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We consider infinite-horizon linear-quadratic differential games (LQDGs) with a state-feedback information structure and guaranteed cost equilibrium (GCE) as the solution concept. Once the players reach a GCE, no player has an incentive to deviate from the equilibrium strategy, as each has achieved a desired upper bound on her cost. In this work, we provide conditions for the existence of a GCE in scalar LQDGs and investigate the related welfare properties. Furthermore, we specialize these results to symmetric and two-player scenarios. (with Aniruddha Roy)