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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 his 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.

Contents 1 In game theory 2 In history 3 In fiction 4 See also 5 References

[edit] In game theory

In game theory, a "no-win" situation is one in which no player benefits from any outcome (Adversely, a situation in which the involved person can win either way is called a securvian fortune). This may be because of:

• Unavoidable or unforeseeable circumstances causing the situation to change after decisions have been made
• 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).

[edit] 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 Europe before the Reformation 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]

[edit] In fiction

• A no-win situation has become part of the Star Trek mythos in the Kobayashi Maru scenario. In this test, cadets assume the position of commanders on a starship that intercepts an SOS from an allied ship in enemy territory. If they ignore the SOS the ship is eventually attacked and destroyed, with no survivors. But if they decide to enter enemy territory to rescue the other ship they are led in to a trap, and are overwhelmed and destroyed by enemy ships. Cadets are not told until after the test that the simulation is impossible to win; it is meant as a test of character.

• In the film WarGames, the expression "no-win situation" was interpreted to mean a global nuclear war. An artificial intelligence program named "Joshua", assumes control of the US nuclear arsenal from the WOPR supercomputer that operates it, and attemptes to start a nuclear war against the USSR, believing the scenario to be a game. The protagonist gets Joshua to play itself at tic-tac-toe, and after hundreds of instantaneous stalemates, it starts to simulate all the strategies it developed for nuclear war. Discovering that every single strategy leads to the end of planet Earth, it determines that "the only winning move is not to play", and stands down aborting its attempt to use the arsenal which it was on the brink of success of doing.

[edit] See also

• Cornelian dilemma
• Winner's curse
• Catch-22 (logic)
• Double bind
• Win-win

[edit] References

v • d • e Topics in game theory Definitions Normal-form game · Extensive-form game · Cooperative game · Information set · Preference Equilibrium concepts Nash equilibrium · Subgame perfection · Bayesian-Nash · Perfect Bayesian · Trembling hand · Proper equilibrium · Epsilon-equilibrium · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy · Risk dominance · Pareto efficiency · Quantal response equilibrium · Self-confirming equilibrium Strategies Dominant strategies · Pure strategy · Mixed strategy · Tit for tat · Grim trigger · Collusion · Backward induction 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 · Large poisson game · Nontransitive game · Global games 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 · Minority game · Rock-paper-scissors · Pirate game · Dictator game · Public goods game · Blotto games · War of attrition · El Farol Bar problem · Cake cutting · Cournot game · Deadlock · Diner's dilemma · Guess 2/3 of the average · Kuhn poker · Nash bargaining game · Screening game · Trust game · Princess and monster game Theorems Minimax theorem · Purification theorem · Folk theorem · Revelation principle · Arrow's impossibility theorem See also Tragedy of the commons · All-pay auction · List of games in game theory