Organizations face challenges when trying to effectively introduce new operational practices that substitute for existing ones. We study how the dynamics due to social comparisons between employees give rise to individual strategic considerations and eventually shape the organizational adoption outcome. We develop an evolutionary game theory model that accounts for these microlevel individual adoption decisions and their impact on macrolevel population adoption equilibria. Social comparisons invoke dynamics that expand the possible outcomes beyond the traditional nonadoption versus full-adoption dichotomy. Specifically, ahead-seeking social comparisons drive the long-term coexistence of practices because employees seek to differentiate their choices from those of others. Meanwhile, behind-averse comparisons create a bandwagon effect that determines adoption depending on the initial fraction of adopters—that is, employees who are trained upfront. These dynamics are robust to various settings: different conceptualizations of social comparisons, each employee responding to more than one kind of social comparison, and nonhomogeneous social comparisons across employees. Moreover, they are material to organizations that seek to maximize their profit when introducing a new practice, by setting the levels of upfront training and adoption rewards. Our results call for senior managers to account for such behavioral traits when managing the introduction of new practices. Profitable adoption critically relies upon matching rewards and training to the type of social comparison. This paper was accepted by Sridhar Tayur, entrepreneurship and innovation. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.00305 .

This article establishes the Poisson optional stopping times (POST) method by [22] as a near-universal method for solving liquidity-constrained American options, or, equivalently, penalised optimal-stopping problems. In this setup, the decision maker is permitted to “stop”, i.e. exercise the option, only at a set of Poisson arrival times; this can be viewed as a liquidity constraint or “penalty” that limits access to optionality. We use monotonicity arguments in function space to establish that the POST algorithm either (i) finds the solution or (ii) demonstrates that no solution exists. The monotonicity of POST carries over to the discretised setting, where we additionally show geometric convergence and provide convergence bounds. For jump-diffusion processes, dense matrix factorisation may be avoided by using a suitable operator-splitting method for which we prove convergence. We also highlight a connection with linear complementarity problems (LCPs). We use the POST algorithm to value American options and compute early-exercise boundaries for Kou’s jump-diffusion model [20] and Heston’s stochastic volatility model [14], illustrating the breadth of application and numerical reliability of the method.

Most large organizations face challenges when trying to effectively introduce new operational practices that substitute existing ones. We study how the social dynamics due to social comparisons between employees gives rise to individual strategic considerations, and eventually shapes the adoption outcome of the firm. We develop an evolutionary game theory model that accounts for these micro-level individual adoption decisions, and their impact on macro-level population adoption equilibria. Social comparisons invoke dynamics that expand the possible outcomes beyond the traditional no-adoption versus full adoption dichotomy. Ahead seeking social comparisons drive the long-term coexistence of practices, because employees seek to differentiate their choices from others'. Meanwhile, behind averse comparisons create a bandwagon effect that determines adoption depending on the initial mass of adopters, i.e., employees who are trained upfront. These dynamics are robust to heterogeneous employee characteristics and positive utility externalities from joint adoption of the practice. Moreover, they persist even when organizations optimize their profit from introduction of the new practice, through upfront training and adoption rewards. Our results call for senior managers to diagnose, and measure such behavioral traits to appropriately manage the introduction of new practices, since profitable adoption, or in some cases, any adoption, relies upon matching rewards and training to the type of social comparisons present. Interestingly, we show under which circumstances the sheer presence of social comparisons benefits the adopting organization.

Responding to an information technology (IT) system failure often requires a collaborative approach in which both the client and the vendor need to invest in response capacity. By investing more in response capacity, the client might make the vendor's response capacity more effective in the system restoration stage. Yet, in doing so, the client also encourages free-riding by the vendor. To understand how a client should balance the need to support the vendor while setting the right incentives for the vendor to invest, we develop a model that combines the key characteristics of value co-creation (i.e., complementarity between the firms' investments in response capacity) with standard maintenance contract practices (i.e., penalty-based contracts that penalize the vendor for system downtime). We study the value of observability by characterizing the difference in the client's expected utility between when her investment is observable and non-observable by the vendor in collaborative environments. Since exposure to increased financial risks is a critical issue for the vendors with performance-based contracts, we consider the impact of risk attitudes of the firms (i.e., vendor risk aversion (VRA) and client risk aversion (CRA)) on the investments in the collaborative response process. We show that the value of observability is decreasing in VRA but increasing in CRA. Secondly, we find that the effect of risk aversion on the average system downtime is diametrically opposite depending on whether or not the client's investment is observable. Finally, the effectiveness of the performance-based contracts decreases with VRA but is more robust to CRA.

In December 2015, a cyber-physical attack took place on the Ukrainian electricity distribution network. This is regarded as one of the first cyber-physical attacks on electricity infrastructure to have led to a substantial power outage and is illustrative of the increasing vulnerability of Critical National Infrastructure to this type of malicious activity. Few data points, coupled with the rapid emergence of cyber phenomena, has held back the development of resilience analytics of cyber-physical attacks, relative to many other threats. We propose to overcome data limitations by applying stochastic counterfactual risk analysis as part of a new vulnerability assessment framework. The method is developed in the context of the direct and indirect socioeconomic impacts of a Ukrainian-style cyber-physical attack taking place on the electricity distribution network serving London and its surrounding regions. A key finding is that if decision-makers wish to mitigate major population disruptions, then they must invest resources more-or-less equally across all substations, to prevent the scaling of a cyber-physical attack. However, there are some substations associated with higher economic value due to their support of other Critical National Infrastructures assets, which justifies the allocation of additional cyber security investment to reduce the chance of cascading failure. Further cyber-physical vulnerability research must address the tradeoffs inherent in a system made up of multiple institutions with different strategic risk mitigation objectives and metrics of value, such as governments, infrastructure operators, and commercial consumers of infrastructure services.

We provide a new framework for valuing multidimensional real options where opportunities to exercise the option are generated by an exogenous Poisson process, which can be viewed as a liquidity constraint on decision times. This approach, which we call the Poisson optional stopping times (POST) method, finds the value function as a monotone sequence of lower bounds. In a case study, we demonstrate that the frequently used quasi-analytic method yields a suboptimal policy and an inaccurate value function. The proposed method is demonstrably correct, straightforward to implement, reliable in computation, and broadly applicable in analyzing multidimensional option-valuation problems.

We present a set of power investment models, the class of risky capacity equilibrium problems, reflecting different assumptions of perfect and imperfect markets. The models are structured in a unified stochastic Nash game framework. Each model is the concatenation of a model of the short-term market operations (perfect competition or Cournot), with a long-term model of investment behavior (risk neutral and risk averse behavior under different assumptions of risk trading). The models can all be formulated as complementarity problems, some of them having an optimization equivalent. We prove existence of solutions and report numerical results to illustrate the relevance of market imperfections on welfare and investment behavior. The models are constructed and discussed as two stage problems but we show that the extension to multistage is achieved by a change of notation and a standard assumption on multistage risk functions. We also treat a large multistage industrial model to illustrate the computational feasibility of the approach.

The paper addresses the problem of recovering a pseudoconvex function from the normal cones to its level sets that we call the convex level sets integration problem . An important application is the revealed preference problem. Our main result can be described as integrating a maximally cyclically pseudoconvex multivalued map that sends vectors or “bundles” of a Euclidean space to convex sets in that space. That is, we are seeking a pseudoconvex (real) function such that the normal cone at each boundary point of each of its lower level sets contains the set value of the multivalued map at the same point. This raises the question of uniqueness of that function up to rescaling. Even after normalizing the function long an orienting direction, we give a counterexample to its uniqueness. We are, however, able to show uniqueness under a condition motivated by the classical theory of ordinary differential equations.

A risky design equilibrium problem is an equilibrium system that involves N designers who invest in risky assets, such as production plants, evaluate these using convex or coherent risk measures, and also trade financial securities in order to manage their risk. Our main finding is that in a complete risk market-when all uncertainties can be replicated by financial products-a risky design equilibrium problem collapses to what we call a risky design game, i.e., a stochastic Nash game in which the original design agents act as risk neutral and there emerges an additional system risk agent. The system risk agent simultaneously prices risk and determines the probability density used by the other agents for their risk neutral evaluations. This situation is stochastic-endogenous: the probability density used by agents to value uncertain investments is endogenous to the risky design equilibrium problem. This result is most striking when design agents use coherent risk measures in which case the intersection of their risk sets turns out to be a risk set for the system risk agent, thereby extending existing results for risk markets. We also investigate existence of equilibria in both the complete and incomplete cases.

The stochastic uncapacitated single allocation p-hub center problem is an extension of the deterministic version which aims to minimize the longest origin-destination path in a hub and spoke network. Considering the stochastic nature of travel times on links is important when designing a network to guarantee the quality of service measured by a maximum delivery time for a proportion of all deliveries. We propose an efficient reformulation for a stochastic p-hub center problem and develop exact solution approaches based on variable reduction and a separation algorithm. We report numerical results to show effectiveness of our new reformulations and approaches by finding global solutions of small-medium sized problems. The combination of model reformulation and a separation algorithm is particularly noteworthy in terms of computational speed.

We consider two game-theoretic models of the generation capacity expansion problem in liberalized electricity markets. The first is an open loop equilibrium model, where generation companies simultaneously choose capacities and quantities to maximize their individual profit. The second is a closed loop model, in which companies first choose capacities maximizing their profit anticipating the market equilibrium outcomes in the second stage. The latter problem is an equilibrium problem with equilibrium constraints. In both models, the intensity of competition among producers in the energy market is frequently represented using conjectural variations. Considering one load period, we show that for any choice of conjectural variations ranging from perfect competition to Cournot, the closed loop equilibrium coincides with the Cournot open loop equilibrium, thereby obtaining a 'Kreps and Scheinkman'-like result and extending it to arbitrary strategic behavior. When expanding the model framework to multiple load periods, the closed loop equilibria for different conjectural variations can diverge from each other and from open loop equilibria. We also present and analyze alternative conjectured price response models with switching conjectures. Surprisingly, the rank ordering of the closed loop equilibria in terms of consumer surplus and market efficiency (as measured by total social welfare) is ambiguous. Thus, regulatory approaches that force marginal cost-based bidding in spot markets may diminish market efficiency and consumer welfare by dampening incentives for investment. We also show that the closed loop capacity yielded by a conjectured price response second stage competition can be less or equal to the closed loop Cournot capacity, and that the former capacity cannot exceed the latter when there are symmetric agents and two load periods.

In most wholesale electricity markets generators must submit step-function offers of supply to a uniform price auction, and the market is cleared at the price of the most expensive offer needed to meet realised demand. Such markets can most elegantly be modelled as the pure-strategy, Nash Equilibrium of continuous supply functions, in which each supplier has a unique profit maximising choice of supply function given the choices of other suppliers. Critics argue that the discreteness and discontinuity of the required steps can rule out pure-strategy equilibria and may result in price instability. This paper argues that if prices must be selected from a finite set the resulting step function converges to the continuous supply function as the number of steps increases, reconciling the apparently very disparate approaches to modelling electricity markets.

This is the first in a new series of contributed, refereed volumes devoted to research in optimization by Australasian researchers and their collaborators. These volumes are intended to have wide scope and include survey papers by established researchers providing up-to-date information on research directions. This volume contains survey papers on the Clarke subdifferential and differentiability in Banach spaces, algorithms for solving nonsmooth equations, and control parametrization schemes in optimal control. Other topics covered include convex optimization, generalized convexity in optimization, nonsmooth analysis, and algorithms using approximations of sub-differentials. Audience: Practitioners, postgraduate students and researchers in optimization.

We investigate risk averse agents who manage risk by trading financial securities in a market that we call a risk market. We assume this market is perfectly competitive and complete. When risk aversion is expressed using risk measures, the (bundle of) prices for financial securities turns out to be a probability density function, PDF. This endogeneity of probability distributions defines a novel template for equilibria under uncertainty and, more specifically, equilibria under risk. It is particularly striking that when agents use coherent risk measures to assess uncertain outcomes, a most risk neutral agent emerges from the risk market: its risk set is precisely the intersection of all agents’ risk sets, and the endogenous price of risk is simultaneously a worst case PDF for the most risk neutral agent and for each agent individually. We also show that risk markets can be conveniently adapted to decision making models like Nash games under risk, where agents are risk averse and optimize their actions under uncertainty.

This paper presents an asymptotic analysis of a Monte Carlo method, variously known as sample average approximation (SAA) or sample path optimization (SPO), for a general two-stage stochastic minimization problem. We study the case when the second-stage problem may have multiple local optima or stationary points that are not global solutions and SAA is implemented using a general nonlinear programming solver that is only guaranteed to find stationary points. New optimality conditions are developed for both the true problem and its SAA problem to accommodate Karush-Kuhn-Tucker points. Because the optimality conditions are essentially stochastic generalized equations, the asymptotic analysis is carried out for the generalized equations first and then applied to optimality conditions. For this purpose, we analyze piecewise continuous (PC0) stochastic mappings to understand when their expectations are piecewise continuous and thereby derive exponential convergence of SAA. It is shown under moderate conditions that, with probability one, an accumulation point of the SAA stationary points satisfies a relaxed stationary condition for the true problem and further that, with probability approaching one exponentially fast with increasing sample size, a stationary point of SAA converges to the set of relaxed stationary points. These results strengthen or complement existing results where the second-stage problem is often assumed to have a unique solution and the exponential convergence is focused on how fast a solution of the true problem becomes an approximate solution of an SAA problem rather than the other way around.