Still fascinated by celestial mechanics, K�hler wrote a dissertation entitled, " On the existence of equilibrium solutions of rotating liquids, which are derived from certain solutions of the n-body problem ", and received his doctorate in 1928.
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Schelling himself illustrated this concept with the following problem : " Tomorrow you have to meet a stranger in NYC . Where and when do you meet them ? " This is a coordination game, where any place and time in the city could be an equilibrium solution.
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One of the essential questions he introduces, often referred to as the Hahn's problem is : " Can one construct an equilibrium where money has value ? " The goal is to find models in which existence of money can alter the equilibrium solutions, perhaps because the initial position of agents depends on monetary prices.
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His research to date includes a number of key results in such diverse areas as : hyperbolic systems of conservation laws and nonlinear wave equations, impulsive control of Lagrangian system, systems of Hamilton Jacobi equations ( related to non-cooperative differential games ), Nash equilibrium solutions in feedback form for infinite-horizon, discounted differential games, dynamic blocking problems ( mathematical models of wild fire confinement ), and optimization problems for elliptic equations.
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