Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a seller with $$k$$ types of items, $$m$$ of each, a sequence of users $$\{u_1, u_2,\ldots \}$$ arrive one by one. Each user is single-minded, i.e., each user is interested only in a particular bundle of items. The seller must set the price and assign some amount of bundles to each user upon his/her arrival. Bundles can be sold fractionally. Each $$u_i$$ has his/her value function $$v_i(\cdot )$$ such that $$v_i(x)$$ is the highest unit price $$u_i$$ is willing to pay for $$x$$ bundles. The objective is to maximize the revenue of the seller by setting the price and amount of bundles for each user. ,  first show that a lor bound of the competitive ratio for this problem is $$\Omega (\log h+\log k)$$ , where $$h$$ is the highest unit price to be paid among all users.  then give a deterministic online algorithm, Pricing, whose competitive ratio is $$O(\sqrt{k}\cdot \log h\log k)$$ . When $$k=1$$ the lor and upper bounds asymptotically match the optimal result $$O(\log h)$$ .
['Yong Zhang', 'Francis Y. L. Chin', 'Hing-Fung Ting']
I am writing a research paper on a idea Online pricing for bundles of multiple items
[{"from": "human", "value": "I am writing a research paper on a idea Online pricing for bundles of multiple items"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a seller with $$k$$ types of items, $$m$$ of each, a sequence of users $$\\{u_1, u_2,\\ldots \\}$$ arrive one by one. Each user is single-minded, i.e., each user is interested only in a particular bundle of items. The seller must set the price and assign some amount of bundles to each user upon his/her arrival. Bundles can be sold fractionally. Each $$u_i$$ has his/her value function $$v_i(\\cdot )$$ such that $$v_i(x)$$ is the highest unit price $$u_i$$ is willing to pay for $$x$$ bundles. The objective is to maximize the revenue of the seller by setting the price and amount of bundles for each user. ,  first show that a lor bound of the competitive ratio for this problem is $$\\Omega (\\log h+\\log k)$$ , where $$h$$ is the highest unit price to be paid among all users.  then give a deterministic online algorithm, Pricing, whose competitive ratio is $$O(\\sqrt{k}\\cdot \\log h\\log k)$$ . When $$k=1$$ the lor and upper bounds asymptotically match the optimal result $$O(\\log h)$$ ."}]