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

<P0-S0> "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. <P0-S1>  It was in reference to the Constitution of the Kingdom of Prussia, which was established following the revolutions of 1848. <P0-S2>  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. <SEP> <P1-S0> 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. <P1-S1>  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. <P1-S2>  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. <SEP> <P2-S0> 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. <P2-S1>  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. <P2-S2>  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. <P2-S3>  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. <SEP> <P3-S0> 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. <P3-S1>  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. <P3-S2>  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. <P3-S3>  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". <P3-S4>  However, his annexation of Alsace-Lorraine gave new fuel to French nationalism and promoted Germanophobia in France. <P3-S5>  This helped set the stage for the First World War.