<p>If $-|x-a|$ represents the monetary payoff associated with the policy choice $a$, then $u(a) =-\left(|x-a|^\gamma\right)$ is risk averse for $\gamma &gt; 1$, and risk loving for $0&lt;\gamma &lt; 1$.</p>

CC BY-SA 4.0
2018-07-19T23:21:18.320Z
2018-07-20T00:28:52.107Z
2018-07-20T00:28:52.107Z
Amit
<p>I am trying to construct utility function for an agent who can be risk-seeking or risk-averse. We have an agent $i$ who has an ideal point $x$ in a policy space $X = [0,1]$. There is a policy (option) given by $a \in X$. Can we construct the agent $i$'s utility function as a distance between his ideal point and $a$ as $u_i (a) = -(x - a)^\gamma$, where $\gamma &gt; 0$ represents $i$'s attitude towards risk, such as $\gamma &gt; 1$ means $i$ is risk-averse and $\gamma &lt; 1$ means that $i$ is risk-seeking? </p>

CC BY-SA 4.0
2018-07-19T22:41:07.430Z
What do you mean by risk here? Usually, risk aversion is defined for lotteries over monetary outcomes.
Michael Greinecker
<utility><expected-utility><risk><risk-aversion>
Construct utility function for a risk-averse agent
Anna
# Construct utility function for a risk-averse agent

(Asked by: username_0 on 2018-07-19)

I am trying to construct utility function for an agent who can be risk-seeking or risk-averse. We have an agent $i$ who has an ideal point $x$ in a policy space $X = [0,1]$. There is a policy (option) given by $a \in X$. Can we construct the agent $i$'s utility function as a distance between his ideal point and $a$ as $u\_i (a) = -(x - a)^\gamma$, where $\gamma > 0$ represents $i$'s attitude towards risk, such as $\gamma > 1$ means $i$ is risk-averse and $\gamma < 1$ means that $i$ is risk-seeking?

**Tags:** utility, expected-utility, risk, risk-aversion

> **Comments:**
> **username_1**: What do you mean by risk here? Usually, risk aversion is defined for lotteries over monetary outcomes.  

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## 1 answers

### Answer by username_2 on 2018-07-19. Score: 3 | Accepted answer

If $-|x-a|$ represents the monetary payoff associated with the policy choice $a$, then $u(a) =-\left(|x-a|^\gamma\right)$ is risk averse for $\gamma > 1$, and risk loving for $0<\gamma < 1$.


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