In posting this question I'm thinking of GURPS, but it would be the same with any game in which:
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players get one action per turn
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players can either move OR attack OR (move only one hex AND attack)
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turns are not simultaneous. Each player acts, then the other acts, etc.
The players are relatively near, non-stunned, with ready weapons, etc and approach each other with hostile intentions. Each one of them wants to approach the other (not wildly) and attack first, to get the first opportunity of injuring the foe. The quickest one acts first, and in his turn, chooses to MOVE to an hex adjacent to the one his foe occupies, to engage in melee combat. Then the other one takes his turn and ATTACKS.
Have I misunderstood something? It seems to me very illogical, that in a simmetrical encounter, the quickest player gets to attack last, or (in GURPS), if he wants to attack in the same turn he moves, only gets an MOVE+ATTACK, a lame attack maxed at 9 effective skill.
If you use the step+Action rules (you can move one hex and take an action in the same turn) the problem persists.
How to resolve this without changing the basic rules? It occurs to me that a possible solution would be something like this: "if you were not in melee combat at the beginning of BOTH of your turns, then no one gets to attack". But will it originate some unexpected problems?
This problem is pervasive: it happens in almost every encounter.
Best Answer
What you're running into is a problem with tactics, not the rules. If there are two characters that are near eachother, but not adjacent, then you are correct that if the faster combatant moves in close, they will be attacked first. However, they don't have to take the Move or Move and Attack action to get the first strike.
Instead, take the Wait action. Wait allows you to:
Emphasis mine. In this case, the faster character should Wait until their enemy comes in melee range, and then Attack or All-Out Attack. Alternately, you could take the All-Out Attack action directly. That lets you move up to half your speed as part of the attack. Note, however, that the character that chooses to move up might choose to take an All-Out Defense (Dodge) which lets them move half their speed and get a +2 to their Dodge defense, possibly negating the stationary character's attack. GURPS melee combat between two intelligent opponents is a lot like actual combat between intelligent opponents; it's a string of bluffs and double-bluffs to try and trick your opponent into giving you the advantage.
In every system that I know of that includes tactical combat, there is a way to respond to an enemy's action like this.
Another possible option is an initiative system from one of the World of Darkness systems. Basically, you have every combatant choose their actions in reverse initiative order: the slowest character picks their action, then the next slowest, all the way to the highest. Once all actions are selected, you execute in order of initiative. Using your situation as an example:
Then, the next round, you do it again. I'm pretty sure this system also had you re-roll initiative each round, so different people went at different times each round.
In combats that involve more than two characters in GURPS, you can use your opponent's reluctance to make the first move to your advantage. Since facing matters in GURPS, you can use the time your opponent spends not charging you to set up a flanking position with an ally, or move off to deal with another threat, or just hold your opponent still until your ranged attacking allies can whittle them down.
The reason for this is that GURPS is meant to model reality very closely, and with a 1 second combat round, there just isn't time to move several yards and also make an accurate attack without also giving up your defenses. If you watch actual melee combat, when the fighters get close they typically have a strongly defensive stance until one of the combatants makes an attack. This would be modeled by both combatants taking All-Out Defense actions until both were in melee range, and then starting to use other Attack options.