mathematics

Homicidal chauffeur problem

Homicidal chauffeur problem is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Homicidal chauffeur problem rather than just read about it. In short: In game theory, the homicidal chauffeur problem is a mathematical pursuit problem which pits a hypothetical runner, who can only move slowly, but is highly maneuverable, against the driver of a motor vehicle, which is much faster but far less maneuverable, who is attempting to run him down. Both runner and driver are assumed to never tire.

Key takeaways

Homicidal chauffeur problem belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Homicidal chauffeur problem to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Homicidal chauffeur problem from memory before moving on to harder problems.

Reference excerpt

In game theory, the homicidal chauffeur problem is a mathematical pursuit problem which pits a hypothetical runner, who can only move slowly, but is highly maneuverable, against the driver of a motor vehicle, which is much faster but far less maneuverable, who is attempting to run him down. Both runner and driver are assumed to never tire. The question to be solved is: under what circumstances, and with what strategy, can the driver of the car guarantee that he can always catch the pedestrian, or the pedestrian guarantee that he can indefinitely elude the car? The problem is often used as an unclassified proxy for missile defense and other military targeting, allowing scientists to publish on it without security implications. The problem was proposed by Rufus Isaacs in a 1951 report for the RAND Corporation, and in the book Differential Games. The homicidal chauffeur problem is a classic example of a differential game played in continuous time in a continuous state space. The calculus of variations and level set methods can be used as a mathematical framework for investigating solutions of the problem. Although the problem is phrased as a recreational problem, it is an important model problem for mathematics used in a number of real-world applications. A discrete version of the problem was described by Martin Gardner (in his book Mathematical Carnival, chapter 16), where a squad car of speed 2 chases a crook of speed 1 on a rectangular grid, where the squad car but not the crook is constrained not to make left-hand turns or U-turns.

See also Variational calculus Level-set method Apollonius pursuit problem Conway's angel problem, another mathematical game which pits a powerful and maneuverable adversary against a highly resourceful but less powerful foe Princess and monster game

References

External links History of the Homicidal Chauffeur Problem, presentation at the Colloquium dedicated to the 60th anniversary of Prof. Pierre Bernhard. Analytical study of a case of the homicidal chauffeur game problem Homicidal Chauffeur Game. Computation of Level Sets of the Value Function The Homicidal Chauffeur Problem

Worked examples

Example 1 — a first encounter with Homicidal chauffeur problem

Start with the simplest possible case. Write down what Homicidal chauffeur problem claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Homicidal chauffeur problem before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Homicidal chauffeur problem ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Homicidal chauffeur problem

In research: Homicidal chauffeur problem appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Homicidal chauffeur problem in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Homicidal chauffeur problem is common in secondary-school and first-year university syllabi. It links to neighbouring topics Calculus of variations, Game theory game classes, Multivariable calculus, so understanding it makes those chapters shorter.
In everyday life: Look for Homicidal chauffeur problem outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Homicidal chauffeur problem” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Homicidal chauffeur problem in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Homicidal chauffeur problem means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Homicidal chauffeur problem out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Homicidal chauffeur problem in simple terms?

Why does Homicidal chauffeur problem matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Homicidal chauffeur problem?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Homicidal chauffeur problem.