Firm’s protection against disasters: are investment and insurance substitutes or complements?


We use a controlled laboratory experiment to study firm’s protection against potential technological damages. The probability of a catastrophic event is known, and the firm’s costly investment in safety reduces it. The firm can also buy an insurance with full or partial refund against the consequences of the catastrophic event, which ultimately reduces the variance of the firm’s investment-in-safety lottery. The firm makes these two choices simultaneously, after observing the insurance contract proposed by an insurer who chooses this contract within a set of premium–deductible combinations. We parametrize the insurer–firm game such that (i) a risk-neutral insurer maximizes his expected profit by offering an actuarially fair contract with full insurance; (ii) a risk-neutral firm is indifferent between investing in safety and accepting a fair insurance contract. We aim at understanding whether investment in safety and insurance are substitutes or complements in the firm’s risk management of catastrophic events. In line with our predictions, the experimental results suggest that they are substitutes rather than complements: the firm’s investment in safety measures is affected by the insurer’s proposed contract, the latter usually involving only partial insurance.

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  1. 1.

    See also Dopuch et al. (1997), who used experimental methods to assess how different legal regimes affect the frequency and amounts of settlements in a three-person setting (one plaintiff and two defendants). In particular, their study explores liability rules applied to the multi-defendant case, namely proportionate vs. joint and several liability rules. The learning of liability rules in a dynamic setting has been investigated by Wittman et al. (1997).

  2. 2.

    Harbaugh et al. (2002) offer evidence that individuals exhibit sharply different behavior when they are offered a choice between gambles (a choice between a certain loss— insurance—and a probabilistic loss) and when they are asked to submit a price they are willing to pay for the same gamble.

  3. 3.

    The experimental instructions are provided as an electronic supplementary material of this paper and they can be found at

  4. 4.

    For example, in real life, a firm may want to hide absence of safety measures, to avoid getting an insurance contract with a too high premium or a too high deductible.

  5. 5.

    As an example, suppose that the insurer offers the insurance contract Z.2 in period 1 of phase A, with premium 150 and deductible 500 (see Table 2). Suppose that the matched firm buys this contract in period 1 and that a damage of small size (200) occurs at the end of period 1. Then the insurer’s payoff in period 1 is 200, i.e., the minimum between damage of small size (200) and the deductible (500).

  6. 6.

    More precisely, we have run: for the increasing probability of damage treatment, 2 sessions in April 2016 (resp., 20 and 34 subjects), and 1 session in April 2017 (20 subjects); for the decreasing probability of damage, 2 sessions in April 2016 (resp., 18 and 22 subjects), and 2 sessions in April 2017 (resp., 16 and 20 subjects).

  7. 7.

    See Section 5.3 of Attanasi et al. (2014) for a discussion on the participants’ higher trust in physical rather than computerized instruments when facing lotteries for the final payment of earnings in laboratory experiments. Another motivation behind this design choice is to make subjects aware that the final (physical) random draw of the phase and period to be paid at the end of the experiment is independent of the (computerized) random draws of the size of the damage in each period of the experiment.

  8. 8.

    This design choice also minimizes payoff differences between subjects in the role of firms (per period expected payoff equal to 12 Euros) and subjects in the role of insurers (phase expected payoff between 6 and 15 Euros, according to the proposed contract, if the contract is accepted).

  9. 9.

    Subjects usually exhibit risk aversion in economic experiments (see Holt and Laury 2002, and a plethora of follow-up papers).

  10. 10.

    We assume that the functional form of the von Neumann–Morgenstern utility \(u(\cdot )\) is independent from the role in the game since in our experiment the roles of firm and insurer are randomly assigned to subjects belonging to the same population.

  11. 11.

    For the use of expected utility to detect and measure risk aversion in laboratory experiments with objective lotteries, see the surveys in Hey (1997) and Hey (1999).

  12. 12.

    Besides Holt and Laury (2002) and follow-up articles, see the recent articles by Crosetto and Filippin (2016) and Attanasi et al. (2018) using expected utility for a theoretical and experimental appraisal of different risk elicitation methods. In all these studies, and independently from the specific risk elicitation task, concavity of the uniparametric utility function is detected for the majority of subjects.

  13. 13.

    The large damage would be perceived as even more unlikely if one allows for understatement of low probabilities in the loss domain under a Prospect Theory approach (see, e.g., the survey in de Palma et al. (2014) about the black swan effect). More precisely, the (low) probability of the large damage in each phase of our experiment (i.e., 10% in phase A, 7% in phase B, and 4% in phase C) would be perceived as lower by a Prospect Theory maximizer. However, this does fit with our approach since we assume Expected Utility.

  14. 14.

    This variable is elicited in the final questionnaire through the question: How do you judge yourself: are you generally a risk-loving person, or do you try to avoid risks? (0 not risk-loving at all; 10 very risk-loving).

  15. 15.

    Would you say that most of the time you try to help others or only follow your own interests? (0 helps others; 6 only follow your own interest).

  16. 16.

    Do you think most people would try to take advantage of you if they got a chance, or would they try to be fair? (0 try to take advantage; 6 try to be fair.)

  17. 17.

    Generally speaking, would you say that most people can be trusted or that you can not be too careful in dealing with people? (0 can be trusted; 6 can not be too careful).

  18. 18.

    Would you say that most of the time people try to be helpful, or that they are mostly just looking out for themselves? (0 try to be helpful; 6 mostly looking out for themselves).


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Correspondence to Giuseppe Attanasi.

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We thank Roman Meleshko for useful research assistantship. We thank for useful discussions and comments: Olivier Armantier, Nikolaos Georgantzis, Yolande Hiriart, Elena Manzoni, Eric Marsden, Nicolas Treich, and the seminar participants at the 2016 International Conference on Economic and Financial Risks in Niort, and the Foundations of Utility and Risk (FUR) 2018 Conference in York. The research leading to these results has received funding from the French Agence Nationale de la Recherche (ANR), under grant ANR-17-CE03-0008-01 (project INDUCED) and under grant ANR-18-CE26-0018-01 (project GRICRIS).



Table 6 Determinants of deductible equal to small damage (200)
Table 7 Determinants of insurance purchase
Table 8 Determinants of investment in safety

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Attanasi, G., Concina, L., Kamaté, C. et al. Firm’s protection against disasters: are investment and insurance substitutes or complements?. Theory Decis 88, 121–151 (2020).

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  • Decision under risk
  • Losses
  • Small probabilities
  • Probability reduction
  • Technological disasters
  • Insurance
  • Deductible