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 a win for the other side than the one that won the "victory". 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.

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. 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".

References

[1] First-Year Reading tackles Catch-22 ^{[dead link]}

[2] BBC - h2g2 - Matthew Hopkins, 'Witchfinder General' of East Anglia

[1]

[2]

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

In game theory

In history

In video games

In other media

See also

References