In this thesis we set out to define network risk in a way that was applicable to any system with a network structure, has generality regarding the risk attitudes of the agents in the network, takes account of the network structure in calculating risk premia, and evaluates risk to the individual and to the network using concepts familiar to economists. One insight was critical to this: the idea that networks can be used to represent lotteries.
In Chapter 2 we used the notion of lotteries represented as networks to define the payoff space of a lottery using the existing network-theoretic notions of value functions and allocation rules. Given the structure of the network, an exogenous value function and allocation rule determined the payoff at each node. An agent’s payoff depended on which node they were assigned to. We defined three forms of network risk: assignment risk, in which an agent making decisions over networks did not know which node she would be assigned to; structural risk, in which the structure of the network graph was subject to change, thus affecting the value of the network and the allocation of the value; and valuation risk, in which the parameters of the value function were state-contingent. We showed that any lottery can be represented as a network graph using assignment risk. A key contribution was the definition of the network certainty equivalent (NCE) of graph ! as a non-risky and symmetric network graph #(!) such that
!~#(!). The network risk premium was defined as the NCE minus the expected payoff for graph !, called the network expected value (NEV). Three classes of methods for estimating the NCE were described: social welfare functions derived from axiomatic requirements, voting procedures such as the Condorcet-Young method, and aggregating the willingness to pay of agents derived from observation of their risk preferences. A preliminary model of social preferences in networks was described.
In Chapter 3 we illustrated the measurement of risk in a large-scale, realistic network model, based on the traffic network of Sioux Falls, South Dakota. We incorporated structural risk to the model in the form of three links, representing roads, that were vulnerable to collapse. The collective risk aversion of the network was measured by estimating the network’s collective willingness to pay (CWTP) for risk management measures that would partially or completely offset these structural risks. Numerous methods of measuring CWTP were demonstrated, based on aggregation of individual WTP, voting, and social welfare functions.
An immediate extension to the work in this thesis would be to experimentally test the predictions made in Chapter 2 in a controlled laboratory setting. Insights from Chapter 3 could be used in designing the experimental tasks. For example, participants might be put into a traffic network and told that some links are vulnerable to collapse, thus affecting their payoffs. Individual WTP for a risk management measure could then be used by taking votes over whether or not to implement the measure at a given price.
Another extension would be to improve the model of social preferences proposed in Section 2.7, particularly to include rank-dependent payoff weighting in the formation of conditional preferences. Another expansion in this section would be to have conditional payoffs decided by a nested CES function, so that agents with social preferences form their conditional payoffs based on a CES function of their own payoff, and a CES aggregation of the payoffs of other agents. This would allow for different elasticity between one’s own payoff and the payoffs of others collectively, and between the payoffs of others separately.
Four extensions are possible in Chapter 3. One is to solve Wardropian equilibrium when agents make ex ante rather than ex post decisions on route choice, and compare differences in (simulated) behavior. Another extension is to apply the models developed in this thesis to supply chain risk management (SCRM), addressing the statement of Ho et al. (2015) that the quantification of benefits and costs in SCRM would be a worthwhile contribution to that
literature. The third extension is to consider the effect of social preferences on CWTP. The fourth is to further examine the winners and losers from the introduction of an additional link.
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