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BOOK of ABSTRACTS Cutting Queues: Customer and System Behaviour in a Repeated Game FOUNDATIONS OF UTILITY AND RISK University of York, 25th – 28th June 2018 BOOK OF ABSTRACTS Cutting Queues: Customer and System Behaviour in a Repeated Game Vasco F. Alves Abstract This paper analyses the individual decisions taken by customers when deciding whether to join an M/M/1 queue where a subset of regular customers who interact repeatedly can both cut the queue and be overtaken once they join, by-passing occasional users. This is shown to be an equilibrium in repeated games with perfect public monitoring for sufficiently patient customers: regular customers allow other regular customers to overtake them as long as the long-term discounted pay-off of doing so exceeds the costs of giving this permission. This equilibrium is shown to exist, and to be possible to describe as regular customers forming a sub-queue under the Last Come First Served discipline, inside the regular FCFS queue. The expected sojourn time for customers under this discipline is obtained, and this is then used to obtain a threshold joining strategy for arrivals. 1 Mean-Dispersion Representation of Multiple Priors Preferences with Monotone Continuous Set of Prior Eric Andre Abstract This paper proves that, under the condition of monotone continuity of the set of priors, general multiple priors preferences have a mean-dispersion representation, that is they are a function of a baseline expected utility evaluation according to a reference probability and of the dispersion of the expected utility around this baseline when the other priors are considered. When constant absolute uncertainty aversion is imposed, this result provide an infinite dimensional extension of Grant and Polak (2013) and show that the VEU preference functional representation of Siniscalchi (2009) has a wider reach while focusing on a specific family of adjustment factors that have links to statistical distances. 2 The Common Ratio Effect with Objects and Money Danae Arroyos-Calvera, Andrea Isoni, Graham Loomes and Rebecca McDonald Abstract The common ratio effect (CRE) is a phenomenon that Allais (1953) and Kahneman and Tversky (1979) used to demonstrate that many people do not behave according to expected utility theory (EUT). In its classic form, the CRE shows that people reverse their preferences over two prospects when the probabilities of the nonzero payoffs are scaled down by the same factor. This is a violation of the independence axiom and has motivated the development of numerous alternative models of decision making. For the ratios of probabilities and payoffs used by Kahneman and Tversky, the CRE is robust when the payoffs are money amounts. However, using money amounts to simplify choices may prompt people to use decision rules that are not so readily available in their everyday decisions involving non-monetary consequences. Our aim was to test whether the CRE would occur when the payoffs are non-monetary rewards – in this case, consumer goods. In our experiment, participants first familiarised themselves with 10 objects. We elicited each participant’s monetary equivalent of each of the goods. Then they were asked to make choices between lotteries, some of which offered goods as payoffs while others offered the stated money equivalents of those goods. The probabilities in these lotteries are the ones featured in most CRE studies: 1 and 0.8 for the ‘scaled up’ pair of alternatives and 0.25 and 0.2 for the ‘scaled down’ pair. The goods were chosen for each participant from the set of objects so that their stated money equivalents approximated the 3:4 ratio typical of the money amounts in the classic CRE experiments. Within the non-monetary treatments, we manipulated object similarity by using some pairs of goods that had common characteristics (alarm clocks with different additional features), and other pairs where the characteristics were rather different and more difficult to compare (such as an airbed and a toaster, or an alarm clock and a suitcase). This design allowed us to explore choice patterns for consequences that differ in nature, but that participants stated were equivalent in value. To our knowledge, this is the first study that elicits incentive compatible answers to these questions. We found that the CRE persisted for monetary consequences, but it was greatly weakened for similar goods and disappeared for dissimilar goods. The stronger tendency for people to choose the risky alternative in the scaled up questions with goods may be at least partially driving this. Because people may find it hard to compare and make trade-offs between multi-dimensional goods, they may need to focus much of their attention on the payoff dimension and take less account of the probabilities, with the result that they more often end up choosing the option with the better payoff. The differences in the ways that money and goods are processed may have important implications for the descriptive validity of EUT in non-monetary settings such as the elicitation of health state indices. 3 Firm's Protection Against Disasters: Are Investment and Insurance Substitutes or Complements? Giuseppe Attanasi, Laura Concina, Caroline Kamate and Valentina Rotondi Abstract In this paper we use a controlled laboratory experiment to study firm's and insurer's behavior when the firm can invest so as to protect itself against potential technological or environmental damages. The probability of a catastrophic event is objective and firm's costly investment in protection reduces it. The firm can also buy an insurance with full or partial refund against the consequences of the catastrophic events. In the insurer-firm dynamic game, first the insurer decides which contract to propose to the firm. After having observed the proposed insurance contract, the firm decides whether or not to buy and whether or not to invest in the reduction of the probability of the catastrophic events. We aim at understanding whether investment in protection and insurance against negative consequences are substitutes or complements in the firm's risk management of catastrophic events. Our experimental results suggest that investment to reduce probability of damages and insurance against their negative consequences are in general substitutes. In partial accordance with our theoretical predictions, investment is chosen more frequently than insurance. This result is independent on whether the probability of damages is increasing or decreasing over time. Furthermore, investment and insurance show complementarity only when the probability of large damages is quite high and the firm has not previously experienced disasters. Insurers are driving these results, since they usually offer contracts with deductibles. This allows firms to care more about large damages with small probabilities. 4 Measuring Multivariate Risk Preferences in the Health Domain Arthur Attema, Olivier l’Haridon and Gijs van de Kuilen Abstract Objectives. In univariate settings, higher order risk attitudes, such as prudence and temperance, have been shown to be an important component of preferences, not only in the monetary domain but also in the health care field. Recent theoretical studies have crossed higher-order risk attitudes and multivariate preferences to prevention choice. However, no experimental tests of these theoretical derivations have been performed thus far. This study investigates univariate and multivariate risk preferences for health and wealth. First, we obtain model-free measurements (in the sense that we do not assume that individuals maximize a behavioral model such as expected utility) of univariate higher order risk preferences for longevity. Second, we are the first to obtain model-free measurements of attitudes toward the correlation structure between health and wealth, as well as higher order preferences toward multivariate risks for health and wealth. Finally, we provide direct evidence on whether these preferences are sign dependent. Methods. In a laboratory experiment, we measure correlation attitude in health- wealth trade-offs, complemented by higher order risk attitudes. We use the risk apportionment technique proposed by Eeckhoudt and Schlesinger (2006) and extended by Ebert and van de Kuilen (2015). We elicit these risk preferences for both gains and losses, since prospect theory predicts potentially different risk attitudes for these domains. Finally, we assemble data on many socio-demographic characteristics including health anxiety. Our results indicate that univariate (higher order) risk preferences are comparable for health and money, but different between gains and losses. Subject switch from risk aversion for gains to risk seeking for losses. The same holds for multivariate risk preferences, where we find correlation aversion and cross-prudence for gains, and correlation seeking and cross-imprudence for losses. We do not find clear evidence for cross-temperance. Finally, these risk preferences are not or only weakly correlated to health-related behaviours, except for anxiety, which shows a clear positive association with risk apportionment. Discussion. The results imply that attitudes toward dependence structures are sign-dependent, but not domain-dependent. In particular, longevity and wealth are considered to be substitutes for gains, but complements for losses. Anxiety about health is positively related to risk apportionment in longevity. 5 On Time Discounting, Impatience and Risk Aversion Yonatan Aumann Abstract Time discounting is a common assumption in economic literature. We (re)explore the foundations of such time
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