If I cannot win, then I will make it impossible for you to win

"Crab mentality" or "crabs in a bucket" describes the frog analogy well, but the driver scenario seems different.

Crab mentality, also known as crab theory, is a way of thinking best described by the phrase "if I can't have it, neither can you". The metaphor is derived from a pattern of behavior noted in crabs when they are trapped in a bucket. While any one crab could easily escape, its efforts will be undermined by others, ensuring the group's collective demise.

The analogy in human behavior is claimed to be that members of a group will attempt to reduce the self-confidence of any member who achieves success beyond the others, out of envy, resentment, spite, conspiracy, or competitive feelings, to halt their progress.

Wikipedia

You are kingmaking or spoiling, and can be called a kingmaker or spoiler. This usage comes from game theory via historical analogy (cf. "Is kingmaking in multiplayer games a problem that can be fixed?"). Here is how Wikipedia defines the kingmaker scenario:

a kingmaker scenario in a game of three or more players,[sic] is an endgame situation where a player who is unable to win has the capacity to determine which player among others will. Said player is referred to as the kingmaker or spoiler. No longer playing for themselves, they may make game decisions to favor a player who played more favorably (to them) earlier in the game.

I've often encountered both terms during board games where an already-losing player intentionally hinders another player in order to enable a favored player's victory. For instance, if one player has been continually acted against during a game of Risk, in a situation where they can no longer win, they may instead act as the spoiler against that player, decimating their armies. I've also heard spoiling in situations where everyone would lose as a result of a player's deliberate actions, in situations where that is possible. (It can happen in some competitive games - see this list on BoardGameGeek.) The usage is a little quirky, but spoiler especially is attested in the OED in American English:

2.c. U.S. One who mars the chance of victory for an opponent, while not being a potential winner. Also, applied to a thing. Esp. in Sport and Politics.

A related usage also carries over to politics (the spoiler effect, e.g. Hiring and Firing Public Officials),

Edwin linked to a question about the expression "If I can't have it, no-one can", but I think this phrase is exactly what you're looking for: it literally means "If I can't win, I will make it impossible for someone else to win".

The wording can be changed to suit the situation, so for example the "Guatemalan frogs" might say "If I can't escape, no-one can".

This pattern of phrase is idiomatic in British English - I believe the same is true in North American English.

You could call it a scorched earth policy This is when you know you can't win in a situation, so you're going to just burn it all down to prevent your opponent from making any use of it. See also: salting the earth. Either way, you're ceding territory to the enemy, but in such a way that it is of little or no use to them. Obviously can be used in a metaphorical sense in addition to the literal meaning.

I would call

a competition to see who can occupy that space first. Usually it ends when neither one can occupy the space, and both drivers have actually missed their turn.

the Prisoner's Dilemma.

The Prisoner's Dilemma game is played like this:

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:

If A and B each betray the other, each of them serves two years in prison If A betrays B but B remains silent, A will be set free and B will serve three years in prison If A remains silent but B betrays A, A will serve three years in prison and B will be set free If A and B both remain silent, both of them will serve only one year in prison (on the lesser charge).

Wikipedia

But, it can also be applied to your situation. Wikipedia states:

The prisoner's dilemma game can be used as a model for many real-world situations involving cooperative behavior. In casual usage, the label "prisoner's dilemma" may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it difficult or expensive—not necessarily impossible—to coordinate their activities.

As a second source, Investopedia says this on the topic:

The prisoner's dilemma is a paradox in decision analysis in which two individuals acting in their own self-interests do not produce the optimal outcome. The typical prisoner's dilemma is set up in such a way that both parties choose to protect themselves at the expense of the other participant. As a result, both participants find themselves in a worse state than if they had cooperated with each other in the decision-making process. The prisoner's dilemma is one of the most well-known concepts in modern game theory.

And finally, MacMillian Dictionary defines the Prisoner's Dilemma as this:

an idea from game theory that two rational individuals may not cooperate even if it is in their best interests to do so

In your example, the drivers could both fall into order and make their turn, but they choose not to coordinate and it results in them both missing their turn.

If you are still interested in this game/idea/idiom, I would check out the following Stanford article:

Standford.edu - Prisoner's Dilemma (a very philosophical and technical look at the prisoner's dilemma which is unrelated to your question- still interesting though)

Much of the game theory of the Cold War dealt with MAD or Mutual Assured Destruction, where the United States and Soviet Union went to great effort to demonstrate they would have the capability to destroy the other no matter what was targeted as a first strike, thus deterring a major war, and so denying both sides a "win".

"Poison Pill" comes to mind, it's used by businesses to have harm any other business that tries to hostilily take over that company, such as buying 50% of their shares on the stock market.

"Poisoning the well" and "Salt the earth" come to mind, both destroy the land, so that no one can live in a particular town. This was done in ancient times when people had to flee an invading army, they would poison the water supply. Salting the earth literally means to throw salt in the fields so that crops can never grow again.

The answer you may be looking for is that colourful American phrase the no-win scenario, also known as the lose-lose scenario, where neither side can achieve victory.

It isn't always used to imply that one side is intentionally depriving the other of victory, but that is one situation in which the expression is applicable.

It is stronger than a scorched earth policy, which does not deny the other victory but only denies him the fruits of victory. In its ultimate expression it is indeed mad (mutual assured destruction), but it applies equally to less apocalyptic situations.

The recently threatened vaccine war between Britain and the EU -- a topical example -- was reported in British newspapers as a lose-lose situation, in which the EU was bound to lose because Britain had the ability to cut off the supplies with which the EU was manufacturing the vaccines that it wanted to prevent being exported.

A common phrase is: "it's not enough to win, others must lose."

This has been attributed to Gore Vidal and Somerset Maugham (as well as Genghis Khan - no doubt on account of his fearsome reputation).

Personally, I think of it as a species of low wit. It's no basis on which to base a philosophy of life and nor a political culture on.

The word "gridlock" comes to mind. It refers to a situation in which no one can make progress because no one involved would compromise. We can say that someone is trapped in a gridlock situation or he is employing a gridlock strategy. If someones adopts a gridlock strategy, he makes sure that "if he can not win, no one else will win".