For a semi-arid region with water shortage, how much yield reduction (with the implementation of deficit irrigation strategy) is acceptable for farmers?
Your question is interesting but it is incomplete, moreover it could be inaccurate in many cases. The concept of "deficit irrigation" was introduced to increase the water use efficiency (i.e., yield per unit of water applied) of crops and was intended to increase farmers net profit, mostly in water scarce regions e.g. arid and semi-arid climates. The yield of the crop can be maintained at a level equal to when the crop is regularly irrigated, provided some strategies for deficit irrigation are followed.
Now, coming to your question, I assume by "deficit irrigation (DI)" you are referring to non-frequent irrigation during critical crop growth period. As far as my knowledge is concerned, it is not possible to generalize this yield reduction, since behavior of each crop is different to water stress or deficit. For instance, crops like potato are stress sensitive, whereas, crops like winter wheat or mustard are stress tolerant. Moreover, the yield reduction is governed by the level of deficit allowed. For e.g. DI at 60% will generally result in lower yield as compared to 50% DI.
You can find many studies in the literature concerning your question, but it will be more or less crop specific (some of them I have attached). In my opinion, the yield reduction should not go beyond 10-15% under deficit irrigation. A greater reduction would mean more losses to farmers. However, you need to verify this figure from literature.
All the best for your work.
Article An improved water-use efficiency for maize grown under regul...
Article Yield Response of Corn to Deficit Irrigation in a Semiarid Climate
Data Effect of deficit irrigation on biomass, yield, water produc...
Article Deficit irrigation for reducing agricultural water use
Apart from biological yield loss, economics should be used to answer your question. Acceptable yield reduction should be based on marginal costing and marginal value for optimality. Said that the acceptance of yield losses by farmers depends on their risk-taking and income levels and varies from farmer to farmer.