Non-credible threat

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."^[1] While a player might make a threat, it is only deemed credible if it serves the best interest of the player.^[2] 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.^[3] This is based on the assumption that the player is rational.^[1]

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.^[4] For a threat to be credible within an equilibrium, whenever a node is reached where a threat should be fulfilled, it will be fulfilled.^[3] Those Nash equilibria that rely on non-credible threats can be eliminated through backward induction; the remaining equilibria are called subgame perfect Nash equilibria.^[2]^[5]

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.^[1]

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.^[4]

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.^[6] 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.^[7]

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."^[8] 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.^[8] In real world applications, non-credible threats must be considered as there is a high possibility players will not act rationally.^[7]

Notes

^ ^a ^b ^c Sun, Shaorong; Sun, Na (2018). Management Game Theory. doi:10.1007/978-981-13-1062-1. ISBN 978-981-13-1061-4. S2CID 169075970.
^ ^a ^b Heifetz, A., & Yalon-Fortus, J. (2012). Game Theory: Interactive Strategies in Economics and Management. Cambridge University Press. ProQuest Ebook Central
^ ^a ^b Schelling, Thomas C. (1956). "An Essay on Bargaining". The American Economic Review. 46 (3): 281–306. JSTOR 1805498.
^ ^a ^b van Damme, Eric (1989). "Extensive Form Games". In Eatwell, J.; Milgate, M.; Newman, P. (eds.). Game Theory. Palgrave Macmillan. pp. 139–144. ISBN 978-1-349-20181-5.
^ Harrington, J. E. (1989). "Noncooperative Games". In Eatwell, John; Milgate, Murray; Newman, Peter (eds.). Game Theory. Palgrave Macmillan. pp. 178–184. doi:10.1007/978-1-349-20181-5. ISBN 978-1-349-20181-5.
^ Monahan, K. (2018). How Behavioral Economics Influences Management Decision-Making: A New Paradigm. Academic Press. doi:10.1016/C2016-0-05106-9. ISBN 9780128135310.
^ ^a ^b Khalil, Elias L. (2011). "Rational, Normative and Procedural Theories of Beliefs: Can They Explain Internal Motivations?". Journal of Economic Issues. 45 (3): 641–664. doi:10.2753/JEI0021-3624450307. S2CID 143987777.
^ ^a ^b Jacquemet, Nicolas; Zylbersztejn, Adam (June 2014). "What Drives Failure to Maximize Payoffs in the Lab? A Test of the Inequality Aversion Hypothesis". doi:10.2139/ssrn.1895287. S2CID 219374150. SSRN 1895287. {{cite journal}}: Cite journal requires |journal= (help)

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.

This game theory article is a stub. You can help Wikipedia by expanding it.

[sun-1] Sun, Shaorong; Sun, Na (2018). Management Game Theory. doi:10.1007/978-981-13-1062-1. ISBN 978-981-13-1061-4. S2CID 169075970.

[heifetz-2] Heifetz, A., & Yalon-Fortus, J. (2012). Game Theory: Interactive Strategies in Economics and Management. Cambridge University Press. ProQuest Ebook Central

[schelling-3] Schelling, Thomas C. (1956). "An Essay on Bargaining". The American Economic Review. 46 (3): 281–306. JSTOR 1805498.

[VanDamme-4] van Damme, Eric (1989). "Extensive Form Games". In Eatwell, J.; Milgate, M.; Newman, P. (eds.). Game Theory. Palgrave Macmillan. pp. 139–144. ISBN 978-1-349-20181-5.

[5] Harrington, J. E. (1989). "Noncooperative Games". In Eatwell, John; Milgate, Murray; Newman, Peter (eds.). Game Theory. Palgrave Macmillan. pp. 178–184. doi:10.1007/978-1-349-20181-5. ISBN 978-1-349-20181-5.

[6] Monahan, K. (2018). How Behavioral Economics Influences Management Decision-Making: A New Paradigm. Academic Press. doi:10.1016/C2016-0-05106-9. ISBN 9780128135310.

[Khalil-7] Khalil, Elias L. (2011). "Rational, Normative and Procedural Theories of Beliefs: Can They Explain Internal Motivations?". Journal of Economic Issues. 45 (3): 641–664. doi:10.2753/JEI0021-3624450307. S2CID 143987777.

[Jacquemet-8] Jacquemet, Nicolas; Zylbersztejn, Adam (June 2014). "What Drives Failure to Maximize Payoffs in the Lab? A Test of the Inequality Aversion Hypothesis". doi:10.2139/ssrn.1895287. S2CID 219374150. SSRN 1895287. {{cite journal}}: Cite journal requires |journal= (help)

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v t e Topics of game theory
Definitions	Congestion game Cooperative game Determinacy Escalation of commitment Extensive-form game First-player and second-player win Game complexity Graphical game Hierarchy of beliefs Information set Normal-form game Preference Sequential game Simultaneous game Simultaneous action selection Solved game Succinct game Mechanism design
Equilibrium concepts	Bayes correlated equilibrium Bayesian Nash equilibrium Berge equilibrium Core Correlated equilibrium Coalition-proof Nash equilibrium Epsilon-equilibrium Evolutionarily stable strategy Gibbs equilibrium Mertens-stable equilibrium Markov perfect equilibrium Nash equilibrium Pareto efficiency Perfect Bayesian equilibrium Proper equilibrium Quantal response equilibrium Quasi-perfect equilibrium Risk dominance Satisfaction equilibrium Self-confirming equilibrium Sequential equilibrium Shapley value Strong Nash equilibrium Subgame perfection Trembling hand equilibrium
Strategies	Appeasement Backward induction Bid shading Collusion Cheap talk De-escalation Deterrence Escalation Forward induction Grim trigger Markov strategy Pairing strategy Dominant strategies Pure strategy Mixed strategy Strategy-stealing argument Tit for tat
Classes of games	Auction Bargaining problem Global game Intransitive game Mean-field game n-player game Perfect information Large Poisson game Potential game Repeated game Screening game Signaling game Strictly determined game Stochastic game Symmetric game Zero-sum game
Games	Go Chess Infinite chess Checkers All-pay auction Prisoner's dilemma Gift-exchange game Optional prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Lewis signaling game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Electronic mail game Rock paper scissors Pirate game Dictator game Public goods game Blotto game War of attrition El Farol Bar problem Fair division Fair cake-cutting Bertrand competition Cournot competition Stackelberg competition Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Induction puzzles Trust game Princess and monster game Rendezvous problem
Theorems	Aumann's agreement theorem Folk theorem Minimax theorem Nash's theorem Negamax theorem Purification theorem Revelation principle Sprague–Grundy theorem Zermelo's theorem
Key figures	Albert W. Tucker Amos Tversky Antoine Augustin Cournot Ariel Rubinstein Claude Shannon Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin John Conway Jean Tirole Jean-François Mertens Jennifer Tour Chayes John Harsanyi John Maynard Smith John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Olga Bondareva Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Axelrod Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Suzanne Scotchmer Thomas Schelling William Vickrey
Search optimizations	Alpha–beta pruning Aspiration window Principal variation search max^n algorithm Paranoid algorithm Lazy SMP
Miscellaneous	Bounded rationality Combinatorial game theory Confrontation analysis Coopetition Evolutionary game theory Glossary of game theory List of game theorists List of games in game theory No-win situation Topological game Tragedy of the commons