No-win situation

A no-win situation, also called a “lose-lose situation”, is one where a person has choices, but no choice leads to a net gain. For example, if an executioner offers the condemned the choice of dying by being hanged, shot, or poisoned, since all choices lead to death, the condemned is in a no-win situation. This bleak situation gives the chooser little room: whatever choice is made, the person making it will lose their life. Less drastic situations might also be considered no-win situations: if one has a choice for lunch between a ham sandwich and a roast beef sandwich, but is a vegetarian or has a wheat allergy, that might be considered a no-win situation.

In game theory

In game theory, a "no-win" situation is one in which no player benefits from any outcome. This may be because of any or all of the following:

Unavoidable or unforeseeable circumstances causing the situation to change after decisions have been made. This is common in Text adventures.
Zugzwang, as in chess, when any move a player chooses makes him worse off than before
A situation in which the player has to accomplish two mutually dependent tasks each of which must be completed before the other or that are mutually exclusive (a Catch-22)^[1]
Ignorance of other players' actions, meaning the best decision for all differs from that for any one player (as in the Prisoner's Dilemma).

In history

Carl von Clausewitz's advice (never to launch a war that one has not already won) characterizes war as a no-win situation. A similar example is the Pyrrhic victory, in which a military victory is so costly that the winning side actually ends up worse off than before it started. Looking at the victory as a part of a larger situation, the situation could either be no-win, or more of a win for the other side than the one that won the "victory", or victory at such cost that the gains are outweighed by the cost and are no longer a source of joy.

For example, the "victorious" side may have accomplished their objective, but the objective may have been worthless, or they may lose a strategic advantage in manpower or positioning. A related concept is sometimes described as winning the battle but losing the war, where a lesser (sub-) objective is won but the true objective beyond it is not well pursued and is lost.

In past Europe, those accused of being witches were sometimes bound and then thrown or dunked in water to test their innocence. A witch would float (by calling upon the Devil to save her from drowning), and then be executed; but a woman not a witch would drown (proving her innocence but causing her death).^[2]

In video games

Unwinnable is a state in many text adventures, graphical adventure games and role-playing video games where it is impossible for the player to win the game (either due to a bug or by design), and where the only options are restarting the game, loading a previously saved game, wandering indefinitely, or a game over (negative game end, such as death). It is also known as a dead end situation. Usually, this is the result of the player's previous choices, and not due to the game itself lacking a path to victory. For example, in games such as Goldeneye 007, Perfect Dark, or TimeSplitters, the level does not end once a player fails an objective short of being killed, but it is impossible to progress to the next level no matter what the player does afterwards. Other games take steps to avoid unwinnable situations; for example, a game may not allow players to drop items which are necessary to continue.

Unwinnable should not be confused with "unbeatable", which is used to describe a character, monster, or puzzle that is too powerful or difficult to be overcome by the player or character at a lower standing, and is normally found in role-playing video games. In many cases, "unbeatable" gamestates occur because of integer overflow or other errors programmers did not take into account, called a kill screen. In this situation, the game may also crash.

In other media

In the film WarGames, the supercomputer WOPR simulates all possible games of Tic-tac-toe as a metaphor for all possible scenarios of a nuclear war, each of them ending in a nuclear holocaust (mutual assured destruction). The computer then exclaims, "A strange game; the only winning move is not to play."

In the Star Trek canon, the Kobayashi Maru simulation is a no-win scenario designed as a character test for command track cadets at Starfleet Academy. It first appears in the film Star Trek II: The Wrath of Khan. In the film, Admiral James T. Kirk claims that he doesn't believe in the no-win situation.

References

↑ First-Year Reading tackles Catch-22 Archived December 2, 2008, at the Wayback Machine.
↑ BBC - h2g2 - Matthew Hopkins, 'Witchfinder General' of East Anglia

Leon F Seltzer Ph.D (2013) Two Ways to "Win" in a No-Win Situation

Topics in game theory

Definitions	Normal-form game Extensive-form game Escalation of commitment Graphical game Cooperative game Succinct game Information set Hierarchy of beliefs Preference

Equilibrium concepts	Nash equilibrium Subgame perfection Mertens-stable equilibrium Bayesian-Nash Perfect Bayesian Trembling hand Proper equilibrium Epsilon-equilibrium Correlated equilibrium Sequential equilibrium Quasi-perfect equilibrium Evolutionarily stable strategy Risk dominance Core Shapley value Pareto efficiency Quantal response equilibrium Self-confirming equilibrium Strong Nash equilibrium Markov perfect equilibrium

Strategies	Dominant strategies Pure strategy Mixed strategy Tit for tat Grim trigger Collusion Backward induction Forward induction Markov strategy

Classes of games	Symmetric game Perfect information Simultaneous game Sequential game Repeated game Signaling game Cheap talk Zero-sum game Mechanism design Bargaining problem Stochastic game n-player game Large Poisson game Nontransitive game Global games Strictly determined game

Games	Prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock-paper-scissors Pirate game Dictator game Public goods game Blotto games War of attrition El Farol Bar problem Fair division Fair cake-cutting Cournot game Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Screening game Prisoners and hats puzzle Trust game Princess and monster game Monty Hall problem Rendezvous problem

Theorems	Minimax theorem Nash's theorem Purification theorem Folk theorem Revelation principle Arrow's impossibility theorem

Key figures	Albert W. Tucker Amos Tversky Ariel Rubinstein Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin Jean Tirole Jean-François Mertens John Harsanyi John Maynard Smith John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Thomas Schelling William Vickrey

See also	All-pay auction Alpha–beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition List of game theorists List of games in game theory No-win situation Tragedy of the commons Tyranny of small decisions

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