids disagree on outdoor games, look for a compromise: If one child wants six turns to kick the ball and another wants two, suggest they split the difference and do four turns each.
Practice handling arguments over game rules or procedures to give kids experience in solving the problems themselves and learning different methods of resolving these petty fights. Role-play some common situations to identify preferred responses -- they'll likely find it particularly entertaining if you play the role of a petulant child during the role-playing. Praise them for successfully defusing game situations before they become bigger fights. If the role-play deteriorates into fighting, tell the kids to stop and try to work it out. Tell them how to settle the problem only if they cannot figure it out on their own.
Instruct the kids to use the techniques they've learned next time a rule disagreement erupts on the playground at school or when playing a game with their siblings or neighborhood friends. When the situation does arise, ask them what happened and how they resolved it. If problems persist, or the kids seem unwilling to work out a version of the rules that all participants can agree on for a given game, make that game off-limits for a predetermined period. Tell them they will get the kickball, basketball or board game back when they can come up with a solution that works.