science

Non-credible threat

Non-credible threat is a science 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 Non-credible threat rather than just read about it. In short: A non-credible threat is a term used in game theory and economics to describe a threat in a sequential game that a rational player would not actually carry out, because it would not be in his best interest to do so. A threat, and its counterpart – a commitment, are both defined by American economist and Nobel prize winner, T.C.

Key takeaways

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

Reference excerpt

A non-credible threat is a term used in game theory and economics to describe a threat in a sequential game that a rational player would not actually carry out, because it would not be in his best interest to do so. A threat, and its counterpart – a commitment, are both defined by American economist and Nobel prize winner, T.C. Schelling, who stated that: "A announces that B's behaviour will lead to a response from A. If this response is a reward, then the announcement is a commitment; if this response is a penalty, then the announcement is a threat." While a player might make a threat, it is only deemed credible if it serves the best interest of the player. In other words, the player would be willing to carry through with the action that is being threatened regardless of the choice of the other player. This is based on the assumption that the player is rational. A non-credible threat is made on the hope that it will be believed, and therefore the threatening undesirable action will not need to be carried out. For a threat to be credible within an equilibrium, whenever a node is reached where a threat should be fulfilled, it will be fulfilled. Those Nash equilibria that rely on non-credible threats can be eliminated through backward induction; the remaining equilibria are called subgame perfect Nash equilibria.

Examples of non-credible threats

Market entry game An example of a non-credible threat is demonstrated by Shaorong Sun & Na Sun in their book Management Game Theory. The example game, the market entry game, describes a situation in which an existing firm, firm 2, has a strong hold on the market and a new firm, firm 1, is considering entering. If firm 1 doesn't enter, the payoff is (4,10). However, if firm 1 does enter, firm 2 has the choice to either attack or not attack. If firm 2 attacks, the payoff is (3,3) whereas if firm 2 doesn't attack, the payoff is (6,6). Given that firm 2's optimum payoff is firm 1 not entering, it can issue a threat that they will attack if firm 1 enters, to discourage firm 1 from entering the market. However, this is a non-credible threat. If firm 1 does decide to enter the market, the action that is in the best interest for firm 2 is to not attack as this leads to a payoff of 6 for the firm, as opposed to the payoff of 3 from attacking.

Eric van Damme's Extensive Form Game Eric van Damme's Extensive Form Game demonstrates another example of a non-credible threat. In this game, player 1 has the choice of L or R, and if player 1 chooses R, then player 2 has the choice of l or r. Player 2 can threaten choosing l with a payoff of (0,0) to entice player 1 to choose L with a payoff of (2,2), as this is the highest payoff for player 2. However, this is a non-credible threat as, if player 1 does decide to choose R, player 2 will choose r as their payoff is 1 as opposed to l which has a payoff of 0 for player 2. Given that action l is not in player 2's best interest, their threat to play that is non-credible.

Rationality The notion of credibility is contingent on the principle of rationality. A rational player always make decisions that maximise their own utility, however, players are not always rational. Therefore, in real world applications, the assumption that all players will be rational and act to maximise their utility is not practical, thus non-credible threats cannot be ignored.

Experiment using the Beard and Beil Game (1994) Nicolas Jacquemet and Adam Zylbersztejn conducted experiments based on the Beard and Beil Game to investigate whether people act to maximise their payoffs. From the study Jacquemet and Zylbersztejn found that failure to maximise utility stemmed from two observations: "subjects are not willing to rely on others’ self-interested maximization, and self-interested maximization is not ubiquitous." A key component of the utility maximising strategy in the game was the elimination of non-credible threats, however, the study found that suboptimal payoffs were a direct result of players following through on these non-credible threats. In real world applications, non-credible threats must be considered as there is a high possibility players will not act rationally.

See also Dynamic inconsistency Subgame perfect equilibrium

Notes

External links Schelling, Thomas C. (1956). "An Essay on Bargaining". The American Economic Review. 46 (3): 281–306. JSTOR 1805498. Ellsberg, Daniel. The theory and practice of blackmail. No. RAND/P-3883. RAND CORP SANTA MONICA CA, 1968. Uri Weiss, 2015. "The Robber Wants To Be Punished," Discussion Paper Series dp685, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

Illustrations

Non-credible threat: Player 2 threatening action an if Player 1 chooses action B is a non-credible threat. This is because if Player 1 chooses action B, Player 2 will choose action b, as this results in a higher payoff than action a for Player 2. — Player 2 threatening action an if Player 1 chooses action B is a non-credible threat. This is because if Player 1 chooses action B, Player 2 will choose action b, as this results in a higher payoff than action a for Player 2.

Worked examples

Example 1 — a first encounter with Non-credible threat

Start with the simplest possible case. Write down what Non-credible threat claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 Non-credible threat 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 Non-credible threat 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 Non-credible threat

In research: Non-credible threat appears in science 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 Non-credible threat 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: Non-credible threat is common in secondary-school and first-year university syllabi. It links to neighbouring topics Game theory, so understanding it makes those chapters shorter.
In everyday life: Look for Non-credible threat 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.

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How to study Non-credible threat in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Non-credible threat 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 Non-credible threat out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Non-credible threat in simple terms?

Why does Non-credible threat matter?

Because it connects several science 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 Non-credible threat?

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 Non-credible threat.