Question: Otto von Bismarck used Lückentheorie while under Prussian leadership in which empire?

Context paragraphs:
Herbert von Bismarck: Nicolaus Heinrich Ferdinand Herbert, Prince von Bismarck (28 December 1849 – 18 September 1904) was a German politician, who served as Foreign Secretary from 1886 to 1890.  His political career was closely tied to that of his father, Otto von Bismarck, and he left office a few days after his father's dismissal.  He succeeded his father as the 2nd Prince of Bismarck in 1898.  He was born in Berlin and died in Friedrichsruh.

A Dream, What Else?: A Dream, What Else?  (German: Ein Traum, was sonst? )  is a 1995 Austrian-German drama film written and directed by Hans-Jürgen Syberberg.  It stars Edith Clever as Sybille von Bismarck, the daughter-in-law of Otto von Bismarck.  The film consists of a monologue where the main character, aged and widowed, mourns the defeat of Prussia at the end of World War II.  She recites from "The Trojan Women" by Euripides, "The Prince of Homburg" by Heinrich von Kleist and "" by Johann Wolfgang von Goethe.

Wilhelm von Bismarck: Count Wilhelm von Bismarck-Schönhausen (né "Wilhelm Otto Albrecht von Bismarck") (1 August 1852 – 30 May 1901) was a German counselor, civil servant and politician, who served as a member of the Reichstag from 1880 to 1881 and president of the Regency of Hanover from 1889 to 1890.  The youngest son of Otto von Bismarck, he and his brother Herbert von Bismarck both resigned their posts after the elder Bismarck was dismissed as Chancellor of Germany in 1890.  Wilhelm subsequently accepted an appointment as Governor of East Prussia in 1894.

Otto von Bismarck: Otto Eduard Leopold, Prince of Bismarck, Duke of Lauenburg (1 April 1815 – 30 July 1898), known as Otto von Bismarck (] ), was a conservative Prussian statesman who dominated German and European affairs from the 1860s until 1890.  In the 1860s, he engineered a series of wars that unified the German states, deliberately excluding Austria, into a powerful German Empire under Prussian leadership.  With that accomplished by 1871, he skillfully used balance of power diplomacy to maintain Germany's position in a Europe which, despite many disputes and war scares, remained at peace.  For historian Eric Hobsbawm, it was Bismarck who "remained undisputed world champion at the game of multilateral diplomatic chess for almost twenty years after 1871, [and] devoted himself exclusively, and successfully, to maintaining peace between the powers".  However, his annexation of Alsace-Lorraine gave new fuel to French nationalism and promoted Germanophobia in France.  This helped set the stage for the First World War.

Treaty of Berlin (1889): The Treaty of Berlin (1889) was the concluding document of the conference at Berlin in 1889 on Samoa.  The conference was proposed by German foreign minister Count Herbert von Bismarck (son of chancellor Otto von Bismarck) to reconvene the adjourned Washington conference on Samoa of 1887.  Herbert von Bismarck invited delegations from the United States and the British Empire to Berlin in April 1889.

Mona von Bismarck: Mona von Bismarck (February 5, 1897 – July 10, 1983), known as Mona Bismarck, was an American socialite, fashion icon, and famed beauty.  Her five husbands included Harrison Williams, said to be the richest man in America, and the Graf von Bismarck-Schönhausen, grandson of German Chancellor Otto von Bismarck.  Mona was the first American to be named "The Best Dressed Woman in the World" by a panel of top couturiers including Chanel, and was also named to the International Best Dressed List Hall of Fame.

Lückentheorie: "Lückentheorie" (] , "gap theory") refers to the theory that when the Crown and the Parliament were unable to come to agreement, the Crown could act as it sees fit.  It was in reference to the Constitution of the Kingdom of Prussia, which was established following the revolutions of 1848.  Its political use occurred in 1862 when Otto von Bismarck used it to justify proceeding with taxes for military reforms over the opposition of the Parliament to avoid a constitutional crisis.

Fürst von Bismarck: The great German statesman and diplomat Otto von Bismarck (1815–1898) received several noble titles during the course of his career.  Already born into a noble Junker family, the House of Bismarck, he began life as simply "Mr (German:"Herr") Otto Eduard Leopold von Bismarck".

Franco-Prussian War: The Franco-Prussian War or Franco-German War (German: "Deutsch-Französischer Krieg" , French: "Guerre franco-allemande" ), often referred to in France as the War of 1870 (19 July 1870 – 10 May 1871), was a conflict between the Second French Empire of Napoleon III and the German states of the North German Confederation led by the Kingdom of Prussia.  The conflict was caused by Prussian ambitions to extend German unification and French fears of the shift in the European balance of power that would result if the Prussians succeeded.  Some historians argue that the Prussian chancellor Otto von Bismarck deliberately provoked a French attack in order to draw the independent southern German states—Baden, Württemberg, Bavaria and Hesse-Darmstadt—into an alliance with the North German Confederation dominated by Prussia, while others contend that Bismarck did not plan anything and merely exploited the circumstances as they unfolded.

William I, German Emperor: William I, or in German Wilhelm I (full name: "William Frederick Louis of Hohenzollern", German: "Wilhelm Friedrich Ludwig von Hohenzollern" , 22 March 1797 – 9 March 1888), of the House of Hohenzollern was King of Prussia from 2 January 1861 and the first German Emperor from 1 January 1871 to his death, the first Head of State of a united Germany.  Under the leadership of William and his Minister President Otto von Bismarck, Prussia achieved the unification of Germany and the establishment of the German Empire.  Despite his long support of Otto von Bismarck as Minister President, William held strong reservations about some of Bismarck's more reactionary policies, including his anti-Catholicism and tough handling of subordinates.  Contrary to the domineering Bismarck, William was described as polite, gentlemanly and, while a staunch conservative, more open to certain classical liberal ideas than his grandson Wilhelm II.

Supporting paragraphs: Lückentheorie Otto von Bismarck
Answer: German Empire