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| Jimmy Teng |
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| ''Status competition, endogenous risk attitudes, and the insurance–lottery puzzle'' |
| ( 2026, Vol. 0 No.0 ) |
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| Individuals purchase insurance while buying lottery tickets, contradicting expected utility's
prediction of globally concave preferences. This paper provides a structural explanation for the
coexistence of risk attitudes commonly associated with insurance purchase and lottery
participation. An agent's utility combines a concave consumption component with a contest-based
status component derived from the difference-form Tullock–Hirshleifer contest success function.
Risk curvature is endogenous: weak agents are strictly risk-loving under re-optimization, while all
agents are strictly risk-averse over background risks at fixed status expenditure, so any weak agent
simultaneously exhibits both risk attitudes. This coexistence rests on irreversibility: background
risks destroy assets that cannot be instantly reallocated, while lottery prizes arrive as liquid cash
permitting immediate reallocation toward status expenditure. Indirect utility is globally S-shaped
around an endogenously determined reference wealth level that shifts one-for-one with rival
expenditure, sharing the S-shaped curvature and endogenous reference point properties of the
prospect theory value function, while remaining silent on loss aversion and probability weighting. |
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| Keywords: Risk preferences; contest success function; insurance–lottery puzzle; Arrow–Pratt risk
aversion; status competition; relative standing; prospect theory; endogenous reference point; S-
shaped utility function |
JEL: D8 - Information, Knowledge, and Uncertainty: General
D3 - Distribution: General |
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| Manuscript Received : Apr 27 2026 | | Manuscript Accepted : Oct 10 2026 |
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