Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   investigate the computational complexity of motivating time-inconsistent agents to complete long term projects.  resort to an elegant graph-theoretic model, introduced by Kleinberg and Oren, which consists of a task graph $G$ with $n$ vertices, including a source $s$ and target $t$, and an agent that incrementally constructs a path from $s$ to $t$ in order to collect rewards. The twist is that the agent is present-biased and discounts future costs and rewards by a factor $\beta\in [0,1]$. Our design objective is to ensure that the agent reaches $t$ i.e.\ completes the project, for as little reward as possible. Such graphs are called motivating.  consider two strategies. First,  place a single reward $r$ at $t$ and try to guide the agent by removing edges from $G$.  prove that deciding the existence of such motivating subgraphs is NP-complete if $r$ is fixed. More importantly,  generalize our reduction to a hardness of approximation result for computing the minimum $r$ that admits a motivating subgraph. In particular,  show that no polynomial-time approximation to within a ratio of $\sqrt{n}/4$ or less is possible, unless ${\rm P}={\rm NP}$. Furthermore,  develop a $(1+\sqrt{n})$-approximation algorithm and thus settle the approximability of computing motivating subgraphs. Secondly,  study motivating reward configurations, where non-negative rewards $r(v)$ may be placed on arbitrary vertices $v$ of $G$. The agent only receives the rewards of visited vertices. Again  give an NP-completeness result for deciding the existence of a motivating reward configuration within a fixed budget $b$. This result even holds if $b=0$, which in turn implies that no efficient approximation of a minimum $b$ within a ration grater or equal to $1$ is possible, unless ${\rm P}={\rm NP}$.
['Susanne Albers', 'Dennis Kraft']
I am writing a research paper on a idea Motivating Time-Inconsistent Agents: A Computational Approach
[{"from": "human", "value": "I am writing a research paper on a idea Motivating Time-Inconsistent Agents: A Computational Approach"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   investigate the computational complexity of motivating time-inconsistent agents to complete long term projects.  resort to an elegant graph-theoretic model, introduced by Kleinberg and Oren, which consists of a task graph $G$ with $n$ vertices, including a source $s$ and target $t$, and an agent that incrementally constructs a path from $s$ to $t$ in order to collect rewards. The twist is that the agent is present-biased and discounts future costs and rewards by a factor $\\beta\\in [0,1]$. Our design objective is to ensure that the agent reaches $t$ i.e.\\ completes the project, for as little reward as possible. Such graphs are called motivating.  consider two strategies. First,  place a single reward $r$ at $t$ and try to guide the agent by removing edges from $G$.  prove that deciding the existence of such motivating subgraphs is NP-complete if $r$ is fixed. More importantly,  generalize our reduction to a hardness of approximation result for computing the minimum $r$ that admits a motivating subgraph. In particular,  show that no polynomial-time approximation to within a ratio of $\\sqrt{n}/4$ or less is possible, unless ${\\rm P}={\\rm NP}$. Furthermore,  develop a $(1+\\sqrt{n})$-approximation algorithm and thus settle the approximability of computing motivating subgraphs. Secondly,  study motivating reward configurations, where non-negative rewards $r(v)$ may be placed on arbitrary vertices $v$ of $G$. The agent only receives the rewards of visited vertices. Again  give an NP-completeness result for deciding the existence of a motivating reward configuration within a fixed budget $b$. This result even holds if $b=0$, which in turn implies that no efficient approximation of a minimum $b$ within a ration grater or equal to $1$ is possible, unless ${\\rm P}={\\rm NP}$."}]