There is a growing trend to design hybrid neural networks (HNNs) by combining spiking neural networks and artificial neural networks to leverage the strengths of both. Here, we propose a framework for general design and computation of HNNs by introducing hybrid units (HUs) as a linkage interface. The framework not only integrates key features of these computing paradigms but also decouples them to improve flexibility and efficiency. HUs are designable and learnable to promote transmission and modulation of hybrid information flows in HNNs. Through three cases, we demonstrate that the framework can facilitate hybrid model design. The hybrid sensing network implements multi-pathway sensing, achieving high tracking accuracy and energy efficiency. The hybrid modulation network implements hierarchical information abstraction, enabling meta-continual learning of multiple tasks. The hybrid reasoning network performs multimodal reasoning in an interpretable, robust and parallel manner. This study advances cross-paradigm modeling for a broad range of intelligent tasks.

Bundling can change consumers' choice set and affect their purchase decision. It is well documented that consumers' preferences depend on the bundling context. In this paper, we investigate the effects of consumers' context-dependent preferences (CDPs) on the firm's optimal bundling strategy in various competitive situations. We consider a market where a monopolist firm in product category A also sells a product in product category B. We analyze three scenarios in category B: (1) an independent firm selling a higher quality product, (2) two independent firms selling the higher quality product, and (3) the monopolist in category A is also a monopolist in category B. We find that CDPs can indeed change the firm's optimal bundling strategy. When the firm has a competitive disadvantage in category B, CDPs encourage the firm to offer the bundle (by either pure bundling or mixed bundling). Furthermore, if category B market is so competitive that the firm possesses negligible market power, mixed bundling can be strictly more effective at increasing the firm's profit than pure bundling because mixed bundling can better take advantage of CDPs. In contrast, if the firm has monopoly power in both categories, CDPs discourage the introduction of the bundle, and pure-component selling is optimal.

W e consider add-on pricing in a distribution channel where a retailer sells a base good and an add-on, supplied by two manufacturers, respectively, to consumers. The retailer decides whether to sell the two products through either bundling or add-on pricing and sets the corresponding retail prices. Under add-on pricing, the add-on price is unobservable to consumers when they make the purchase decision of the base good. Each manufacturer, if independent of the retailer, sets the wholesale price. Under four channel structures differed by whether either manufacturer is independent of the retailer, we specify the scenario that is optimal for the retailer to adopt add-on pricing and show the contrasting impact from the two manufacturers. When all three firms are integrated, the retailer in general prefers add-on pricing to bundling when the cost of base good is low and the cost of add-on is high. Using this case as the benchmark, we show that add-on pricing is more (less) likely to be adopted when the add-on (base) manufacturer is independent, and add-on pricing is again more likely to be adopted when all three firms are independent. In addition to the demand smoothing effect of bundling, we identify two drivers from the supply side: the margin squeezing effect of bundling from the addon manufacturer and the margin smoothing effect of bundling from the base manufacturer, where the former encourages add-on pricing whereas the latter discourages it. The interplay of these drivers largely influences the retailer's add-on strategy and renders the preceding results. Several extensions are discussed, including correlated consumer valuations of base good and add-on, an alternate decision sequence, knowledgeable consumers (about add-on price), simultaneous offering of bundling and add-on pricing, and bilateral monopoly.

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