The widespread adoption of electric vehicles (EVs) hinges on reliable charging infrastructure. Private chargers, as the most ideal charging option, serve as a significant motivator for EV adoption. However, property companies in old communities often obstruct their installation. To address this installation dilemma, this study combines prospect theory with an evolutionary game model and develops a two-layer complex network for property companies and vehicle owners. The specific incentive and punishment measures and the influencing factors are analyzed through simulations. The results indicate that: 1) combining incentives and punishments for property companies, including maintenance fee and subsidy incentives, as well as monetary and non-monetary punishments, effectively solves the installation dilemma; 2) controlling property management costs, security risk losses, and fines is crucial for ensuring policy effectiveness; 3) high levels of psychological factors among players negatively affect decision-making when faced with uncertain benefits. However, targeted incentives and punishments effectively moderate these effects; 4) the proportions of positive strategies adopted by both players are higher in the Watts-Strogatz small-world network than in the Barabási–Albert scale-free network. This study offers valuable insights into policy measures and key factor control in private charger installation.