# Function-Coherent Gambles with Non-Additive Sequential Dynamics

arXiv: https://arxiv.org/abs/2503.02889 · HTML: https://mlsanity.com/paper/2503.02889/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 31 references that are in the map.
- First posted on arXiv 22 Feb 2025.

## Builds on (most cited first, 2 of 2)

- [A theory of desirable things](https://mlsanity.com/paper/2302.07412/) (2023)
- [Nonlinear desirability theory](https://mlsanity.com/paper/2209.00686/) (2022)

## Abstract (arXiv)

The desirable gambles framework provides a rigorous foundation for imprecise probability theory but relies heavily on linear utility via its coherence axioms. In our related work, we introduced function-coherent gambles to accommodate non-linear utility. However, when repeated gambles are played over time -- especially in intertemporal choice where rewards compound multiplicatively -- the standard additive combination axiom fails to capture the appropriate long-run evaluation. In this paper we extend the framework by relaxing the additive combination axiom and introducing a nonlinear combination operator that effectively aggregates repeated gambles in the log-domain. This operator preserves the time-average (geometric) growth rate and addresses the ergodicity problem. We prove the key algebraic properties of the operator, discuss its impact on coherence, risk assessment, and representation, and provide a series of illustrative examples. Our approach bridges the gap between expectation values and time averages and unifies normative theory with empirically observed non-stationary reward dynamics.